ALBERT

Description: In the classic k -center problem, we are given a metric graph, and the objective is to select k nodes as centers such that the maximum distance from any vertex to its closest center is minimized. In this paper, we consider two important generalizations of k -center, the matroid center problem and the knapsack center problem. Both problems are motivated by recent content distribution network applications. Our contributions can be summarized as follows: (1) We consider the matroid center problem in which the centers are required to form an independent set of a given matroid. We show this problem is NP-hard even on a line. We present a 3-approximation algorithm for the problem on general metrics. We also consider the outlier version of the problem where a given number of vertices can be excluded as outliers from the solution. We present a 7-approximation for the outlier version. (2) We consider the (multi-)knapsack center problem in which the centers are required to satisfy one (or more) knapsack constraint(s). It is known that the knapsack center problem with a single knapsack constraint admits a 3-approximation. However, when there are at least two knapsack constraints, we show this problem is not approximable at all. To complement the hardness result, we present a polynomial time algorithm that gives a 3-approximate solution such that one knapsack constraint is satisfied and the others may be violated by at most a factor of \(1+\epsilon \) . We also obtain a 3-approximation for the outlier version that may violate the knapsack constraint by \(1+\epsilon \) .

Description: We design a succinct data structure for representing a poset that, given two elements, can report whether one precedes the other in constant time. This is equivalent to succinctly representing the transitive closure graph of the poset, and we note that the same method can also be used to succinctly represent the transitive reduction graph. For an n element poset, the data structure occupies \(n^2/4 + o(n^2)\) bits in the worst case. Furthermore, a slight extension to this data structure yields a succinct oracle for reachability in arbitrary directed graphs. Thus, using no more than a quarter of the space required to represent an arbitrary directed graph, reachability queries can be supported in constant time. We also consider the operation of listing all the successors or predecessors of a given element, and show how to do this in constant time per element reported using a slightly modified version of our succinct data structure.

Description: We consider a graph observability problem: how many edge colors are needed for an unlabeled graph so that an agent, walking from node to node, can uniquely determine its location from just the observed color sequence of the walk? Specifically, let G ( n ,  d ) be an edge-colored subgraph of d -dimensional (directed or undirected) lattice of size \(n^d = n \times n \times \cdots \times n\) . We say that G ( n ,  d ) is t -observable if an agent can uniquely determine its current position in the graph from the color sequence of any t -dimensional walk, where the dimension is the number of different directions spanned by the edges of the walk. A walk in an undirected lattice G ( n ,  d ) has dimension between 1 and d , but a directed walk can have dimension between 1 and 2 d because of two different orientations for each axis. We derive bounds on the number of colors needed for t -observability. Our main result is that \(\varTheta (n^{d/t})\) colors are both necessary and sufficient for t -observability of G ( n ,  d ), where d is considered a constant. This shows an interesting dependence of graph observability on the ratio between the dimension of the lattice and that of the walk. In particular, the number of colors for full-dimensional walks is \(\varTheta (n^{1/2})\) in the directed case, and \(\varTheta (n)\) in the undirected case, independent of the lattice dimension. All of our results extend easily to non-square lattices: given a lattice graph of size \(N = n_1 \times n_2 \times \cdots \times n_d\) , the number of colors for t -observability is \(\varTheta (\root t \of {N})\) .

Description: The goal of cross-domain matching (CDM) is to find correspondences between two sets of objects in different domains in an unsupervised way. CDM has various interesting applications, including photo album summarization where photos are automatically aligned into a designed frame expressed in the Cartesian coordinate system, and temporal alignment which aligns sequences such as videos that are potentially expressed using different features. In this paper, we propose an information-theoretic CDM framework based on squared-loss mutual information (SMI). The proposed approach can directly handle non-linearly related objects/sequences with different dimensions, with the ability that hyper-parameters can be objectively optimized by cross-validation. We apply the proposed method to several real-world problems including image matching, unpaired voice conversion, photo album summarization, cross-feature video and cross-domain video-to-mocap alignment, and Kinect -based action recognition, and experimentally demonstrate that the proposed method is a promising alternative to state-of-the-art CDM methods.

Description: The skeleton of a 2D shape is an important geometric structure in pattern analysis and computer vision. In this paper we study the skeleton of a 2D shape in a two-manifold $mathcal {M}$ , based on a geodesic metric. We present a formal definition of the skeleton $S(Omega )$ for a shape $Omega$ in $mathcal {M}$ and show several properties that make $S(Omega )$ distinct from its Euclidean counterpart in $mathbb {R}^2$ . We further prove that for a shape sequence $lbrace Omega _irbrace$ that converge to a shape $Omega$ in $mathcal {M}$ , the mapping $Omega righta- row overline{S}(Omega )$ is lower semi-continuous. A direct application of this result is that we can use a set $P$ of sample points to approximate the boundary of a 2D shape $Omega$ in $mathcal {M}$ , and the Voronoi diagram of $P$ inside $Omega subset mathcal {M}$ gives a good approximation to the skeleton $S(Omega )$ . Examples of skeleton computation in topography and brain morphometry are illustrated.

Description: A widely used approach for locating points on deformable objects in images is to generate feature response images for each point, and then to fit a shape model to these response images. We demonstrate that Random Forest regression-voting can be used to generate high quality response images quickly. Rather than using a generative or a discriminative model to evaluate each pixel, a regressor is used to cast votes for the optimal position of each point. We show that this leads to fast and accurate shape model matching when applied in the Constrained Local Model framework. We evaluate the technique in detail, and compare it with a range of commonly used alternatives across application areas: the annotation of the joints of the hands in radiographs and the detection of feature points in facial images. We show that our approach outperforms alternative techniques, achieving what we believe to be the most accurate results yet published for hand joint annotation and state-of-the-art performance for facial feature point detection.

Description: We present a novel method to recognise planar structures in a single image and estimate their 3D orientation. This is done by exploiting the relationship between image appearance and 3D structure, using machine learning methods with supervised training data. As such, the method does not require specific features or use geometric cues, such as vanishing points. We employ general feature representations based on spatiograms of gradients and colour, coupled with relevance vector machines for classification and regression. We first show that using hand-labelled training data, we are able to classify pre-segmented regions as being planar or not, and estimate their 3D orientation. We then incorporate the method into a segmentation algorithm to detect multiple planar structures from a previously unseen image.

Description: Multiple view segmentation consists in segmenting objects simultaneously in several views. A key issue in that respect and compared to monocular settings is to ensure propagation of segmentation information between views while minimizing complexity and computational cost. In this work, we first investigate the idea that examining measurements at the projections of a sparse set of 3D points is sufficient to achieve this goal. The proposed algorithm softly assigns each of these 3D samples to the scene background if it projects on the background region in at least one view, or to the foreground if it projects on foreground region in all views. Second, we show how other modalities such as depth may be seamlessly integrated in the model and benefit the segmentation. The paper exposes a detailed set of experiments used to validate the algorithm, showing results comparable with the state of art, with reduced computational complexity. We also discuss the use of different modalities for specific situations, such as dealing with a low number of viewpoints or a scene with color ambiguities between foreground and background.

Description: We revisit the matrix problems sparse null space and matrix sparsification , and show that they are equivalent. We then proceed to seek algorithms for these problems: we prove the hardness of approximation of these problems, and also give a powerful tool to extend algorithms and heuristics for sparse approximation theory to these problems.

Description: We introduce Planar Disjoint Paths Completion , a completion counterpart of the Disjoint Paths problem, and study its parameterized complexity. The problem can be stated as follows: given a, not necessarily connected, plane graph G ,  k pairs of terminals, and a face F of G ,  find a minimum-size set of edges, if one exists, to be added inside F so that the embedding remains planar and the pairs become connected by k disjoint paths in the augmented network. Our results are twofold: first, we give an upper bound on the number of necessary additional edges when a solution exists. This bound is a function of k , independent of the size of G . Second, we show that the problem is fixed-parameter tractable, in particular, it can be solved in time \(f(k)\cdot n^{2}\) .

Description: Text detection in natural scene images is an important prerequisite for many content-based image analysis tasks, while most current research efforts only focus on horizontal or near horizontal scene text. In this paper, first we present a unified distance metric learning framework for adaptive hierarchical clustering, which can simultaneously learn similarity weights (to adaptively combine different feature similarities) and the clustering threshold (to automatically determine the number of clusters). Then, we propose an effective multi-orientation scene text detection system, which constructs text candidates by grouping characters based on this adaptive clustering. Our text candidates construction method consists of several sequential coarse-to-fine grouping steps: morphology-based grouping via single-link clustering, orientation-based grouping via divisive hierarchical clustering, and projection-based grouping also via divisive clustering. The effectiveness of our proposed system is evaluated on several public scene text databases, e.g., ICDAR Robust Reading Competition data sets (2011 and 2013), MSRA-TD500 and NEOCR. Specifically, on the multi-orientation text data set MSRA-TD500, the $f$ measure of our system is $71$ percent, much better than the state-of-the-art performance. We also construct and release a practical challenging multi-orientation scene text data set (USTB-SV1K), which is available at http://prir.ustb.edu.cn/TexStar/MOMV-text-detection/.

Description: We prove that in a graph with n vertices, induced chordal and interval subgraphs with the maximum number of vertices can be found in time \(\mathcal {O}(2^{\lambda n})\) for some \(\lambda 〈1\) . These are the first algorithms breaking the trivial \(2^n n^{\mathcal {O}(1)}\) bound of the brute-force search for these problems.

Description: We investigate the effect of limiting the number of reserve prices on the revenue in a probabilistic single item auction. In the model considered, bidders compete for an impression drawn from a known distribution of possible types. The auction mechanism sets up to \(\ell \) reserve prices, and each impression type is assigned the highest reserve price lower than the valuation of some bidder for it. The bidder proposing the highest bid for an arriving impression gets it provided his bid is at least the corresponding reserve price, and pays the maximum between the reserve price and the second highest bid. Since the number of impression types may be huge, we consider the revenue \(R_{\ell }\) that can be ensured using only \(\ell \) reserve prices. Our main results are tight lower bounds on \(R_{\ell }\) for the cases where the impressions are drawn from the uniform or a general probability distribution.

Description: A novel approach for event summarization and rare event detection is proposed. Unlike conventional methods that deal with event summarization and rare event detection independently, our method solves them in a single framework by transforming them into a graph editing problem. In our approach, a video is represented by a graph, each node of which indicates an event obtained by segmenting the video spatially and temporally. The edges between nodes describe the relationship between events. Based on the degree of relations, edges have different weights. After learning the graph structure, our method finds subgraphs that represent event summarization and rare events in the video by editing the graph, that is, merging its subgraphs or pruning its edges. The graph is edited to minimize a predefined energy model with the Markov Chain Monte Carlo (MCMC) method. The energy model consists of several parameters that represent the causality, frequency, and significance of events. We design a specific energy model that uses these parameters to satisfy each objective of event summarization and rare event detection. The proposed method is extended to obtain event summarization and rare event detection results across multiple videos captured from multiple views. For this purpose, the proposed method independently learns and edits each graph of individual videos for event summarization or rare event detection. Then, the method matches the extracted multiple graphs to each other, and constructs a single composite graph that represents event summarization or rare events from multiple views. Experimental results show that the proposed approach accurately summarizes multiple videos in a fully unsupervised manner . Moreover, the experiments demonstrate that the approach is advantageous in detecting rare transition of events .

