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  • 1
    Electronic Resource
    Electronic Resource
    Opponent color coding: A mechanistic model and a new metric for color space (1972)
    Springer
    Biological cybernetics 10 (1972), S. 78-98 
    Details
    ISSN: 1432-0770
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Computer Science , Physics
    Notes: Abstract A mechanistic model of opponent color coding in the human retina is described. This description is based on the concept of the scaling-ensemble (Koenderink et al., 1971). All receptors that are a member of the same scaling-ensemble adapt together, regardless of their type. If the adaptation is the Weber-type adaptation, then it is shown that the sum of the outputs of receptors of an ensemble displays typical on-cell characteristics. In contradistinction with the phasic response of the sum signal, difference signals are of a typical tonic type. With three kinds of cones, one can essentially form two opponent signals and one non-opponent signal. The responses of the opponent and the non-opponent channels to spatiotemporal modulations of the input signal are entirely different. In this model the interaction betweenthe opponent and the non-opponent channels is such that even large intensity modulations do not disturb the opponent responses very much. The opponent signals carry almost entirely information about the spectral distribution of the input signal. The results of computer simulation studies of the proposed model are compared to electrophysiologically determined responses of cells in the monkeys lateral geniculate body. In the second part of this paper we make use of the line element approach in order to be able to confront the model's predictions with psychophysical measurements. This line element is closely related to those proposed earlier by Helmholtz (1896) and Schrödinger (1920). It introduces a hyperbolic geometry in perceptual color space. This specific metric leads to the vector model for brightness addition. In addition it is possible to regard the Bezold-Brücke hue shift as the direct result of the curvature of color space, induced by our metric.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00292233
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  • 2
    Electronic Resource
    Electronic Resource
    Geometry of binocular vision and a model for stereopsis (1976)
    Springer
    Biological cybernetics 21 (1976), S. 29-35 
    Details
    ISSN: 1432-0770
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Computer Science , Physics
    Notes: Abstract If a binocular observer looks at surfaces, the disparity is a continuous vector field defined on the manifold of cyclopean visual directions. We derive this field for the general case that the observer is presented with a curved surface and fixates an arbitrary point. We expand the disparity field in the neighbourhood of a visual direction. The first order approximation can be decomposed into congruences, similarities and deformations. The deformation component is described by the traceless part of the symmetric part of the gradient of the disparity. The deformation component carries all information concerning the slant of a surface element that is contained in the disparity field itself; it is invariant for changes of fixation, differential cyclotorsion and uniform aniseikonia. The deformation component can be found from a comparison of the orientation of surface details in the left and right retinal images. The theory provides a geometric explanation of the percepts obtained with uniform and oblique meridional aniseikonia. We utilize the geometric theory to construct a mechanistic model of stereopsis that obviates the need for internal zooming mechanisms, but nevertheless is insensitive to differential cyclotorsion or uniform aniseikonia.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00326670
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  • 3
    Electronic Resource
    Electronic Resource
    Event train decoders with many inputs, pulse density versus momentaneous frequency (1973)
    Springer
    Biological cybernetics 13 (1973), S. 215-222 
    Details
    ISSN: 1432-0770
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Computer Science , Physics
    Notes: Abstract An analysis is made of the transformations a graded signal undergoes if it is first encoded as a train of identical impulses, and subsequently decoded into a graded signal again. The case treated is that of a sinusoidally modulated input signal. As a paradigm for the encoding stage we employ the I.P.F.M. (Integral Pulse Frequency Modulator). An exact solution for the times of occurrence of output impulses is offered. This solution permits us to treat some curious beat phenomena that are found if an I.P.F.M. is excited with a frequency that is in a nearly rational ratio to the steady state output frequency of the I.P.F.M. It is shown that an I.P.F.M. is a phase sensitive device. In order to avoid a phase sensitivity of the complete signal transmission link, we consider a group of encoders feeding their signals into the decoding stage. For such a group it is meaningful to talk about the momentaneous interpulse interval. We derive the interval histogram and the spectral decomposition of this momentaneous interval. It is shown that the spectrum is very different from the spectrum derived by Bayly (1968) of the output signal of a single I.P.F.M. Two extreme types of decoding mechanisms lead to different transfer functions for the complete signal transmission link, both of which are shown to be of some neurophysiological relevance.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00274886
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  • 4
    Electronic Resource
    Electronic Resource
    The internal representation of solid shape with respect to vision (1979)
    Springer
    Biological cybernetics 32 (1979), S. 211-216 
    Details
    ISSN: 1432-0770
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Computer Science , Physics
    Notes: Abstract It is argued that the internal model of any object must take the form of a function, such that for any intended action the resulting reafference is predictable. This function can be derived explicitly for the case of visual perception of rigid bodies by ambulant observers. The function depends on physical causation, not physiology; consequently, one can make a priori statements about possible internal models. A posteriori it seems likely that the orientation sensitive units described by Hubel and Wiesel constitute a physiological substrate subserving the extraction of the invariants of this function. The function is used to define a measure for the visual complexity of solid shape. Relations with Gestalt theories of perception are discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00337644
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  • 5
    Electronic Resource
    Electronic Resource
    The construction of a simultaneous functional order in nervous systems (1987)
    Springer
    Biological cybernetics 57 (1987), S. 331-340 
    Details
    ISSN: 1432-0770
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Computer Science , Physics
