Hugh R. Wilson

Bio: Hugh R. Wilson is an academic researcher from York University. The author has contributed to research in topics: Spatial frequency & Face perception. The author has an hindex of 61, co-authored 199 publications receiving 17108 citations. Previous affiliations of Hugh R. Wilson include Keele University & University of Chicago.

A Mathematical Theory of the Functional Dynamics of Cortical and Thalamic Nervous Tissue

Abstract: It is proposed that distinct anatomical regions of cerebral cortex and of thalamic nuclei are functionally two-dimensional. On this view, the third (radial) dimension of cortical and thalamic structures is associated with a redundancy of circuits and functions so that reliable signal processing obtains in the presence of noisy or ambiguous stimuli. A mathematical model of simple cortical and thalamic nervous tissue is consequently developed, comprising two types of neurons (excitatory and inhibitory), homogeneously distributed in planar sheets, and interacting by way of recurrent lateral connexions. Following a discussion of certain anatomical and physiological restrictions on such interactions, numerical solutions of the relevant non-linear integro-differential equations are obtained. The results fall conveniently into three categories, each of which is postulated to correspond to a distinct type of tissue: sensory neo-cortex, archior prefrontal cortex, and thalamus. The different categories of solution are referred to as dynamical modes. The mode appropriate to thalamus involves a variety of non-linear oscillatory phenomena. That appropriate to archior prefrontal cortex is defined by the existence of spatially inhomogeneous stable steady states which retain contour information about prior stimuli. Finally, the mode appropriate to sensory neo-cortex involves active transient responses. It is shown that this particular mode reproduces some of the phenomenology of visual psychophysics, including spatial modulation transfer function determinations, certain metacontrast effects, and the spatial hysteresis phenomenon found in stereopsis.

A psychophysically motivated model for two-dimensional motion perception.

Abstract: A quantitative model is developed to predict the perceived direction of moving two-dimensional patterns. The model incorporates both a simple motion energy pathway and a “texture boundary motion” pathway that incorporates response squaring before the extraction of motion energy. These pathways correspond to Fourier and non-Fourier motion pathways and are hypothesized to reflect processing in the VI-MT and V1-V2-MT pathway, respectively. A cosine-weighted sum of these pathways followed by competitive feedback inhibition accurately predicts the perceived direction for patterns composed of two cosine gratings at different orientations (“plaids”). The model also predicts direction discrimination, differences between foveal and peripheral viewing, changes in perceived direction with exposure duration, motion masking, and motion transparency.

Self-organized formation of topologically correct feature maps

Abstract: This work contains a theoretical study and computer simulations of a new self-organizing process. The principal discovery is that in a simple network of adaptive physical elements which receives signals from a primary event space, the signal representations are automatically mapped onto a set of output responses in such a way that the responses acquire the same topological order as that of the primary events. In other words, a principle has been discovered which facilitates the automatic formation of topologically correct maps of features of observable events. The basic self-organizing system is a one- or two-dimensional array of processing units resembling a network of threshold-logic units, and characterized by short-range lateral feedback between neighbouring units. Several types of computer simulations are used to demonstrate the ordering process as well as the conditions under which it fails.

Theory of Edge Detection

Abstract: A theory of edge detection is presented. The analysis proceeds in two parts. (1) Intensity changes, which occur in a natural image over a wide range of scales, are detected separately at different scales. An appropriate filter for this purpose at a given scale is found to be the second derivative of a Gaussian, and it is shown that, provided some simple conditions are satisfied, these primary filters need not be orientation-dependent. Thus, intensity changes at a given scale are best detected by finding the zero values of delta 2G(x,y)*I(x,y) for image I, where G(x,y) is a two-dimensional Gaussian distribution and delta 2 is the Laplacian. The intensity changes thus discovered in each of the channels are then represented by oriented primitives called zero-crossing segments, and evidence is given that this representation is complete. (2) Intensity changes in images arise from surface discontinuities or from reflectance or illumination boundaries, and these all have the property that they are spatially. Because of this, the zero-crossing segments from the different channels are not independent, and rules are deduced for combining them into a description of the image. This description is called the raw primal sketch. The theory explains several basic psychophysical findings, and the operation of forming oriented zero-crossing segments from the output of centre-surround delta 2G filters acting on the image forms the basis for a physiological model of simple cells (see Marr & Ullman 1979).

Shifts in selective visual attention: towards the underlying neural circuitry.

Abstract: Psychophysical and physiological evidence indicates that the visual system of primates and humans has evolved a specialized processing focus moving across the visual scene. This study addresses the question of how simple networks of neuron-like elements can account for a variety of phenomena associated with this shift of selective visual attention. Specifically, we propose the following: (1) A number of elementary features, such as color, orientation, direction of movement, disparity etc. are represented in parallel in different topographical maps, called the early representation. (2) There exists a selective mapping from the early topographic representation into a more central non-topographic representation, such that at any instant the central representation contains the properties of only a single location in the visual scene, the selected location. We suggest that this mapping is the principal expression of early selective visual attention. One function of selective attention is to fuse information from different maps into one coherent whole. (3) Certain selection rules determine which locations will be mapped into the central representation. The major rule, using the conspicuity of locations in the early representation, is implemented using a so-called Winner-Take-All network. Inhibiting the selected location in this network causes an automatic shift towards the next most conspicious location. Additional rules are proximity and similarity preferences. We discuss how these rules can be implemented in neuron-like networks and suggest a possible role for the extensive back-projection from the visual cortex to the LGN.

Dynamical Systems in Neuroscience

Abstract: This book explains the relationship of electrophysiology, nonlinear dynamics, and the computational properties of neurons, with each concept presented in terms of both neuroscience and mathematics and illustrated using geometrical intuition In order to model neuronal behavior or to interpret the results of modeling studies, neuroscientists must call upon methods of nonlinear dynamics This book offers an introduction to nonlinear dynamical systems theory for researchers and graduate students in neuroscience It also provides an overview of neuroscience for mathematicians who want to learn the basic facts of electrophysiology "Dynamical Systems in Neuroscience" presents a systematic study of the relationship of electrophysiology, nonlinear dynamics, and computational properties of neurons It emphasizes that information processing in the brain depends not only on the electrophysiological properties of neurons but also on their dynamical properties The book introduces dynamical systems starting with one- and two-dimensional Hodgkin-Huxley-type models and continuing to a description of bursting systems Each chapter proceeds from the simple to the complex, and provides sample problems at the end The book explains all necessary mathematical concepts using geometrical intuition; it includes many figures and few equations, making it especially suitable for non-mathematicians Each concept is presented in terms of both neuroscience and mathematics, providing a link between the two disciplines Nonlinear dynamical systems theory is at the core of computational neuroscience research, but it is not a standard part of the graduate neuroscience curriculum - or taught by math or physics department in a way that is suitable for students of biology This book offers neuroscience students and researchers a comprehensive account of concepts and methods increasingly used in computational neuroscience

Spatiotemporal energy models for the perception of motion

Abstract: A motion sequence may be represented as a single pattern in x–y–t space; a velocity of motion corresponds to a three-dimensional orientation in this space. Motion sinformation can be extracted by a system that responds to the oriented spatiotemporal energy. We discuss a class of models for human motion mechanisms in which the first stage consists of linear filters that are oriented in space-time and tuned in spatial frequency. The outputs of quadrature pairs of such filters are squared and summed to give a measure of motion energy. These responses are then fed into an opponent stage. Energy models can be built from elements that are consistent with known physiology and psychophysics, and they permit a qualitative understanding of a variety of motion phenomena.