Description: Object tracking has been one of the most important and active research areas in the field of computer vision. A large number of tracking algorithms have been proposed in recent years with demonstrated success. However, the set of sequences used for evaluation is often not sufficient or is sometimes biased for certain types of algorithms. Many datasets do not have common ground-truth object positions or extents, and this makes comparisons among the reported quantitative results difficult. In addition, the initial conditions or parameters of the evaluated tracking algorithms are not the same, and thus, the quantitative results reported in literature are incomparable or sometimes contradictory. To address these issues, we carry out an extensive evaluation of the state-of-the-art online object-tracking algorithms with various evaluation criteria to understand how these methods perform within the same framework. In this work, we first construct a large dataset with ground-truth object positions and extents for tracking and introduce the sequence attributes for the performance analysis. Second, we integrate most of the publicly available trackers into one code library with uniform input and output formats to facilitate large-scale performance evaluation. Third, we extensively evaluate the performance of 31 algorithms on 100 sequences with different initialization settings. By analyzing the quantitative results, we identify effective approaches for robust tracking and provide potential future research directions in this field.

Description: Fused Lasso is a popular regression technique that encodes the smoothness of the data. It has been applied successfully to many applications with a smooth feature structure. However, the computational cost of the existing solvers for fused Lasso is prohibitive when the feature dimension is extremely large. In this paper, we propose novel screening rules that are able to quickly identity the adjacent features with the same coefficients. As a result, the number of variables to be estimated can be significantly reduced, leading to substantial savings in computational cost and memory usage. To the best of our knowledge, the proposed approach is the first attempt to develop screening methods for the fused Lasso problem with general data matrix. Our major contributions are: 1) we derive a new dual formulation of fused Lasso that comes with several desirable properties; 2) we show that the new dual formulation of fused Lasso is equivalent to that of the standard Lasso by two affine transformations; 3) we propose a novel framework for developing effective and efficient screening rules for f used La sso via the m onotonicity of the s ubdifferentials (FLAMS). Some appealing features of FLAMS are: 1) our methods are safe in the sense that the detected adjacent features are guaranteed to have the same coefficients; 2) the dataset needs to be scanned only once to run the screening, whose computational cost is negligible compared to that of solving the fused Lasso; (3) FLAMS is independent of the solvers and can be integrated with any existing solvers. We have evaluated the proposed FLAMS rules on both synthetic and real datasets. The experiments indicate that FLAMS is very effective in identifying the adjacent features with the same coefficients. The speedup gained by FLAMS can be orders of magnitude.

Description: Hidden conditional random fields (HCRFs) are discriminative latent variable models which have been shown to successfully learn the hidden structure of a given classification problem. An Infinite hidden conditional random field is a hidden conditional random field with a countably infinite number of hidden states, which rids us not only of the necessity to specify a priori a fixed number of hidden states available but also of the problem of overfitting. Markov chain Monte Carlo (MCMC) sampling algorithms are often employed for inference in such models. However, convergence of such algorithms is rather difficult to verify, and as the complexity of the task at hand increases the computational cost of such algorithms often becomes prohibitive. These limitations can be overcome by variational techniques. In this paper, we present a generalized framework for infinite HCRF models, and a novel variational inference approach on a model based on coupled Dirichlet Process Mixtures, the HCRF-DPM. We show that the variational HCRF-DPM is able to converge to a correct number of represented hidden states, and performs as well as the best parametric HCRFs—chosen via cross-validation—for the difficult tasks of recognizing instances of agreement, disagreement, and pain in audiovisual sequences.

Description: In this paper, we address the challenging problem of detecting pedestrians who appear in groups. A new approach is proposed for single-pedestrian detection aided by two-pedestrian detection. A mixture model of two-pedestrian detectors is designed to capture the unique visual cues which are formed by nearby pedestrians but cannot be captured by single-pedestrian detectors. A probabilistic framework is proposed to model the relationship between the configurations estimated by single- and two-pedestrian detectors, and to refine the single-pedestrian detection result using two-pedestrian detection. The two-pedestrian detector can integrate with any single-pedestrian detector. Twenty-five state-of-the-art single-pedestrian detection approaches are combined with the two-pedestrian detector on three widely used public datasets: Caltech, TUD-Brussels, and ETH. Experimental results show that our framework improves all these approaches. The average improvement is $9$ percent on the Caltech-Test dataset, $11$ percent on the TUD-Brussels dataset and $17$ percent on the ETH dataset in terms of average miss rate. The lowest average miss rate is reduced from $37$ to percent on the Caltech-Test dataset, from $55$ to $50$ percent on the TUD-Brussels dataset and from $43$ to $38$ percent on the ETH dataset.

Description: The new dual-pivot Quicksort by Vladimir Yaroslavskiy—used in Oracle’s Java runtime library since version 7—features intriguing asymmetries. They make a basic variant of this algorithm use less comparisons than classic single-pivot Quicksort. In this paper, we extend the analysis to the case where the two pivots are chosen as fixed order statistics of a random sample. Surprisingly, dual-pivot Quicksort then needs more comparisons than a corresponding version of classic Quicksort, so it is clear that counting comparisons is not sufficient to explain the running time advantages observed for Yaroslavskiy’s algorithm in practice. Consequently, we take a more holistic approach and give also the precise leading term of the average number of swaps, the number of executed Java Bytecode instructions and the number of scanned elements, a new simple cost measure that approximates I/O costs in the memory hierarchy. We determine optimal order statistics for each of the cost measures. It turns out that the asymmetries in Yaroslavskiy’s algorithm render pivots with a systematic skew more efficient than the symmetric choice. Moreover, we finally have a convincing explanation for the success of Yaroslavskiy’s algorithm in practice: compared with corresponding versions of classic single-pivot Quicksort, dual-pivot Quicksort needs significantly less I/Os, both with and without pivot sampling.

Description: In this paper, we consider the Unsplittable (hard) Capacitated Facility Location Problem (UCFLP) with uniform capacities and present new approximation algorithms for it. This problem is a generalization of the classical facility location problem where each facility can serve at most u units of demand and each client must be served by exactly one facility. This problem is motivated by its applications in many practical problems including supply chain problems of indivisible goods (Verter in Foundations of location analysis, chapter 2. International series in operations research and management science. Springer, Berlin, 2011 ) and the assignment problem in the content distribution networks (Bateni and Hajiaghayi in Proceedings of the nineteenth annual ACM-SIAM symposium on discrete algorithms, pp 805–814, 2009 ). While there are several approximation algorithms for the soft capacitated version of this problem (in which one can open multiple copies of each facility) or the splittable version (in which the demand of each client can be divided to be served by multiple open facilities), there are very few results for the UCFLP. It is known that it is NP-hard to approximate this problem within any factor without violating the capacities. So we consider bicriteria \((\alpha ,\beta )\) -approximations where the algorithm returns a solution whose cost is within factor \(\alpha \) of the optimum and violates the capacity constraints within factor \(\beta \) . Shmoys et al. (Proceedings of the twenty-ninth annual ACM symposium on theory of computing, pp 265–274, 1997 ) were the first to consider this problem and gave a (9, 4)-approximation. Later results imply ( O (1), 2)-approximations, however, no constant factor approximation is known with capacity violation of less than 2. We present a framework for designing bicriteria approximation algorithms for this problem and show two new approximation algorithms with factors (9, 3 / 2) and (29.315, 4 / 3). These are the first algorithms with constant approximation in which the violation of capacities is below 2. The heart of our algorithm is a reduction from the UCFLP to a restricted version of the problem. One feature of this reduction is that any \((O(1),1+{\epsilon })\) -approximation for the restricted version implies an \((O(1),1+{\epsilon })\) -approximation for the UCFLP and we believe our techniques might be useful towards finding such approximations or perhaps \((f({\epsilon }),1+{\epsilon })\) -approximation for the UCFLP for some function f . In addition, we present a quasi-polynomial time \((1+\epsilon ,1+\epsilon )\) -approximation for the (uniform) UCFLP in Euclidean metrics, for any constant \({\epsilon }〉0\) .

Description: Systems based on bag-of-words models from image features collected at maxima of sparse interest point operators have been used successfully for both computer visual object and action recognition tasks. While the sparse, interest-point based approach to recognition is not inconsistent with visual processing in biological systems that operate in ‘saccade and fixate’ regimes, the methodology and emphasis in the human and the computer vision communities remains sharply distinct. Here, we make three contributions aiming to bridge this gap. First, we complement existing state-of-the art large scale dynamic computer vision annotated datasets like Hollywood-2  [1] and UCF Sports  [2] with human eye movements collected under the ecological constraints of visual action and scene context recognition tasks. To our knowledge these are the first large human eye tracking datasets to be collected and made publicly available for video, vision.imar.ro/eyetracking (497,107 frames, each viewed by 19 subjects), unique in terms of their (a) large scale and computer vision relevance, (b) dynamic, video stimuli, (c) task control, as well as free-viewing . Second, we introduce novel dynamic consistency and alignment measures , which underline the remarkable stability of patterns of visual search among subjects. Third, we leverage the significant amount of collected data in order to pursue studies and build automatic, end-to-end trainable computer vision systems based on human eye movements. Our studies not only shed light on the differences between computer vision spatio-temporal interest point image sampling strategies and the human fixations, as well as their impact for visual recognition performance, but also demonstrate that human fixations can be accurately predicted, and when used in an end-to-end automatic system, leveraging some of the advanced computer vision practice, can lead to state of the art results.

Description: We consider the problem of parameter estimation and energy minimization for a region-based semantic segmentation model. The model divides the pixels of an image into non-overlapping connected regions, each of which is to a semantic class. In the context of energy minimization, the main problem we face is the large number of putative pixel-to-region assignments. We address this problem by designing an accurate linear programming based approach for selecting the best set of regions from a large dictionary. The dictionary is constructed by merging and intersecting segments obtained from multiple bottom-up over-segmentations. The linear program is solved efficiently using dual decomposition. In the context of parameter estimation, the main problem we face is the lack of fully supervised data. We address this issue by developing a principled framework for parameter estimation using diverse data. More precisely, we propose a latent structural support vector machine formulation, where the latent variables model any missing information in the human annotation. Of particular interest to us are three types of annotations: (i) images segmented using generic foreground or background classes; (ii) images with bounding boxes specified for objects; and (iii) images labeled to indicate the presence of a class. Using large, publicly available datasets we show that our methods are able to significantly improve the accuracy of the region-based model.

Description: In this paper we address the problem of finding the most probable state of a discrete Markov random field (MRF), also known as the MRF energy minimization problem. The task is known to be NP-hard in general and its practical importance motivates numerous approximate algorithms. We propose a submodular relaxation approach (SMR) based on a Lagrangian relaxation of the initial problem. Unlike the dual decomposition approach of Komodakis et al. [29] SMR does not decompose the graph structure of the initial problem but constructs a submodular energy that is minimized within the Lagrangian relaxation. Our approach is applicable to both pairwise and high-order MRFs and allows to take into account global potentials of certain types. We study theoretical properties of the proposed approach and evaluate it experimentally.

Description: Higher-order Markov Random Fields, which can capture important properties of natural images, have become increasingly important in computer vision. While graph cuts work well for first-order MRF’s, until recently they have rarely been effective for higher-order MRF’s. Ishikawa’s graph cut technique [1] , [2] shows great promise for many higher-order MRF’s. His method transforms an arbitrary higher-order MRF with binary labels into a first-order one with the same minima. If all the terms are submodular the exact solution can be easily found; otherwise, pseudoboolean optimization techniques can produce an optimal labeling for a subset of the variables. We present a new transformation with better performance than [1] , [2] , both theoretically and experimentally. While [1] , [2] transforms each higher-order term independently, we use the underlying hypergraph structure of the MRF to transform a group of terms at once. For $n$ binary variables, each of which appears in terms with $k$ other variables, at worst we produce $n$ non-submodular terms, while [1] , [2] produces $O(- k)$ . We identify a local completeness property under which our method perform even better, and show that under certain assumptions several important vision problems (including common variants of fusion moves) have this property. We show experimentally that our method produces smaller weight of non-submodular edges, and that this metric is directly related to the effectiveness of QPBO [3] . Running on the same field of experts dataset used in [1] , [2] we optimally label significantly more variables (96 versus 80 percent) and converge more rapidly to a lower energy. Preliminary experiments suggest that some other higher-order MRF’s used in stereo [4] and segmentation [5] are also locally complete and would thus benefit from our work.

