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  • 1
    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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  • 2
    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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  • 3
    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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  • 4
    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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  • 5
    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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  • 6
    Electronic Resource
    Electronic Resource
    Dynamic shape (1986)
    Springer
    Biological cybernetics 53 (1986), S. 383-396 
    Details
    ISSN: 1432-0770
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Computer Science , Physics
    Notes: Abstract Many useful notions of partial order and/or similarity and relatedness of different geometrical features of smooth shapes that occur in psychologically valid descriptions of shape have no equivalents in the usual geometrical shape theories. This is especially true where similarities are noted between objects of different connectivity: in almost all of the present theories the topological type generates the primary categorization. It is argued that such relations find a logical place only in shape theories that involve morphogenesis. Any object can be embedded uniquely in a morphogenetic sequence if one takes resolution as the parameter of the sequence. A theory of measurement is presented that allows one to define surfaces and (boundary-) curves on multiple levels of resolution. The embedding is essentially unique and is generated via a partial differential equation that governs the evolution. A canonical projection connects any high resolution specimen to lower resolution versions. The bifurcation set of the projection generates natural part boundaries. Singularities of the evolution are completely characterized as emergence, accretion and versification processes (involving topological change) and singularities by which inflections (inflection points for curves, parabolic curves for surfaces) are generated. The latter singularities involve a single process for the generation of inflections and three other processes by which the existing inflection structure may be changed. Relations with existing theories in vogue in robotics and AI, as well as in psychophysics are discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00318204
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  • 7
    Electronic Resource
    Electronic Resource
    Representation of local geometry in the visual system (1987)
    Springer
    Biological cybernetics 55 (1987), S. 367-375 
    Details
    ISSN: 1432-0770
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Computer Science , Physics
    Notes: Abstract It is shown that a convolution with certain reasonable receptive field (RF) profiles yields the exact partial derivatives of the retinal illuminance blurred to a specified degree. Arbitrary concatenations of such RF profiles yield again similar ones of higher order and for a greater degree of blurring. By replacing the illuminance with its third order jet extension we obtain position dependent geometries. It is shown how such a representation can function as the substrate for “point processors” computing geometrical features such as edge curvature. We obtain a clear dichotomy between local and multilocal visual routines. The terms of the truncated Taylor series representing the jets are partial derivatives whose corresponding RF profiles closely mimic the well known units in the primary visual cortex. Hence this description provides a novel means to understand and classify these units. Taking the receptive field outputs as the basic input data one may devise visual routines that compute geometric features on the basis of standard differential geometry exploiting the equivalence with the local jets (partial derivatives with respect to the space coordinates).
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00318371
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  • 8
    Electronic Resource
    Electronic Resource
    A directionally sensitive network (1976)
    Springer
    Biological cybernetics 21 (1976), S. 161-170 
    Details
    ISSN: 1432-0770
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Computer Science , Physics
    Notes: Abstract A network is discussed that is selectively sensitive to the direction of moving patterns. The network is studied by means of computer simulation. It is shown that the network can be used as a paradigm for information processing at ganglion cell level in the retina of certain mammals. The responses of the network are in good qualitative agreement with results obtained by Michael (1968) on the ground squirrel. The connectivity of the network conforms to known retinal structure. The directionally sensitive property of the network is the result of the connectivity of the “inner plexiform layer”. Retinal cells distal to the ganglion cells are not committed to any directional sensitivity.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00337423
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  • 9
    Electronic Resource
    Electronic Resource
    Visibility of movement gradients (1982)
    Springer
    Biological cybernetics 44 (1982), S. 167-175 
    Details
    ISSN: 1432-0770
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Computer Science , Physics
    Notes: Abstract We report on the sensitivity of human observers with respect to the detection of transients in otherwise uniformly moving two-dimensional random-dot patterns. The target field is divided into two halfs that each contains a moving random-dot pattern. The patterns in the two halffields are mutually uncorrelated. Parameters are the average velocity and the difference-velocity for the two halfs. These velocities are both vectors that can be varied in magnitude and in their direction with respect to the border of the two halffields. In order to quantify the sensitivity of the visual system to such patterns, we added (linear addition) spatio-temporal white noise (“snow”) to the pattern. Then the sensitivity is quantified by way of the threshold signal-to-noise ratio necessary to discriminate the composite pattern from a single smoothly uniformly moving pattern. The signal-to-noise ratio specifies the square of the ratio between the signal r.m.s. contrast and the r.m.s. contrast of the masking stimulus (spatio-temporal white noise or “snow”). The r.m.s. contrast of the complex pattern (signal and noise) is kept invariant. We find that the detection performance is independent of the direction of either the average or difference-velocity with respect to the border, and can be completely described in terms of a minimum requirement for the magnitude of the difference-velocity. The magnitude of the difference-velocity must exceed the magnitude of the average velocity in order to lead to a perceivable transient. In his formulation the Weberlaw for the detection of velocity transients in uniformly moving noise patterns is applicable to both differences in magnitude and direction of the velocities.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00344272
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  • 10
    Electronic Resource
    Electronic Resource
    The influence of the retinal inhomogeneity on the perception of spatial patterns (1972)
    Springer
    Biological cybernetics 10 (1972), S. 223-230 
    Details
    ISSN: 1432-0770
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Computer Science , Physics
    Notes: Abstract From the fact that the retina is rather inhomogeneous, it can be inferred that the perception of spatial patterns of appreciable extent will be dependent on the retinal location. Anatomical, electrophysiological and psychophysical findings substantiate the claim that the retina is very inhomogeneous of composition. In order to investigate the influence of this inhomogeneity on the perception of patterns, a model of spatiotemporal signal processing in the retina was developed on the basis of a paradigm for the Weber type adaptation. Such “scaling-ensembles” proved successful in the prediction of spatiotemporal modulation transfer in the human fovea (Koenderink et al., 1971). One prediction of the present model is that certain spatial patterns are optimally detected at well defined retinal locations, dependent on the spatial frequency content of the stimulus. A confrontation of the model's predictions with measurements published by Bryngdahl (1966) enabled us to estimate some of the relevant parameters of the retinal receptive fields as a function of the eccentricity. We obtained estimates that compare reasonably well with previously known values; for instance with values of acuity and anatomical measurements. The present discussion bears relevance on the question of whether the retina is composed of independently tuned spatial frequency filters at any retinal location, or whether the tuning is with respect to the eccentricity.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00288741
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