Neural network model of visual cortex for determining surface curvature from images of shaded surfaces

The visual system can extract information about shape from the pattern of light and dark surface shading on an object. Very little is known about how this is accomplished. We have used a learning algorithm to construct a neural network model that computes the principal curvatures and orientation of elliptic paraboloids independently of the illumination direction. Our chief finding is that receptive fields developed by units of such model network are surprisingly similar to some found in the visual cortex. It appears that neurons that can make use of the continuous gradations of shading have receptive fields similar to those previously interpreted as dealing with contours (i. e. ‘bar’ detectors or ‘edge’ detectors). This study illustrates the difficulty of deducing neuronal function within a network solely from receptive fields. It is also important to consider the pattern of connections a neuron makes with subsequent stages, which we call the ‘projective field’.

[1]  D. Hubel,et al.  Receptive fields, binocular interaction and functional architecture in the cat's visual cortex , 1962, The Journal of physiology.

[2]  D H HUBEL,et al.  RECEPTIVE FIELDS AND FUNCTIONAL ARCHITECTURE IN TWO NONSTRIATE VISUAL AREAS (18 AND 19) OF THE CAT. , 1965, Journal of neurophysiology.

[3]  R. Gregory.  The intelligent eye , 1970 .

[4]  A. Sillito.  The contribution of inhibitory mechanisms to the receptive field properties of neurones in the striate cortex of the cat. , 1975, The Journal of physiology.

[5]  M. Kimura,et al.  Convergence of retinal inputs onto visual cortical cells: II. A study of the cells disynaptically excited from the lateral geniculate body , 1977, Brain Research.

[6]  K. Maekawa,et al.  Convergence of retinal inputs onto visual cortical cells: I. A study of the cells monosynaptically excited from the lateral geniculate body , 1977, Brain Research.

[7]  Mike Brady.  Inferring the Direction of the Sun from Intensity Values on a Generalised Cone , 1979, IJCAI.

[8]  T. Wiesel,et al.  Morphology and intracortical projections of functionally characterised neurones in the cat visual cortex , 1979, Nature.

[9]  E. Yund,et al.  Responses of striate cortex cells to grating and checkerboard patterns. , 1979, The Journal of physiology.

[10]  D. Pollen,et al.  Relationship between spatial frequency selectivity and receptive field profile of simple cells. , 1979, The Journal of physiology.

[11]  J. Koenderink,et al.  Photometric Invariants Related to Solid Shape , 1980 .

[12]  Katsushi Ikeuchi,et al.  Numerical Shape from Shading and Occluding Boundaries , 1981, Artif. Intell..

[13]  B. Boycott,et al.  Morphology and mosaic of on- and off-beta cells in the cat retina and some functional considerations , 1981, Proceedings of the Royal Society of London. Series B. Biological Sciences.

[14]  C. Gilbert.  Microcircuitry of the visual cortex. , 1983, Annual review of neuroscience.

[15]  Richard S. Sutton,et al.  Neuronlike adaptive elements that can solve difficult learning control problems , 1983, IEEE Transactions on Systems, Man, and Cybernetics.

[16]  E. Mingolla,et al.  Perception of surface curvature and direction of illumination from patterns of shading. , 1983, Journal of experimental psychology. Human perception and performance.

[17]  Jonathan Stone,et al.  Parallel Processing in the Visual System , 1983, Perspectives in Vision Research.

[18]  Alex Pentland,et al.  Local Shading Analysis , 1984, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[19]  T. Poggio,et al.  Biophysics of Computation: Neurons, Synapses and Membranes , 1984 .

[20]  C. B. Wilson,et al.  The mathematical description of shape and form , 1984 .

[21]  Geoffrey E. Hinton,et al.  Learning internal representations by error propagation , 1986 .

[22]  A. P. Georgopoulos,et al.  Neuronal population coding of movement direction. , 1986, Science.

[23]  R Linsker,et al.  From basic network principles to neural architecture: emergence of spatial-opponent cells. , 1986, Proceedings of the National Academy of Sciences of the United States of America.

[24]  James L. McClelland,et al.  Parallel distributed processing: explorations in the microstructure of cognition, vol. 1: foundations , 1986 .

[25]  Paul J. Werbos,et al.  Building and Understanding Adaptive Systems: A Statistical/Numerical Approach to Factory Automation and Brain Research , 1987, IEEE Transactions on Systems, Man, and Cybernetics.

[26]  Pineda,et al.  Generalization of back-propagation to recurrent neural networks. , 1987, Physical review letters.

[27]  S. Zucker,et al.  Endstopped neurons in the visual cortex as a substrate for calculating curvature , 1987, Nature.

[28]  Teuvo Kohonen,et al.  Self-Organization and Associative Memory , 1988 .

[29]  Terrence J. Sejnowski,et al.  Network model of shape-from-shading: neural function arises from both receptive and projective fields , 1988, Nature.

[30]  H H Bülthoff,et al.  Integration of depth modules: stereo and shading. , 1988, Journal of the Optical Society of America. A, Optics and image science.

[31]  V S Ramachandran,et al.  Perceiving shape from shading. , 1988, Scientific American.

[32]  V. S. Ramachandran,et al.  Perception of shape from shading , 1988, Nature.

[33]  D. Sparks,et al.  Population coding of saccadic eye movements by neurons in the superior colliculus , 1988, Nature.

[34]  Richard A. Andersen,et al.  A back-propagation programmed network that simulates response properties of a subset of posterior parietal neurons , 1988, Nature.

[35]  Christof Koch,et al.  Modeling the mammalian visual system , 1989 .

[36]  Y. J. Tejwani,et al.  Robot vision , 1989, IEEE International Symposium on Circuits and Systems,.

[37]  Geoffrey E. Hinton.  Connectionist Learning Procedures , 1989, Artif. Intell..

[38]  Geoffrey E. Hinton,et al.  Distributed Representations , 1986, The Philosophy of Artificial Intelligence.