Description: We introduce a conceptually novel structured prediction model, GPstruct , which is kernelized, non-parametric and Bayesian, by design. We motivate the model with respect to existing approaches, among others, conditional random fields (CRFs), maximum margin Markov networks (M $^3$ N), and structured support vector machines (SVMstruct), which embody only a subset of its properties. We present an inference procedure based on Markov Chain Monte Carlo. The framework can be instantiated for a wide range of structured objects such as linear chains, trees, grids, and other general graphs. As a proof of concept, the model is benchmarked on several natural language processing tasks and a video gesture segmentation task involving a linear chain structure. We show prediction accuracies for GPstruct which are comparable to or exceeding those of CRFs and SVMstruct.

Description: Improving the quality of degraded images is a key problem in image processing, but the breadth of the problem leads to domain-specific approaches for tasks such as super-resolution and compression artifact removal. Recent approaches have shown that a general approach is possible by learning application-specific models from examples; however, learning models sophisticated enough to generate high-quality images is computationally expensive, and so specific per-application or per-dataset models are impractical. To solve this problem, we present an efficient semi-local approximation scheme to large-scale Gaussian processes. This allows efficient learning of task-specific image enhancements from example images without reducing quality. As such, our algorithm can be easily customized to specific applications and datasets, and we show the efficiency and effectiveness of our approach across five domains: single-image super-resolution for scene, human face, and text images, and artifact removal in JPEG- and JPEG 2000-encoded images.

Description: Parsimony, including sparsity and low rank, has been shown to successfully model data in numerous machine learning and signal processing tasks. Traditionally, such modeling approaches rely on an iterative algorithm that minimizes an objective function with parsimony-promoting terms. The inherently sequential structure and data-dependent complexity and latency of iterative optimization constitute a major limitation in many applications requiring real-time performance or involving large-scale data. Another limitation encountered by these modeling techniques is the difficulty of their inclusion in discriminative learning scenarios. In this work, we propose to move the emphasis from the model to the pursuit algorithm, and develop a process-centric view of parsimonious modeling, in which a learned deterministic fixed-complexity pursuit process is used in lieu of iterative optimization. We show a principled way to construct learnable pursuit process architectures for structured sparse and robust low rank models, derived from the iteration of proximal descent algorithms. These architectures learn to approximate the exact parsimonious representation at a fraction of the complexity of the standard optimization methods. We also show that appropriate training regimes allow to naturally extend parsimonious models to discriminative settings. State-of-the-art results are demonstrated on several challenging problems in image and audio processing with several orders of magnitude speed-up compared to the exact optimization algorithms.

Description: CANDECOMP/PARAFAC (CP) tensor factorization of incomplete data is a powerful technique for tensor completion through explicitly capturing the multilinear latent factors. The existing CP algorithms require the tensor rank to be manually specified, however, the determination of tensor rank remains a challenging problem especially for CP rank . In addition, existing approaches do not take into account uncertainty information of latent factors, as well as missing entries. To address these issues, we formulate CP factorization using a hierarchical probabilistic model and employ a fully Bayesian treatment by incorporating a sparsity-inducing prior over multiple latent factors and the appropriate hyperpriors over all hyperparameters, resulting in automatic rank determination. To learn the model, we develop an efficient deterministic Bayesian inference algorithm, which scales linearly with data size. Our method is characterized as a tuning parameter-free approach, which can effectively infer underlying multilinear factors with a low-rank constraint, while also providing predictive distributions over missing entries. Extensive simulations on synthetic data illustrate the intrinsic capability of our method to recover the ground-truth of CP rank and prevent the overfitting problem, even when a large amount of entries are missing. Moreover, the results from real-world applications, including image inpainting and facial image synthesis, demonstrate that our method outperforms state-of-the-art approaches for both tensor factorization and tensor completion in terms of predictive performance.

Description: Existing deep convolutional neural networks (CNNs) require a fixed-size (e.g., 224 $times$ 224) input image. This requirement is “artificial” and may reduce the recognition accuracy for the images or sub-images of an arbitrary size/scale. In this work, we equip the networks with another pooling strategy, “spatial pyramid pooling”, to eliminate the above requirement. The new network structure, called SPP-net, can generate a fixed-length representation regardless of image size/scale. Pyramid pooling is also robust to object deformations. With these advantages, SPP-net should in general improve all CNN-based image classification methods. On the ImageNet 2012 dataset, we demonstrate that SPP-net boosts the accuracy of a variety of CNN architectures despite their different designs. On the Pascal VOC 2007 and Caltech101 datasets, SPP-net achieves state-of-the-art classification results using a single full-image representation and no fine-tuning. The power of SPP-net is also significant in object detection. Using SPP-net, we compute the feature maps from the entire image only once, and then pool features in arbitrary regions (sub-images) to generate fixed-length representations for training the detectors. This method avoids repeatedly computing the convolutional features. In processing test images, our method is 24-102 $times$ faster than the R-CNN method, while achieving better or comparable accuracy on Pascal VOC 2007. In ImageNet Large Scale Visual Recognition Challenge (ILSVRC) 2014, our methods rank #2 in object detection and #3 in image classification among all 38 teams. This manuscript also introduces the improvement made for this - ompetition.

Description: We present efficient graph cut algorithms for three problems: (1) finding a region in an image, so that the histogram (or distribution) of an image feature within the region most closely matches a given model; (2) co-segmentation of image pairs and (3) interactive image segmentation with a user-provided bounding box. Each algorithm seeks the optimum of a global cost function based on the Bhattacharyya measure, a convenient alternative to other matching measures such as the Kullback–Leibler divergence. Our functionals are not directly amenable to graph cut optimization as they contain non-linear functions of fractional terms, which make the ensuing optimization problems challenging. We first derive a family of parametric bounds of the Bhattacharyya measure by introducing an auxiliary labeling. Then, we show that these bounds are auxiliary functions of the Bhattacharyya measure, a result which allows us to solve each problem efficiently via graph cuts. We show that the proposed optimization procedures converge within very few graph cut iterations. Comprehensive and various experiments, including quantitative and comparative evaluations over two databases, demonstrate the advantages of the proposed algorithms over related works in regard to optimality, computational load, accuracy and flexibility.

Description: A commonly studied means of parameterizing graph problems is the deletion distance from triviality (Guo et al., Parameterized and exact computation, Springer, Berlin, pp. 162–173, 2004 ), which counts vertices that need to be deleted from a graph to place it in some class for which efficient algorithms are known. In the context of graph isomorphism, we define triviality to mean a graph with maximum degree bounded by a constant, as such graph classes admit polynomial-time isomorphism tests. We generalise deletion distance to a measure we call elimination distance to triviality, based on elimination trees or tree-depth decompositions. We establish that graph canonisation, and thus graph isomorphism, is \(\mathsf {FPT}\) when parameterized by elimination distance to bounded degree, extending results of Bouland et al. (Parameterized and exact computation, Springer, Berlin, pp. 218–230, 2012 ).

Description: Recent advances in drift analysis have given us better and better tools for understanding random processes, including the run time of randomized search heuristics. In the setting of multiplicative drift we do not only have excellent bounds on the expected run time, but also more general results showing the strong concentration of the run time. In this paper we investigate the setting of additive drift under the assumption of strong concentration of the “step size” of the process. Under sufficiently strong drift towards the goal we show a strong concentration of the hitting time. In contrast to this, we show that in the presence of small drift a Gambler’s-Ruin-like behavior of the process overrides the influence of the drift, leading to a maximal movement of about \(\sqrt{t}\) steps within t iterations. Finally, in the presence of sufficiently strong negative drift the hitting time is superpolynomial with high probability; this corresponds to the well-known Negative Drift Theorem.

Description: Binets and trinets are phylogenetic networks with two and three leaves, respectively. Here we consider the problem of deciding if there exists a binary level-1 phylogenetic network displaying a given set  \(\mathbb {T}\) of binary binets or trinets over a taxon set  X , and constructing such a network whenever it exists. We show that this is NP-hard for trinets but polynomial-time solvable for binets. Moreover, we show that the problem is still polynomial-time solvable for inputs consisting of binets and trinets as long as the cycles in the trinets have size three. Finally, we present an  \(O(3^{|X|} poly(|X|))\) time algorithm for general sets of binets and trinets. The latter two algorithms generalise to instances containing level-1 networks with arbitrarily many leaves, and thus provide some of the first supernetwork algorithms for computing networks from a set of rooted phylogenetic networks.

Description: We consider stochastic versions of OneMax and LeadingOnes and analyze the performance of evolutionary algorithms with and without populations on these problems. It is known that the ( \(1+1\) ) EA on OneMax performs well in the presence of very small noise, but poorly for higher noise levels. We extend these results to LeadingOnes and to many different noise models, showing how the application of drift theory can significantly simplify and generalize previous analyses. Most surprisingly, even small populations (of size \(\varTheta (\log n)\) ) can make evolutionary algorithms perform well for high noise levels, well outside the abilities of the ( \(1+1\) ) EA. Larger population sizes are even more beneficial; we consider both parent and offspring populations. In this sense, populations are robust in these stochastic settings.

Description: Since Tinhofer proposed the MinGreedy algorithm for maximum cardinality matching in 1984, several experimental studies found the randomized algorithm to perform excellently for various classes of random graphs and benchmark instances. In contrast, only few analytical results are known. We show that MinGreedy cannot improve on the trivial approximation ratio of  \(\frac{1}{2}\) whp., even for bipartite graphs. Our hard inputs seem to require a small number of high-degree nodes. This motivates an investigation of greedy algorithms on graphs with maximum degree  \(\varDelta \) : we show that  MinGreedy achieves a  \({\frac{{\varDelta }-1}{2{\varDelta }-3}} \) -approximation for graphs with  \({\varDelta } {=} 3\) and for \(\varDelta \) -regular graphs, and a guarantee of  \({\frac{{\varDelta }-1/2}{2{\varDelta }-2}} \) for graphs with maximum degree  \({\varDelta } \) . Interestingly, our bounds even hold for the deterministic MinGreedy that breaks all ties arbitrarily. Moreover, we investigate the limitations of the greedy paradigm, using the model of priority algorithms introduced by Borodin, Nielsen, and Rackoff. We study deterministic priority algorithms and prove a  \({\frac{{\varDelta }-1}{2{\varDelta }-3}}\) -inapproximability result for graphs with maximum degree  \({\varDelta } \) ; thus, these greedy algorithms do not achieve a  \(\frac{1}{2} {+} \varepsilon \) -approximation and in particular the  \(\frac{2}{3}\) -approximation obtained by the deterministic MinGreedy for  \({\varDelta } {=} 3\) is optimal in this class. For  k -uniform hypergraphs we show a tight  \(\frac{1}{k}\) -inapproximability bound. We also study fully randomized priority algorithms and give a  \(\frac{5}{6}\) -inapproximability bound. Thus, they cannot compete with matching algorithms of other paradigms.

