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New Invariant Moments for Non-Uniformly Scaled Images (2000)

Palaniappan, R. ; Raveendran, P. ; Omatu, S.

Springer

Pattern analysis and applications 3 (2000), S. 78-87

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ISSN: 1433-755X

Keywords: Keywords:Neural network; Non-uniform scaling; Principal axis; Regular moments; Rotation; Tilt angle

Source: Springer Online Journal Archives 1860-2000

Topics: Computer Science

Notes: Abstract: The usual regular moment functions are only invariant to image translation, rotation and uniform scaling. These moment invariants are not invariant when an image is scaled non-uniformly in the x- and y-axes directions. This paper addresses this problem by presenting a new technique to obtain moments that are invariant to non-uniform scaling. However, this technique produces a set of features that are only invariant to translation and uniform/non-uniform scaling. To obtain invariance to rotation, moments are calculated with respect to the x-y-axis of the image. To perform this, a neural network is used to estimate the angle of rotation from the x-y-axis and the image is unrotated to the x-y-axis. Consequently, we are able to obtain features that are invariant to translation, rotation and uniform/non-uniform scaling. The mathematical background behind the development and invariance of the new moments are presented. The results of experimental studies using English alphabets and Arabic numerals scaled uniformly/non-uniformly, rotated and translated are discussed to further verify the validity of the new moments.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/s100440070014

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Existence and comparison theorems for partial differential equations of Riccati type (1982)

Omatu, S. ; Seinfeld, J. H.

Springer

Journal of optimization theory and applications 36 (1982), S. 263-276

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ISSN: 1573-2878

Keywords: Partial differential equations ; Riccati equations ; successive approximation technique ; comparison theorems ; existence and uniqueness theorems ; optimal sensor location ; fundamental solution

Source: Springer Online Journal Archives 1860-2000

Topics: Mathematics

Notes: Abstract In this paper, we discuss the partial differential equation of Riccati type that describes the optimal filtering error covariance function for a linear distributed-parameter system with pointwise observations. Since this equation contains the Dirac delta function, it is impossible to apply directly the usual methods of functional analysis to prove existence and uniqueness of a bounded solution. By using properties of the fundamental solution and the classical technique of successive approximation, we prove the existence and uniqueness theorem. We then prove the comparison theorem for partial differential equations of Riccati type. Finally, we consider some applications of these theorems to the distributed-parameter optimal sensor location problem.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/BF00933833

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Efficient Genetic Algorithms Using Simple Genes Exchange Local Search Policy for the Quadratic Assignment Problem (2000)

Lim, M.H. ; Yuan, Y. ; Omatu, S.

Springer

Computational optimization and applications 15 (2000), S. 249-268

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ISSN: 1573-2894

Keywords: quadratic assignment ; combinatorial optimization ; genetic algorithm ; local search ; k-gene exchange

Source: Springer Online Journal Archives 1860-2000

Topics: Computer Science

Notes: Abstract In this paper, we describe an approach for solving the quadratic assignment problem (QAP) that is based on genetic algorithms (GA). It will be shown that a standard canonical GA (SGA), which involves genetic operators of selection, reproduction, crossover, and mutation, tends to fall short of the desired performance expected of a search algorithm. The performance deteriorates significantly as the size of the problem increases. To address this syndrome, it is common for GA-based techniques to be embedded with deterministic local search procedures. It is proposed that the local search should involve simple procedure of genome reordering that should not be too complex. More importantly, from a computational point of view, the local search should not carry with it the full cost of evaluating a chromosome after each move in the localized landscape. Results of simulation on several difficult QAP benchmarks showed the effectiveness of our approaches.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1023/A:1008743718053

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