    Notes: Abstract In a previous paper (Part I) we introduced a model that constructs a simultaneous functional order in a set of neuronal elements by monitoring the coincidences in their signal activities (the so-called coincidence-model). The simultaneous signal activity in a neural net will be constrained both by its physical restrictions and by environmental constraints. In this paper we present the results of simulation experiments that were performed to study the influence of environmental constraits on the resulting functional order in a set of neural elements corresponding to a onedimensional detector array. We show that the coincidence-model produces a functional order that encodes the physical constraints of the environment. Moreover, we demonstrate that the signal activity in the neural net (the “perceptions”) can be related to events in the outer world. We provide some examples to demonstrate that our model may prove useful to gain insight into certain developmental disorders.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00338825
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  • 6
    Electronic Resource
    Electronic Resource
    Receptive field families (1990)
    Springer
    Biological cybernetics 63 (1990), S. 291-297 
    Details
    ISSN: 1432-0770
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Computer Science , Physics
    Notes: Abstract It is generally agreed upon that size invariance and the absence of spurious resolution are two requirements that characterize well behaved spatial samping in visual systems. We show that these properties taken together constrain the structure of receptive fields to a very large degree. Only those field structures that arise as solutions of a certain linear partial differential equation of the second order prove to satisfy these general constraints. The equation admits of complete, orthonormal families of solutions. These families have to be regarded as the possible receptive field families subject to certain symmetry conditions. They can be transformed into each other via unitary transformations. Thus a single representation suffices to construct all the others. This theory permits us to classify the possible linear receptive field structures exhaustively, and to define their internal and external interrelations. This induces a principled taxonomy of linear receptive fields.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00203452
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  • 7
    Electronic Resource
    Electronic Resource
    Extraction of motion parallax structure in the visual system I (1990)
    Springer
    Biological cybernetics 63 (1990), S. 185-191 
    Details
    ISSN: 1432-0770
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Computer Science , Physics
    Notes: Abstract We present a paradigm to estimate local affine motion parallax structure from a varying image irradiance pattern. The method is based on a matching of jets of irradiance rather than the local image irradiance pattern or features of it. It does not put any constraints on the structure of the image irradiance pattern. Moreover, the aperture problem does not arise and additional ad hoc constraints on the velocity field like the “smoothness constraint” are superfluous. An implementation is designed such that the affine structure of the local motion parallax field is represented through simple combinations of the outputs of physiologically plausible receptive fields and their temporal derivatives.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00195857
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  • 8
    Electronic Resource
    Electronic Resource
    Extraction of motion parallax structure in the visual system II (1990)
    Springer
    Biological cybernetics 63 (1990), S. 193-199 
    Details
    ISSN: 1432-0770
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Computer Science , Physics
    Notes: Abstract We have developed an algorithm to extract local affine motion parallax structure of a varying image irradiance pattern in Part I. In Part II, we present computational results of this algorithm for situations in which the information about the affine structure is contained in only two successive images. This applies to a large class of problems (e.g. two-image motion sequences and stereoscopic vision). The results show the effects of spatio-temporal discretisation and internal noise on the performance of this algorithm.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00195858
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  • 9
    Electronic Resource
    Electronic Resource
    The singularities of the visual mapping (1976)
    Springer
    Biological cybernetics 24 (1976), S. 51-59 
    Details
    ISSN: 1432-0770
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Computer Science , Physics
    Notes: Abstract In this article we treat purely metrical properties of the visual image, e.g. the time changes of the relative positions and orientations of image details. Self-induced movements of an observer relative to rigid bodies in his environment generate charactertistic motion parallax fields. The observer may regard those fields as proprioceptive and interprete the geometrical invariants of the fields as indicators of solid shape. In this way his perceptions become object-oriented, which is the normal case as the many constancy-phenomena show. Similar arguments apply to the disparity field of binocular vision. In this paper we treat the qualitative nature of such fields. [In this case the qualitative nature is basic. Compare the case of an equation with a single unknown. Often one is interested primarily in the qualitative solution (are there roots? How many?), and only slightly in the quantitative information (the numerical value of a root).] The qualitative nature of the fields is fixed if their singularities are known. It is shown that the singularities are of two types: isolated points (so-called specular points) and line-singularities (so-called folds, cusps and T-junctions). It is shown that for most vantage points that an observer can occupy, the topological structure of the set of singularities does not change if the observer performs small exploratory movements. That is most vantage points are stable. At an unstable vantage point the set of singularities changes and the observer experiences an event. Because certain properties of the set of singularities are shown to be preserved, only a few simple types of event are possible. A complete list is presented. The occurrence of an event is shown to be simply related to the solid shape of the objects of vision. Our geometrical theory enables us to understand the structure of the observer's internal models of external bodies.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00365595
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  • 10
    Electronic Resource
    Electronic Resource
    Scale-time (1988)
    Springer
    Biological cybernetics 58 (1988), S. 159-162 
    Details
    ISSN: 1432-0770
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Computer Science , Physics
    Notes: Abstract A conceptually simple and logically consistent version of “scale-space” for the temporal domain is proposed. The method does not violate temporal causality, yet conserves causality in the resolution domain at any given moment in time. The filter kernels are not Gaussians (that would certainly lead to a violation of temporal causality) but are related to the Gaussians via a simple transformation of the time axis. They depend on a pair of parameters, one that has the character of a temporal delay and one that specifies the temporal resolution. In the limit for long delays (but fixed resolution) these kernels asymptotically approach the Gaussian again. Extensions of the theory towards a scale space-time are discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00364135
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