Description: We discuss how string sorting algorithms can be parallelized on modern multi-core shared memory machines. As a synthesis of the best sequential string sorting algorithms and successful parallel sorting algorithms for atomic objects, we first propose string sample sort. The algorithm makes effective use of the memory hierarchy, uses additional word level parallelism, and largely avoids branch mispredictions. Then we focus on NUMA architectures, and develop parallel multiway LCP-merge and -mergesort to reduce the number of random memory accesses to remote nodes. Additionally, we parallelize variants of multikey quicksort and radix sort that are also useful in certain situations. As base-case sorter for LCP-aware string sorting we describe sequential LCP-insertion sort which calculates the LCP array and accelerates its insertions using it. Comprehensive experiments on five current multi-core platforms are then reported and discussed. The experiments show that our parallel string sorting implementations scale very well on real-world inputs and modern machines.

Description: Stochastic boolean function evaluation (SBFE) is the problem of determining the value of a given boolean function f on an unknown input x , when each bit \(x_i\) of x can only be determined by paying a given associated cost \(c_i\) . Further, x is drawn from a given product distribution: for each \(x_i\) , \(\mathbf{Pr}[x_i=1] = p_i\) and the bits are independent. The goal is to minimize the expected cost of evaluation. In this paper, we study the complexity of the SBFE problem for classes of DNF formulas. We consider both exact and approximate versions of the problem for subclasses of DNF, for arbitrary costs and product distributions, and for unit costs and/or the uniform distribution.

Description: Interval graphs are intersection graphs of closed intervals of the real-line. The well-known computational problem, called recognition , asks whether an input graph G can be represented by closed intervals, i.e., whether G is an interval graph. There are several linear-time algorithms known for recognizing interval graphs, the oldest one is by Booth and Lueker (J Comput Syst Sci 13:335–379, 1976 ) based on PQ-trees. In this paper, we study a generalization of recognition, called partial representation extension . The input of this problem consists of a graph G with a partial representation \({{{\mathcal {R}}}}'\) fixing the positions of some intervals. The problem asks whether it is possible to place the remaining interval and create an interval representation \({{{\mathcal {R}}}}\) of the entire graph G extending \({{{\mathcal {R}}}}'\) . We generalize the characterization of interval graphs by Fulkerson and Gross (Pac J Math 15:835–855, 1965 ) to extendible partial representations. Using it, we give a linear-time algorithm for partial representation extension based on a reordering problem of PQ-trees.

Description: Modern data management systems often need to deal with massive, dynamic and inherently distributed data sources. We collect the data using a distributed network, and at the same time try to maintain a global view of the data at a central coordinator using a minimal amount of communication. Such applications have been captured by the distributed monitoring model which has attracted a lot of attention in recent years. In this paper we investigate the monitoring of the entropy functions, which are very useful in network monitoring applications such as detecting distributed denial-of-service attacks. Our results improve the previous best results by Arackaparambil et al. in ICLP 1: 95–106 ( 2009 ). Our technical contribution also includes implementing the celebrated AMS sampling method (by Alon et al. in J Comput Syst Sci 58(1): 137–147 1999 ) in the distributed monitoring model, which could be of independent interest.

Description: Provides a listing of board members, committee members, editors, and society officers.

Description: Certain inner feelings and physiological states like pain are subjective states that cannot be directly measured, but can be estimated from spontaneous facial expressions. Since they are typically characterized by subtle movements of facial parts, analysis of the facial details is required. To this end, we formulate a new regression method for continuous estimation of the intensity of facial behavior interpretation, called Doubly Sparse Relevance Vector Machine (DSRVM). DSRVM enforces double sparsity by jointly selecting the most relevant training examples (a.k.a. relevance vectors) and the most important kernels associated with facial parts relevant for interpretation of observed facial expressions. This advances prior work on multi-kernel learning, where sparsity of relevant kernels is typically ignored. Empirical evaluation on challenging Shoulder Pain videos, and the benchmark DISFA and SEMAINE datasets demonstrate that DSRVM outperforms competing approaches with a multi-fold reduction of running times in training and testing.

Description: In the Boundary Labeling problem, we are given a set of  n points, referred to as sites , inside an axis-parallel rectangle  R , and a set of  n pairwise disjoint rectangular labels that are attached to  R from the outside. The task is to connect the sites to the labels by non-intersecting rectilinear paths, so-called leaders , with at most one bend. In this paper, we study the Multi-Sided Boundary Labeling problem, with labels lying on at least two sides of the enclosing rectangle. We present a polynomial-time algorithm that computes a crossing-free leader layout if one exists. So far, such an algorithm has only been known for the cases in which labels lie on one side or on two opposite sides of  R (here a crossing-free solution always exists). The case where labels may lie on adjacent sides is more difficult. We present efficient algorithms for testing the existence of a crossing-free leader layout that labels all sites and also for maximizing the number of labeled sites in a crossing-free leader layout. For two-sided boundary labeling with adjacent sides, we further show how to minimize the total leader length in a crossing-free layout.

Description: In this paper we consider the problem of the strict self-assembly of infinite fractals within tile self-assembly. In particular, we provide tile assembly algorithms for the assembly of a Sierpinski triangle and the discrete Sierpinski carpet within a class of models we term the h - handed assembly model ( h -HAM), which generalizes the 2-HAM to allow up to h assemblies to combine in a single assembly step. Despite substantial consideration, no purely growth self-assembly model has yet been shown to strictly assemble an infinite fractal without significant modification to the fractal shape. In this paper we not only achieve this, but in the case of the Sierpinski carpet are able to achieve it within the 2-HAM, one of the most well studied tile assembly models in the literature. Our specific results are as follows: We provide a 6-HAM construction for a Sierpinski triangle that works at scale factor 1, 30 tile types, and assembles the fractal in a near perfect way in which all intermediate assemblies are finite-sized iterations of the recursive fractal. We further assemble a Sierpinski triangle within the 3-HAM at scale factor 3 and 990 tile types. For the Sierpinski carpet, we present a 2-HAM result that works at scale factor 3 and uses 1216 tile types. We further include analysis showing that the aTAM is incapable of strictly assembling the Sierpinski triangle considered in this paper, and that multiple hands are needed for the near-perfect assembly of a Sierpinski triangle and the Sierpinski carpet.

Description: We consider k -Facility Location games, where n strategic agents report their locations on the real line and a mechanism maps them to k facilities. Each agent seeks to minimize his connection cost, given by a nonnegative increasing function of his distance to the nearest facility. Departing from previous work, that mostly considers the identity cost function, we are interested in mechanisms without payments that are (group) strategyproof for any given cost function, and achieve a good approximation ratio for the social cost and/or the maximum cost of the agents. We present a randomized mechanism, called Equal Cost , which is group strategyproof and achieves a bounded approximation ratio for all k and n , for any given concave cost function. The approximation ratio is at most 2 for Max Cost and at most n for Social Cost . To the best of our knowledge, this is the first mechanism with a bounded approximation ratio for instances with \(k \ge 3\) facilities and any number of agents. Our result implies an interesting separation between deterministic mechanisms, whose approximation ratio for Max Cost jumps from 2 to unbounded when k increases from 2 to 3, and randomized mechanisms, whose approximation ratio remains at most 2 for all k . On the negative side, we exclude the possibility of a mechanism with the properties of Equal Cost for strictly convex cost functions. We also present a randomized mechanism, called Pick the Loser , which applies to instances with k facilities and only \(n = k+1\) agents. For any given concave cost function, Pick the Loser is strongly group strategyproof and achieves an approximation ratio of 2 for Social Cost .

Description: We give a deterministic #SAT algorithm for de Morgan formulas of size up to \(n^{2.63}\) , which runs in time \(2^{n-n^{{\varOmega }(1)}}\) . This improves upon the deterministic #SAT algorithm of Chen et al. (Proceedings of the twenty-ninth annual IEEE conference on computational complexity, 2014 ), which has similar running time but works only for formulas of size less than \(n^{2.5}\) . Our new algorithm is based on the shrinkage of de Morgan formulas under random restrictions, shown by Paterson and Zwick (Random Struct Algorithms 4(2):135–150, 1993 ). We prove a concentrated and constructive version of their shrinkage result. Namely, we give a deterministic polynomial-time algorithm that selects variables in a given de Morgan formula so that, with high probability over the random assignments to the chosen variables, the original formula shrinks in size, when simplified using a given deterministic polynomial-time formula-simplification algorithm.

Description: We consider Conditional random fields ( CRFs ) with pattern-based potentials defined on a chain. In this model the energy of a string (labeling) \(x_1\ldots x_n\) is the sum of terms over intervals [ i ,  j ] where each term is non-zero only if the substring \(x_i\ldots x_j\) equals a prespecified pattern w . Such CRFs can be naturally applied to many sequence tagging problems. We present efficient algorithms for the three standard inference tasks in a CRF, namely computing (i) the partition function, (ii) marginals, and (iii) computing the MAP. Their complexities are respectively \(O(\textit{nL})\) , \(O(\textit{nL} \ell _{\max })\) and \(O(\textit{nL} \min \{|D|,\log (\ell _{\max }\!+\!1)\})\) where L is the combined length of input patterns, \(\ell _{\max }\) is the maximum length of a pattern, and D is the input alphabet. This improves on the previous algorithms of Ye et al. (NIPS, 2009 ) whose complexities are respectively \(O(\textit{nL} |D|)\) , \(O\left( n |\varGamma | L^2 \ell _{\max }^2\right) \) and \(O(\textit{nL} |D|)\) , where \(|\varGamma |\) is the number of input patterns. In addition, we give an efficient algorithm for sampling, and revisit the case of MAP with non-positive weights.

Description: Estimating the number of triangles in graph streams using a limited amount of memory has become a popular topic in the last decade. Different variations of the problem have been studied, depending on whether the graph edges are provided in an arbitrary order or as incidence lists. However, with a few exceptions, the algorithms have considered insert-only streams. We present a new algorithm estimating the number of triangles in dynamic graph streams where edges can be both inserted and deleted. We show that our algorithm achieves better time and space complexity than previous solutions for various graph classes, for example sparse graphs with a relatively small number of triangles. Also, for graphs with constant transitivity coefficient, a common situation in real graphs, this is the first algorithm achieving constant processing time per edge. The result is achieved by a novel approach combining sampling of vertex triples and sparsification of the input graph. In the course of the analysis of the algorithm we present a lower bound on the number of pairwise independent 2-paths in general graphs which might be of independent interest. At the end of the paper we discuss lower bounds on the space complexity of triangle counting algorithms that make no assumptions on the structure of the graph.

Description: We consider the problems of finding optimal identifying codes, (open) locating-dominating sets and resolving sets (denoted Identifying Code , (Open) Open Locating-Dominating Set and Metric Dimension ) of an interval or a permutation graph. In these problems, one asks to distinguish all vertices of a graph by a subset of the vertices, using either the neighbourhood within the solution set or the distances to the solution vertices. Using a general reduction for this class of problems, we prove that the decision problems associated to these four notions are NP-complete, even for interval graphs of diameter 2 and permutation graphs of diameter 2. While Identifying Code and (Open) Locating-Dominating Set are trivially fixed-parameter-tractable when parameterized by solution size, it is known that in the same setting Metric Dimension is W [2]-hard. We show that for interval graphs, this parameterization of Metric Dimension is fixed-parameter-tractable.

Description: Given a partition of an n element set into equivalence classes, we study the problem of assigning unique labels to these elements in order to support the query that asks whether the elements corresponding to two given labels belong to the same equivalence class. This has various applications including for testing whether two vertices are in the same connected component in an undirected graph or in the same strongly connected component in a directed graph. We consider the problem in several models. Concerning labeling schemes where we assign labels to elements and the query is to be answered just by examining the labels of the queried elements (without any extra space): if each vertex is required to have a unique label, then we show that a label space of \(\sum _{i=1}^n \lfloor {n \over i} \rfloor \) is necessary and sufficient. In other words, \(\lg n + \lg \lg n + O(1)\) bits of space are necessary and sufficient for representing each of the labels. This slightly strengthens the known lower bound and is in contrast to the known necessary and sufficient bound of \(\lceil \lg n \rceil \) for the label length, if each vertex need not get a unique label. Concerning succinct data structures for the problem when the n elements are to be uniquely assigned labels from label set \(\{1,\ldots , n\}\) , we first show that \(\varTheta (\sqrt{n})\) bits are necessary and sufficient to represent the equivalence class information. This space includes the space for implicitly encoding the vertex labels. We can support the query in such a structure in O (1) time in the standard word RAM model. We also develop a dynamic structure that uses \(O(\sqrt{n} \lg n)\) bits to support equivalence queries and unions in \(O(\lg n/\lg \lg n)\) worst case time or \(O(\alpha (n))\) expected amortized time where \(\alpha (n)\) is the inverse Ackermann function. Concerning succinct data structures for the problem when the n elements are to be uniquely assigned labels from label set \(\{1,\ldots , cn\}\) for any constant \(c 〉 1\) , we show that \(\varTheta (\lg n)\) bits are necessary and sufficient to represent the equivalence class information. Moreover, we can support the query in such a structure in O (1) time in the standard word RAM model. We believe that our work can trigger further work on tradeoffs between label space and auxiliary data structure space for other labeling problems.

Description: We perform a thorough study of various characteristics of the asynchronous push–pull protocol for spreading a rumor on Erdős–Rényi random graphs \(G_{n,p}\) , for any \(p〉c\ln (n)/n\) with \(c〉1\) . In particular, we provide a simple strategy for analyzing the asynchronous push–pull protocol on arbitrary graph topologies and apply this strategy to \(G_{n,p}\) . We prove tight bounds of logarithmic order for the total time that is needed until the information has spread to all nodes. Surprisingly, the time required by the asynchronous push–pull protocol is asymptotically almost unaffected by the average degree of the graph. Similarly tight bounds for Erdős–Rényi random graphs have previously only been obtained for the synchronous push protocol, where it has been observed that the total running time increases significantly for sparse random graphs. Finally, we quantify the robustness of the protocol with respect to transmission and node failures. Our analysis suggests that the asynchronous protocols are particularly robust with respect to these failures compared to their synchronous counterparts.

Description: We study connectivity relations among points, where the precise location of each input point lies in a region of uncertainty. We distinguish two fundamental scenarios under which uncertainty arises. In the favorable Best-Case Uncertainty , each input point can be chosen from a given set to yield the best possible objective value. In the unfavorable Worst-Case Uncertainty , the input set has worst possible objective value among all possible point locations, which are uncertain due, for example, to imprecise data. We consider these notions of uncertainty for the bottleneck spanning tree problem, giving rise to the following Best-Case Connectivity with Uncertainty problem: given a family of geometric regions, choose one point per region, such that the longest edge length of an associated geometric spanning tree is minimized. We show that this problem is NP-hard even for very simple scenarios in which the regions are line segments or squares. On the other hand, we give an exact solution for the case in which there are \(n+k\) regions, where k of the regions are line segments and n of the regions are fixed points. We then give approximation algorithms for cases where the regions are either all line segments or all unit discs. We also provide approximation methods for the corresponding Worst-Case Connectivity with Uncertainty problem: Given a set of uncertainty regions, find the minimal distance r such that for any choice of points, one per region, there is a spanning tree among the points with edge length at most r .

Description: Raindrops adhered to a windscreen or window glass can significantly degrade the visibility of a scene. Modeling, detecting and removing raindrops will, therefore, benefit many computer vision applications, particularly outdoor surveillance systems and intelligent vehicle systems. In this paper, a method that automatically detects and removes adherent raindrops is introduced. The core idea is to exploit the local spatio-temporal derivatives of raindrops. To accomplish the idea, we first model adherent raindrops using law of physics, and detect raindrops based on these models in combination with motion and intensity temporal derivatives of the input video. Having detected the raindrops, we remove them and restore the images based on an analysis that some areas of raindrops completely occludes the scene, and some other areas occlude only partially. For partially occluding areas, we restore them by retrieving as much as possible information of the scene, namely, by solving a blending function on the detected partially occluding areas using the temporal intensity derivative. For completely occluding areas, we recover them by using a video completion technique. Experimental results using various real videos show the effectiveness of our method.

Description: Deep convolutional networks have proven to be very successful in learning task specific features that allow for unprecedented performance on various computer vision tasks. Training of such networks follows mostly the supervised learning paradigm, where sufficiently many input-output pairs are required for training. Acquisition of large training sets is one of the key challenges, when approaching a new task. In this paper, we aim for generic feature learning and present an approach for training a convolutional network using only unlabeled data. To this end, we train the network to discriminate between a set of surrogate classes. Each surrogate class is formed by applying a variety of transformations to a randomly sampled ‘seed’ image patch. In contrast to supervised network training, the resulting feature representation is not class specific. It rather provides robustness to the transformations that have been applied during training. This generic feature representation allows for classification results that outperform the state of the art for unsupervised learning on several popular datasets (STL-10, CIFAR-10, Caltech-101, Caltech-256). While features learned with our approach cannot compete with class specific features from supervised training on a classification task, we show that they are advantageous on geometric matching problems, where they also outperform the SIFT descriptor.

Description: We address the video-based face association problem, in which one attempts to extract the face tracks of multiple subjects while maintaining label consistency. Traditional tracking algorithms have difficulty in handling this task, especially when challenging nuisance factors like motion blur, low resolution or significant camera motions are present. We demonstrate that contextual features, in addition to face appearance itself, play an important role in this case. We propose principled methods to combine multiple features using Conditional Random Fields and Max-Margin Markov networks to infer labels for the detected faces. Different from many existing approaches, our algorithms work in online mode and hence have a wider range of applications. We address issues such as parameter learning, inference and handling false positves/negatives that arise in the proposed approach. Finally, we evaluate our approach on several public databases.

Description: There are many scenarios in artificial intelligence, signal processing or medicine, in which a temporal sequence consists of several unknown overlapping independent causes, and we are interested in accurately recovering those canonical causes. Factorial hidden Markov models (FHMMs) present the versatility to provide a good fit to these scenarios. However, in some scenarios, the number of causes or the number of states of the FHMM cannot be known or limited a priori. In this paper, we propose an infinite factorial unbounded-state hidden Markov model (IFUHMM), in which the number of parallel hidden Markovmodels (HMMs) and states in each HMM are potentially unbounded. We rely on a Bayesian nonparametric (BNP) prior over integer-valued matrices, in which the columns represent the Markov chains, the rows the time indexes, and the integers the state for each chain and time instant. First, we extend the existent infinite factorial binary-state HMM to allow for any number of states. Then, we modify this model to allow for an unbounded number of states and derive an MCMC-based inference algorithm that properly deals with the trade-off between the unbounded number of states and chains. We illustrate the performance of our proposed models in the power disaggregation problem.

Description: The speed with which intelligent systems can react to an action depends on how soon it can be recognized. The ability to recognize ongoing actions is critical in many applications, for example, spotting criminal activity. It is challenging, since decisions have to be made based on partial videos of temporally incomplete action executions. In this paper, we propose a novel discriminative multi-scale kernelized model for predicting the action class from a partially observed video. The proposed model captures temporal dynamics of human actions by explicitly considering all the history of observed features as well as features in smaller temporal segments. A compositional kernel is proposed to hierarchically capture the relationships between partial observations as well as the temporal segments, respectively. We develop a new learning formulation, which elegantly captures the temporal evolution over time, and enforces the label consistency between segments and corresponding partial videos. We prove that the proposed learning formulation minimizes the upper bound of the empirical risk. Experimental results on four public datasets show that the proposed approach outperforms state-of-the-art action prediction methods.

Description: Evidence is mounting that Convolutional Networks (ConvNets) are the most effective representation learning method for visual recognition tasks. In the common scenario, a ConvNet is trained on a large labeled dataset (source) and the feed-forward units activation of the trained network, at a certain layer of the network, is used as a generic representation of an input image for a task with relatively smaller training set (target). Recent studies have shown this form of representation transfer to be suitable for a wide range of target visual recognition tasks. This paper introduces and investigates several factors affecting the transferability of such representations. It includes parameters for training of the source ConvNet such as its architecture, distribution of the training data, etc. and also the parameters of feature extraction such as layer of the trained ConvNet, dimensionality reduction, etc. Then, by optimizing these factors, we show that significant improvements can be achieved on various (17) visual recognition tasks. We further show that these visual recognition tasks can be categorically ordered based on their similarity to the source task such that a correlation between the performance of tasks and their similarity to the source task w.r.t. the proposed factors is observed.

Description: Graph matching (GM) is a fundamental problem in computer science, and it plays a central role to solve correspondence problems in computer vision. GM problems that incorporate pairwise constraints can be formulated as a quadratic assignment problem (QAP). Although widely used, solving the correspondence problem through GM has two main limitations: (1) the QAP is NP-hard and difficult to approximate; (2) GM algorithms do not incorporate geometric constraints between nodes that are natural in computer vision problems. To address aforementioned problems, this paper proposes factorized graph matching (FGM). FGM factorizes the large pairwise affinity matrix into smaller matrices that encode the local structure of each graph and the pairwise affinity between edges. Four are the benefits that follow from this factorization: (1) There is no need to compute the costly (in space and time) pairwise affinity matrix; (2) The factorization allows the use of a path-following optimization algorithm, that leads to improved optimization strategies and matching performance; (3) Given the factorization, it becomes straight-forward to incorporate geometric transformations (rigid and non-rigid) to the GM problem. (4) Using a matrix formulation for the GM problem and the factorization, it is easy to reveal commonalities and differences between different GM methods. The factorization also provides a clean connection with other matching algorithms such as iterative closest point; Experimental results on synthetic and real databases illustrate how FGM outperforms state-of-the-art algorithms for GM. The code is available at http://humansensing.cs.cmu.edu/fgm .

Description: Existing data association techniques mostly focus on matching pairs of data-point sets and then repeating this process along space-time to achieve long term correspondences. However, in many problems such as person re-identification, a set of data-points may be observed at multiple spatio-temporal locations and/or by multiple agents in a network and simply combining the local pairwise association results between sets of data-points often leads to inconsistencies over the global space-time horizons. In this paper, we propose a Novel Network Consistent Data Association (NCDA) framework formulated as an optimization problem that not only maintains consistency in association results across the network, but also improves the pairwise data association accuracies. The proposed NCDA can be solved as a binary integer program leading to a globally optimal solution and is capable of handling the challenging data-association scenario where the number of data-points varies across different sets of instances in the network. We also present an online implementation of NCDA method that can dynamically associate new observations to already observed data-points in an iterative fashion, while maintaining network consistency. We have tested both the batch and the online NCDA in two application areas—person re-identification and spatio-temporal cell tracking and observed consistent and highly accurate data association results in all the cases.

Description: This paper presents a method for learning an And-Or model to represent context and occlusion for car detection and viewpoint estimation. The learned And-Or model represents car-to-car context and occlusion configurations at three levels: (i) spatially-aligned cars, (ii) single car under different occlusion configurations, and (iii) a small number of parts. The And-Or model embeds a grammar for representing large structural and appearance variations in a reconfigurable hierarchy. The learning process consists of two stages in a weakly supervised way (i.e., only bounding boxes of single cars are annotated). First, the structure of the And-Or model is learned with three components: (a) mining multi-car contextual patterns based on layouts of annotated single car bounding boxes, (b) mining occlusion configurations between single cars, and (c) learning different combinations of part visibility based on CAD simulations. The And-Or model is organized in a directed and acyclic graph which can be inferred by Dynamic Programming. Second, the model parameters (for appearance, deformation and bias) are jointly trained using Weak-Label Structural SVM. In experiments, we test our model on four car detection datasets—the KITTI dataset [1] , the PASCAL VOC2007 car dataset  [2] , and two self-collected car datasets, namely the Street-Parking car dataset and the Parking-Lot car dataset, and three datasets for car viewpoint estimation—the PASCAL VOC2006 car dataset  [2] , the 3D car dataset  [3] , and the PASCAL3D+ car dataset  [4] . Compared with state-of-the-art variants of deformable part-based models and other methods, our model achieves significant improvement consistently on the four detection datasets, and comparable performance on car viewpo- nt estimation.

Description: Convolutional Neural Network (CNN) has demonstrated promising performance in single-label image classification tasks. However, how CNN best copes with multi-label images still remains an open problem, mainly due to the complex underlying object layouts and insufficient multi-label training images. In this work, we propose a flexible deep CNN infrastructure, called Hypotheses-CNN-Pooling (HCP), where an arbitrary number of object segment hypotheses are taken as the inputs, then a shared CNN is connected with each hypothesis, and finally the CNN output results from different hypotheses are aggregated with max pooling to produce the ultimate multi-label predictions. Some unique characteristics of this flexible deep CNN infrastructure include: 1) no ground-truth bounding box information is required for training; 2) the whole HCP infrastructure is robust to possibly noisy and/or redundant hypotheses; 3) the shared CNN is flexible and can be well pre-trained with a large-scale single-label image dataset, e.g., ImageNet; and 4) it may naturally output multi-label prediction results. Experimental results on Pascal VOC 2007 and VOC 2012 multi-label image datasets well demonstrate the superiority of the proposed HCP infrastructure over other state-of-the-arts. In particular, the mAP reaches 90.5% by HCP only and 93.2% after the fusion with our complementary result in  [12] based on hand-crafted features on the VOC 2012 dataset.

Description: Wiberg matrix factorization breaks a matrix $Y$ into low-rank factors $U$ and $V$ by solving for $V$ in closed form given $U$ , linearizing $V(U)$ about $U$ , and iteratively minimizing $||Y - UV(U)||_2$ with respect to $U$ only. This approach factors the matrix while effectively removing $V$ from the minimization. Recently Eriksson and van den Hengel extended this approach to $L_1$ , minimizing $||Y - UV(U)||_1$ . We generalize their approach beyond factorization to minimize $||Y - f(U, V)||_1$ for more general functions $f(U, V)$ that are nonlinear in each of two sets of variables. We demonstrate the idea with a practical Wiberg algorithm for $L_1$ bundle adjustment. One Wiberg minimization can be nested inside another, effectively removing two of three sets of variables from a minimization. We demonstrate this idea with a nested Wiberg algorithm for $L_1$ projective bundle adjustment, solving for camera matrices, points, and projective depths. Wiberg minimization also generalizes to handle nonlinear constraints, and we demonstrate this idea with Constrained Wiberg Minimization for Multiple Instance Learning (CWM-MIL), which removes one set of variable

Description: In this paper, we propose a novel subspace learning algorithm called Local Feature Discriminant Projection (LFDP) for supervised dimensionality reduction of local features. LFDP is able to efficiently seek a subspace to improve the discriminability of local features for classification. We make three novel contributions. First, the proposed LFDP is a general supervised subspace learning algorithm which provides an efficient way for dimensionality reduction of large-scale local feature descriptors. Second, we introduce the Differential Scatter Discriminant Criterion (DSDC) to the subspace learning of local feature descriptors which avoids the matrix singularity problem. Third, we propose a generalized orthogonalization method to impose on projections, leading to a more compact and less redundant subspace. Extensive experimental validation on three benchmark datasets including UIUC-Sports, Scene-15 and MIT Indoor demonstrates that the proposed LFDP outperforms other dimensionality reduction methods and achieves state-of-the-art performance for image classification.

Description: We propose a real-time method to accurately track the human head pose in the 3-dimensional (3D) world. Using a RGB-Depth camera, a face template is reconstructed by fitting a 3D morphable face model, and the head pose is determined by registering this user-specific face template to the input depth video.

Description: Euclidean statistics are often generalized to Riemannian manifolds by replacing straight-line interpolations with geodesic ones. While these Riemannian models are familiar-looking, they are restricted by the inflexibility of geodesics, and they rely on constructions which are optimal only in Euclidean domains. We consider extensions of Principal Component Analysis (PCA) to Riemannian manifolds. Classic Riemannian approaches seek a geodesic curve passing through the mean that optimizes a criteria of interest. The requirements that the solution both is geodesic and must pass through the mean tend to imply that the methods only work well when the manifold is mostly flat within the support of the generating distribution. We argue that instead of generalizing linear Euclidean models, it is more fruitful to generalize non-linear Euclidean models. Specifically, we extend the classic Principal Curves from Hastie & Stuetzle to data residing on a complete Riemannian manifold. We show that for elliptical distributions in the tangent of spaces of constant curvature, the standard principal geodesic is a principal curve. The proposed model is simple to compute and avoids many of the pitfalls of traditional geodesic approaches. We empirically demonstrate the effectiveness of the Riemannian principal curves on several manifolds and datasets.

Description: An end-to-end real-time text localization and recognition method is presented. Its real-time performance is achieved by posing the character detection and segmentation problem as an efficient sequential selection from the set of Extremal Regions. The ER detector is robust against blur, low contrast and illumination, color and texture variation. In the first stage, the probability of each ER being a character is estimated using features calculated by a novel algorithm in constant time and only ERs with locally maximal probability are selected for the second stage, where the classification accuracy is improved using computationally more expensive features. A highly efficient clustering algorithm then groups ERs into text lines and an OCR classifier trained on synthetic fonts is exploited to label character regions. The most probable character sequence is selected in the last stage when the context of each character is known. The method was evaluated on three public datasets. On the ICDAR 2013 dataset the method achieves state-of-the-art results in text localization; on the more challenging SVT dataset, the proposed method significantly outperforms the state-of-the-art methods and demonstrates that the proposed pipeline can incorporate additional prior knowledge about the detected text. The proposed method was exploited as the baseline in the ICDAR 2015 Robust Reading competition, where it compares favourably to the state-of-the art.

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Description: This paper addresses modelling data using the Watson distribution. The Watson distribution is one of the simplest distributions for analyzing axially symmetric data. This distribution has gained some attention in recent years due to its modeling capability. However, its Bayesian inference is fairly understudied due to difficulty in handling the normalization factor. Recent development of Markov chain Monte Carlo (MCMC) sampling methods can be applied for this purpose. However, these methods can be prohibitively slow for practical applications. A deterministic alternative is provided by variational methods that convert inference problems into optimization problems. In this paper, we present a variational inference for Watson mixture models. First, the variational framework is used to side-step the intractability arising from the coupling of latent states and parameters. Second, the variational free energy is further lower bounded in order to avoid intractable moment computation. The proposed approach provides a lower bound on the log marginal likelihood and retains distributional information over all parameters. Moreover, we show that it can regulate its own complexity by pruning unnecessary mixture components while avoiding over-fitting. We discuss potential applications of the modeling with Watson distributions in the problem of blind source separation, and clustering gene expression data sets.

Description: We define the modular treewidth of a graph as its treewidth after contraction of modules. This parameter properly generalizes treewidth and is itself properly generalized by clique-width. We show that the number of satisfying assignments can be computed in polynomial time for CNF formulas whose incidence graphs have bounded modular treewidth. Our result generalizes known results for the treewidth of incidence graphs and is incomparable with known results for clique-width (or rank-width) of signed incidence graphs. The contraction of modules is an effective data reduction procedure. Our algorithm is the first one to harness this technique for #SAT. The order of the polynomial bounding the runtime of our algorithm depends on the modular treewidth of the input formula. We show that it is unlikely that this dependency can be avoided by proving that SAT is W[1]-hard when parameterized by the modular incidence treewidth of the given CNF formula.

Description: In a classical online network design problem, traffic requirements are gradually revealed to an algorithm. Each time a new request arrives, the algorithm has to satisfy it by augmenting the network under construction in a proper way (with no possibility of recovery). In this paper we study a natural generalization of online network design problems, where a fraction of the requests (the outliers ) can be disregarded. Now, each time a request arrives, the algorithm first decides whether to satisfy it or not, and only in the first case it acts accordingly. We cast three classical network design problems into this framework: (i) Online Steiner tree with outliers In this case a set of t terminals that belong to an n -node graph is presented, one at a time, to an algorithm. Each time a new terminal arrives, the algorithm can either discard or select it. In the latter case, the algorithm connects it to the Steiner tree under construction (initially consisting of a given root node). At the end of the process, at least k terminals must be selected. (ii) Online TSP with outliers This is the same problem as above, but with the Steiner tree replaced by a TSP tour. (iii) Online facility location with outliers In this case, we are also given a set of facility nodes, each one with an opening cost. Each time a terminal is selected, we have to connect it to some facility (and open that facility, if it is not already open). We focus on the known distribution model, where terminals are independently sampled from a given distribution. For all the above problems, we present bicriteria online algorithms that, for any constant \(\epsilon 〉0\) , select at least \((1-\epsilon )k\) terminals with high probability and pay in expectation \(O(\log ^2n)\) times more than the expected cost of the optimal offline solution (selecting k terminals). These upper bounds are complemented by inapproximability results for the case that one insists on selecting exactly k terminals, and by lower bounds including an \(\varOmega (\log n/\log \log n)\) lower bound for the case that the online algorithm is allowed to select \(\alpha \,k\) terminals only, for a sufficiently large constant \(\alpha \in (0,1)\) .

Description: A well known result in graph algorithms, due to Edmonds, states that given a digraph D and a positive integer \(\ell \) , we can test whether D contains \(\ell \) arc-disjoint out-branchings in polynomial time. However, if we ask whether there exists an out-branching and an in-branching which are arc-disjoint, then the problem becomes NP -complete. In fact, even deciding whether a digraph D contains an out-branching which is arc-disjoint from some spanning tree in the underlying undirected graph remains NP -complete. In this paper we formulate some natural optimization questions around these problems and initiate its study in the realm of parameterized complexity. More precisely, the problems we study are the following: Arc - Disjoint Branchings and Non - Disconnecting Out - Branching . In Arc - Disjoint Branchings ( Non - Disconnecting Out - Branching ), a digraph D and a positive integer k are given as input and the goal is to test whether there exist an out-branching and in-branching (respectively, a spanning tree in the underlying undirected graph) that differ on at least k arcs. We obtain the following results for these problems. Non - Disconnecting Out - Branching is fixed parameter tractable (FPT) and admits a linear vertex kernel. Arc - Disjoint Branchings is FPT on strong digraphs. The algorithm for Non - Disconnecting Out - Branching runs in time \(2^{\mathcal {O}(k)}n^{\mathcal {O}(1)}\) and the approach we use to obtain this algorithms seems useful in designing other moderately exponential time algorithms for edge/arc partitioning problems.

Description: We study the stable roommates problem in networks where players are embedded in a social context and may incorporate positive externalities into their decisions. Each player is a node in a social network and strives to form a good match with a neighboring player. We consider the existence, computation, and inefficiency of stable matchings from which no pair of players wants to deviate. We characterize prices of anarchy and stability, which capture the ratio of the total profit in the optimum matching over the total profit of the worst and best stable matching, respectively. When the benefit from a match (which we model by associating a reward with each edge) is the same for both players, we show that externalities can significantly improve the price of stability, while the price of anarchy remains unaffected. Furthermore, a good stable matching achieving the bound on the price of stability can be obtained in polynomial time. We extend these results to more general matching rewards, when players matched to each other may receive different benefits from the match. For this more general case, we show that network externalities (i.e., “caring about your friends”) can make an even larger difference and greatly reduce the price of anarchy. We show a variety of existence results and present upper and lower bounds on the prices of anarchy and stability for various structures of matching benefits. All our results on stable matchings immediately extend to the more general case of fractional stable matchings.

Description: We present the first general bounds on the mixing time of the Markov chain associated to the logit dynamics for wide classes of strategic games. The logit dynamics with inverse noise \(\beta \) describes the behavior of a complex system whose individual components act selfishly according to some partial (“noisy”) knowledge of the system, where the capacity of the agent to know the system and compute her best move is measured by parameter \(\beta \) . In particular, we prove nearly tight bounds for potential games and games with dominant strategies. Our results show that for potential games the mixing time is bounded by an exponential in \(\beta \) and in the maximum potential difference. Instead, for games with dominant strategies the mixing time cannot grow arbitrarily with \(\beta \) . Finally, we refine our analysis for a subclass of potential games called graphical coordination games, often used for modeling the diffusion of new technologies. We prove that the mixing time of the logit dynamics for these games can be upper bounded by a function that is exponential in the cutwidth of the underlying graph and in \(\beta \) . Moreover, we consider two specific and popular network topologies, the clique and the ring. For the clique, we prove an almost matching lower bound on the mixing time of the logit dynamics that is exponential in \(\beta \) and in the maximum potential difference, while for the ring we prove that the time of convergence of the logit dynamics to its stationary distribution is significantly shorter.

Description: Given a plane graph G (i.e., a planar graph with a fixed planar embedding and outer face) and a biconnected subgraph \(G^{\prime }\) with a fixed planar straight-line convex drawing, we consider the question whether this drawing can be extended to a planar straight-line drawing of G . We characterize when this is possible in terms of simple necessary conditions, which we prove to be sufficient. This also leads to a linear-time testing algorithm. If a drawing extension exists, one can be computed in the same running time.

Description: The rotor–router model , also called the Propp machine , was first considered as a deterministic alternative to the random walk. The edges adjacent to each node  v (or equivalently, the exit ports at  v ) are arranged in a fixed cyclic order, which does not change during the exploration. Each node  v maintains a port pointer   \(\pi _v\) which indicates the exit port to be adopted by an agent on the conclusion of the next visit to this node (the “next exit port”). The rotor–router mechanism guarantees that after each consecutive visit at the same node, the pointer at this node is moved to the next port in the cyclic order. It is known that, in an undirected graph  G with  m edges, the route adopted by an agent controlled by the rotor–router mechanism eventually forms an Euler tour based on arcs obtained via replacing each edge in  G by two arcs with opposite direction. The process of ushering the agent to an Euler tour is referred to as the lock-in problem . In Yanovski et al. (Algorithmica 37(3):165–186, 2003 ), it was proved that, independently of the initial configuration of the rotor–router mechanism in  G , the agent locks-in in time bounded by  \(2mD\) , where \(D\) is the diameter of  G . In this paper we examine the dependence of the lock-in time on the initial configuration of the rotor–router mechanism. Our analysis is performed in the form of a game between a player \({\mathcal {P}}\) intending to lock-in the agent in an Euler tour as quickly as possible and its adversary \({\mathcal {A}}\) with the counter objective. We consider all cases of who decides the initial cyclic orders and the initial values \(\pi _v\) . We show, for example, that if \({\mathcal {A}}\) provides its own port numbering after the initial setup of pointers by \({\mathcal {P}}\) , the worst-case complexity of the lock-in problem is \({\varTheta }(m\cdot \min \{\log m,D\})\) . We also investigate the robustness of the rotor–router graph exploration in presence of faults in the pointers \(\pi _v\) or dynamic changes in the graph. We show, for example, that after the exploration establishes an Eulerian cycle, if k edges are added to the graph, then a new Eulerian cycle is established within \(\mathcal {O}(km)\) steps.

Description: Recently, head pose estimation (HPE) from low-resolution surveillance data has gained in importance. However, monocular and multi-view HPE approaches still work poorly under target motion , as facial appearance distorts owing to camera perspective and scale changes when a person moves around. To this end, we propose FEGA-MTL , a novel framework based on Multi-Task Learning (MTL) for classifying the head pose of a person who moves freely in an environment monitored by multiple, large field-of-view surveillance cameras. Upon partitioning the monitored scene into a dense uniform spatial grid, FEGA-MTL simultaneously clusters grid partitions into regions with similar facial appearance, while learning region-specific head pose classifiers. In the learning phase, guided by two graphs which a-priori model the similarity among (1) grid partitions based on camera geometry and (2) head pose classes, FEGA-MTL derives the optimal scene partitioning and associated pose classifiers. Upon determining the target's position using a person tracker at test time, the corresponding region-specific classifier is invoked for HPE. The FEGA-MTL framework naturally extends to a weakly supervised setting where the target's walking direction is employed as a proxy in lieu of head orientation. Experiments confirm that FEGA-MTL significantly outperforms competing single-task and multi-task learning methods in multi-view settings.

Description: Recent literature shows that facial attributes, i.e., contextual facial information, can be beneficial for improving the performance of real-world applications, such as face verification, face recognition, and image search. Examples of face attributes include gender, skin color, facial hair, etc. How to robustly obtain these facial attributes (traits) is still an open problem, especially in the presence of the challenges of real-world environments: non-uniform illumination conditions, arbitrary occlusions, motion blur and background clutter. What makes this problem even more difficult is the enormous variability presented by the same subject, due to arbitrary face scales, head poses, and facial expressions. In this paper, we focus on the problem of facial trait classification in real-world face videos. We have developed a fully automatic hierarchical and probabilistic framework that models the collective set of frame class distributions and feature spatial information over a video sequence. The experiments are conducted on a large real-world face video database that we have collected, labelled and made publicly available. The proposed method is flexible enough to be applied to any facial classification problem. Experiments on a large, real-world video database McGillFaces  [1] of 18,000 video frames reveal that the proposed framework outperforms alternative approaches, by up to 16.96 and 10.13%, for the facial attributes of gender and facial hair, respectively.

Description: Typical feature selection methods choose an optimal global feature subset that is applied over all regions of the sample space. In contrast, in this paper we propose a novel localized feature selection (LFS) approach whereby each region of the sample space is associated with its own distinct optimized feature set, which may vary both in membership and size across the sample space. This allows the feature set to optimally adapt to local variations in the sample space. An associated method for measuring the similarities of a query datum to each of the respective classes is also proposed. The proposed method makes no assumptions about the underlying structure of the samples; hence the method is insensitive to the distribution of the data over the sample space. The method is efficiently formulated as a linear programming optimization problem. Furthermore, we demonstrate the method is robust against the over-fitting problem. Experimental results on eleven synthetic and real-world data sets demonstrate the viability of the formulation and the effectiveness of the proposed algorithm. In addition we show several examples where localized feature selection produces better results than a global feature selection method.

Description: Many typical applications of object detection operate within a prescribed false-positive range. In this situation the performance of a detector should be assessed on the basis of the area under the ROC curve over that range, rather than over the full curve, as the performance outside the prescribed range is irrelevant. This measure is labelled as the partial area under the ROC curve (pAUC). We propose a novel ensemble learning method which achieves a maximal detection rate at a user-defined range of false positive rates by directly optimizing the partial AUC using structured learning. In addition, in order to achieve high object detection performance, we propose a new approach to extracting low-level visual features based on spatial pooling. Incorporating spatial pooling improves the translational invariance and thus the robustness of the detection process. Experimental results on both synthetic and real-world data sets demonstrate the effectiveness of our approach, and we show that it is possible to train state-of-the-art pedestrian detectors using the proposed structured ensemble learning method with spatially pooled features. The result is the current best reported performance on the Caltech-USA pedestrian detection dataset.

Description: This paper addresses the problem of matching common node correspondences among multiple graphs referring to an identical or related structure. This multi-graph matching problem involves two correlated components: i) the local pairwise matching affinity across pairs of graphs; ii) the global matching consistency that measures the uniqueness of the pairwise matchings by different composition orders. Previous studies typically either enforce the matching consistency constraints in the beginning of an iterative optimization, which may propagate matching error both over iterations and across graph pairs; or separate affinity optimization and consistency enforcement into two steps. This paper is motivated by the observation that matching consistency can serve as a regularizer in the affinity objective function especially when the function is biased due to noises or inappropriate modeling. We propose composition-based multi-graph matching methods to incorporate the two aspects by optimizing the affinity score, meanwhile gradually infusing the consistency. We also propose two mechanisms to elicit the common inliers against outliers. Compelling results on synthetic and real images show the competency of our algorithms.

Description: Standard edge detection operators such as the Laplacian of Gaussian and the gradient of Gaussian can be used to track contours in image sequences. When using edge operators, a contour, which is determined on a frame of the sequence, is simply used as a starting contour to locate the nearest contour on the subsequent frame. However, the strategy used to look for the nearest edge points may not work when tracking contours of non isolated gray level discontinuities. In these cases, strategies derived from the optical flow equation, which look for similar gray level distributions, appear to be more appropriate since these can work with a lower frame rate than that needed for strategies based on pure edge detection operators. However, an optical flow strategy tends to propagate the localization errors through the sequence and an additional edge detection procedure is essential to compensate for such a drawback. In this paper a spatio-temporal intensity moment is proposed which integrates the two basic functions of edge detection and tracking.

Description: Design and development of efficient and accurate feature descriptors is critical for the success of many computer vision applications. This paper proposes a new feature descriptor, referred to as DoN, for the 2D palmprint matching. The descriptor is extracted for each point on the palmprint. It is based on the ordinal measure which partially describes the difference of the neighboring points’ normal vectors. DoN has at least two advantages: 1) it describes the 3D information, which is expected to be highly stable under commonly occurring illumination variations during contactless imaging; 2) the size of DoN for each point is only one bit, which is computationally simple to extract, easy to match, and efficient to storage. We show that such 3D information can be extracted from a single 2D palmprint image. The analysis for the effectiveness of ordinal measure for palmprint matching is also provided. Four publicly available 2D palmprint databases are used to evaluate the effectiveness of DoN, both for identification and the verification. Our method on all these databases achieves the state-of-the-art performance.

Description: Searching for matches to high-dimensional vectors using hard/soft vector quantization is the most computationally expensive part of various computer vision algorithms including the bag of visual word (BoW). This paper proposes a fast computation method, Neighbor-to-Neighbor (NTN) search [1] , which skips some calculations based on the similarity of input vectors. For example, in image classification using dense SIFT descriptors, the NTN search seeks similar descriptors from a point on a grid to an adjacent point. Applications of the NTN search to vector quantization, a Gaussian mixture model, sparse coding, and a kernel codebook for extracting image or video representation are presented in this paper. We evaluated the proposed method on image and video benchmarks: the PASCAL VOC 2007 Classification Challenge and the TRECVID 2010 Semantic Indexing Task. NTN-VQ reduced the coding cost by 77.4 percent, and NTN-GMM reduced it by 89.3 percent, without any significant degradation in classification performance.

Description: Consider the problem of selecting k items that maximize the value of a monotone submodular set function f , where f can be accessed using value queries. It is well known that polynomially many queries suffice in order to obtain an approximation ratio of \(1 - \frac{1}{e}\) . We consider a variation on this problem in which the value queries are required to be of uniform size: each queried set, like the desired solution itself, must contain k items. We show that polynomially many uniform size queries suffice in order to obtain an approximation ratio of \(\frac{1}{2}\) , and that an approximation ratio of \(\frac{1 + \epsilon }{2}\) requires a number of queries that is exponential in \(\epsilon k\) . For the interesting special case of coverage functions, we show that an approximation ratio strictly better than \(\frac{1}{2}\) is attainable with polynomially many uniform size queries. The “uniform size” requirement is motivated by situations in which a firm may offer a menu of exactly k items to its clients, where k is a parameter determined by external considerations. Performing a query corresponds to physically changing the identities of the items offered, and the reply to the query is deduced by observing the behavior of clients in response to the change. Queries that involve a number of items that differs from k may not be desirable due to these external considerations. In such situations it is natural to ask whether the same approximation ratios that can be guaranteed by general value queries can also be obtained by uniform size queries.

Description: In this paper, we study the approximability of the Maximum Labeled Path problem: given a vertex-labeled directed acyclic graph D , find a path in D that collects a maximum number of distinct labels. For any \(\epsilon 〉0\) , we provide a polynomial time approximation algorithm that computes a solution of value at least \(OPT^{1-\epsilon }\) and a self-reduction showing that any constant ratio approximation algorithm for this problem can be converted into a PTAS. This last result, combined with the APX -hardness of the problem, shows that the problem cannot be approximated within any constant ratio unless \(P=NP\) .

Description: We present the first results on the parameterized complexity of reconfiguration problems, where a reconfiguration variant of an optimization problem \(\mathcal {Q}\) takes as input two feasible solutions S and T and determines if there is a sequence of reconfiguration steps, i.e. a reconfiguration sequence, that can be applied to transform S into T such that each step results in a feasible solution to \(\mathcal {Q}\) . For most of the results in this paper, S and T are sets of vertices of a given graph and a reconfiguration step adds or removes a vertex. Our study is motivated by results establishing that for many NP -hard problems, the classical complexity of reconfiguration is PSPACE -complete. We address the question for several important graph properties under two natural parameterizations: k , a bound on the size of solutions, and \(\ell \) , a bound on the length of reconfiguration sequences. Our first general result is an algorithmic paradigm, the reconfiguration kernel, used to obtain fixed-parameter tractable algorithms for reconfiguration variants of Vertex Cover and, more generally, Bounded Hitting Set and Feedback Vertex Set , all parameterized by k . In contrast, we show that reconfiguring Unbounded Hitting Set is W[2] -hard when parameterized by \(k+\ell \) . We also demonstrate the W[1] -hardness of reconfiguration variants of a large class of maximization problems parameterized by \(k+\ell \) , and of their corresponding deletion problems parameterized by \(\ell \) ; in doing so, we show that there exist problems in FPT when parameterized by k , but whose reconfiguration variants are W[1] -hard when parameterized by \(k+\ell \) .

Description: The greedy spanner is the highest quality geometric spanner (in e.g. edge count and weight, both in theory and practice) known to be computable in polynomial time. Unfortunately, all known algorithms for computing it on n points take \(\varOmega (n^2)\) time, limiting its applicability on large data sets. We propose a novel algorithm design which uses the observation that for many point sets, the greedy spanner has many ‘short’ edges that can be determined locally and usually quickly. To find the usually few remaining ‘long’ edges, we use a combination of already determined local information and the well-separated pair decomposition. We give experimental results showing large to massive performance increases over the state-of-the-art on nearly all tests and real-life data sets. On the theoretical side we prove a near-linear expected time bound on uniform point sets and a near-quadratic worst-case bound. Our bound for point sets drawn uniformly and independently at random in a square follows from a local characterization of t -spanners we give on such point sets. We give a geometric property that holds with high probability, which in turn implies that if an edge set on these points has t -paths between pairs of points ‘close’ to each other, then it has t -paths between all pairs of points. This characterization gives an \(O(n \log ^2 n \log ^2 \log n)\) expected time bound on our greedy spanner algorithm, making it the first subquadratic time algorithm for this problem on any interesting class of points. We also use this characterization to give an \(O((n + |E|) \log ^2 n \log \log n)\) expected time algorithm on uniformly distributed points that determines whether E is a t -spanner, making it the first subquadratic time algorithm for this problem that does not make assumptions on E .

Description: Let \(\mathcal {D} = \{\mathsf {T}_1,\mathsf {T}_2, \ldots ,\mathsf {T}_D\}\) be a collection of D string documents of n characters in total, that are drawn from an alphabet set \(\varSigma =[\sigma ]\) . The top-k document retrieval problem is to preprocess \(\mathcal{D}\) into a data structure that, given a query \((P[1\ldots p],k)\) , can return the k documents of \(\mathcal{D}\) most relevant to the pattern P . The relevance is captured using a predefined ranking function, which depends on the set of occurrences of P in \(\mathsf {T}_d\) . For example, it can be the term frequency (i.e., the number of occurrences of P in \(\mathsf {T}_d\) ), or it can be the term proximity (i.e., the distance between the closest pair of occurrences of P in \(\mathsf {T}_d\) ), or a pattern-independent importance score of \(\mathsf {T}_d\) such as PageRank. Linear space and optimal query time solutions already exist for the general top- k document retrieval problem. Compressed and compact space solutions are also known, but only for a few ranking functions such as term frequency and importance. However, space efficient data structures for term proximity based retrieval have been evasive. In this paper we present the first sub-linear space data structure for this relevance function, which uses only o ( n ) bits on top of any compressed suffix array of \(\mathcal{D}\) and solves queries in \(O((p+k) {{\mathrm{polylog}}}\,\,n)\) time. We also show that scores that consist of a weighted combination of term proximity, term frequency, and document importance, can be handled using twice the space required to represent the text collection.

Description: We study the parameterized complexity of Geometric Graph Isomorphism (Known as the Point Set Congruence problem in computational geometry): given two sets of n points A and B with rational coordinates in k -dimensional euclidean space, with k as the fixed parameter, the problem is to decide if there is a bijection \(\pi :A \rightarrow B\) such that for all \(x,y \in A\) , \(\Vert x-y\Vert = \Vert \pi (x)-\pi (y)\Vert \) , where \(\Vert \cdot \Vert \) is the euclidean norm. Our main result is the following: We give a \(O^*(k^{O(k)})\) time (The \(O^*(\cdot )\) notation here, as usual, suppresses polynomial factors) FPT algorithm for Geometric Isomorphism. This is substantially faster than the previous best time bound of \(O^*(2^{O(k^4)})\) for the problem (Evdokimov and Ponomarenko in Pure Appl Algebra 117–118:253–276, 1997 ). In fact, we show the stronger result that even canonical forms for finite point sets with rational coordinates can also be computed in \(O^*(k^{O(k)})\) time. We also briefly discuss the isomorphism problem for other \(l_p\) metrics. Specifically, we describe a deterministic polynomial-time algorithm for finite point sets in \(\mathbb {Q}^2\) .

Description: We present deterministic and randomized algorithms for the problem of online packet routing in grids in the competitive network throughput model (Aiello et al. in SODA, pp 771–780 2003 ). In this model the network has nodes with bounded buffers and bounded link capacities. The goal in this model is to maximize the throughput, i.e., the number of delivered packets. Our deterministic algorithm is the first online algorithm with an \(O\left( \log ^{O(1)}(n)\right) \) competitive ratio for uni-directional grids (where n denotes the size of the network). The deterministic online algorithm is centralized and handles packets with deadlines. This algorithm is applicable to various ranges of values of buffer sizes and communication link capacities. In particular, it holds for buffer size and communication link capacity in the range \([3 \ldots \log n]\) . Our randomized algorithm achieves an expected competitive ratio of \(O(\log n)\) for the uni-directional line. This algorithm is applicable to a wide range of buffer sizes and communication link capacities. In particular, it holds also for unit size buffers and unit capacity links. This algorithm improves the best previous \(O(\log ^2 n)\) -competitive ratio of Azar and Zachut (ESA, pp 484–495, 2005 ).

Description: In the Shortest Superstring problem we are given a set of strings \(S=\{s_1, \ldots , s_n\}\) and integer \(\ell \) and the question is to decide whether there is a superstring s of length at most \(\ell \) containing all strings of S as substrings. We obtain several parameterized algorithms and complexity results for this problem. In particular, we give an algorithm which in time \(2^{\mathcal {O}(k)} {\text {poly}}(n)\) finds a superstring of length at most \(\ell \) containing at least k strings of S . We complement this by a lower bound showing that such a parameterization does not admit a polynomial kernel up to some complexity assumption. We also obtain several results about “below guaranteed values” parameterization of the problem. We show that parameterization by compression admits a polynomial kernel while parameterization “below matching” is hard.

Description: We prove that given a bipartite graph G with vertex set V and an integer  k , deciding whether there exists a subset of V of size at most k hitting all maximal independent sets of G is complete for the class \(\varSigma_{2}^{\mathrm{P}}\) .

Description: We present the first approximate distance oracle for sparse directed networks with time-dependent arc-travel-times determined by continuous, piecewise linear, positive functions possessing the FIFO property. Our approach precomputes \((1+\varepsilon )\) -approximate distance summaries from selected landmark vertices to all other vertices in the network. Our oracle uses subquadratic space and time preprocessing, and provides two sublinear-time query algorithms that deliver constant and \((1+\sigma )\) -approximate shortest-travel-times, respectively, for arbitrary origin–destination pairs in the network, for any constant \(\sigma 〉 \varepsilon \) . Our oracle is based only on the sparsity of the network, along with two quite natural assumptions about travel-time functions which allow the smooth transition towards asymmetric and time-dependent distance metrics.

Description: A new data structure for efficient similarity search in very large datasets of high-dimensional vectors is introduced. This structure called the inverted multi-index generalizes the inverted index idea by replacing the standard quantization within inverted indices with product quantization. For very similar retrieval complexity and pre-processing time, inverted multi-indices achieve a much denser subdivision of the search space compared to inverted indices, while retaining their memory efficiency. Our experiments with large datasets of SIFT and GIST vectors demonstrate that because of the denser subdivision, inverted multi-indices are able to return much shorter candidate lists with higher recall. Augmented with a suitable reranking procedure, multi-indices were able to significantly improve the speed of approximate nearest neighbor search on the dataset of 1 billion SIFT vectors compared to the best previously published systems, while achieving better recall and incurring only few percent of memory overhead.

Description: While 3D object-centered shape-based models are appealing in comparison with 2D viewer-centered appearance-based models for their lower model complexities and potentially better view generalizabilities, the learning and inference of 3D models has been much less studied in the recent literature due to two factors: i) the enormous complexities of 3D shapes in geometric space; and ii) the gap between 3D shapes and their appearances in images. This paper aims at tackling the two problems by studying an And-Or Tree (AoT) representation that consists of two parts: i) a geometry-AoT quantizing the geometry space, i.e. the possible compositions of 3D volumetric parts and 2D surfaces within the volumes; and ii) an appearance-AoT quantizing the appearance space, i.e. the appearance variations of those shapes in different views. In this AoT, an And-node decomposes an entity into constituent parts, and an Or-node represents alternative ways of decompositions. Thus it can express a combinatorial number of geometry and appearance configurations through small dictionaries of 3D shape primitives and 2D image primitives. In the quantized space, the problem of learning a 3D object template is transformed to a structure search problem which can be efficiently solved in a dynamic programming algorithm by maximizing the information gain. We focus on learning 3D car templates from the AoT and collect a new car dataset featuring more diverse views. The learned car templates integrate both the shape-based model and the appearance-based model to combine the benefits of both. In experiments, we show three aspects: 1) the AoT is more efficient than the frequently used octree method in space representation; 2) the learned 3D car template matches the state-of-the art performances on car detection and pose estimation in a public multi-view car dataset; and 3) in our new dataset, the learned 3D template solves the joint task of simultaneous object detection, pose/view estimation, and part locali- ation. It can generalize over unseen views and performs better than the version 5 of the DPM model in terms of object detection and semantic part localization.