this article we investigate to what extent the statistical properties of natural images can be used to understand the variation of receptive field properties of simple cells in the mammalian primary visual cortex. The receptive fields of simple cells have been studied extensively (e.g., Hubel & Wiesel 1968, DeValois et al. 1982a, DeAngelis et al. 1993): they are localised in space and time, have band-pass characteristics in the spatial and temporal frequency domains, are oriented, and are often sensitive to the direction of motion of a stimulus. Here we will concentrate on the spatial properties of simple cells. Several hypotheses as to the function of these cells have been proposed. As the cells preferentially respond to oriented edges or lines, they can be viewed as edge or line detectors. Their joint localisation in both the spatial domain and the spatial frequency domain has led to the suggestion that they mimic Gabor filters, minimising uncertainty in both domains (Daugman 1980, Marcelja 1980). More recently, the match between the operations performed by simple cells and the wavelet transform has attracted attention (e.g., Field 1993). The approaches based on Gabor filters and wavelets basically consider processing by the visual cortex as a general image processing strategy, relatively independent of detailed assumptions about image statistics. On the other hand, the edge and line detector hypothesis is based on the intuitive notion that edges and lines are both abundant and important in images. This theme of relating simple cell properties with the statistics of natural images was explored extensively by Field (1987, 1994). He proposed that the cells are optimized specifically for coding natural images. He argued that one possibility for such a code, sparse coding...

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Natural images contain characteristic statistical regularities that set them apart from purely random images. Understanding what these regularities are can enable natural images to be coded more efficiently. In this paper, we describe some of the forms of structure that are contained in natural images, and we show how these are related to the response properties of neurons at early stages of the visual system. Many of the important forms of structure require higher-order (i.e. more than linear, pairwise) statistics to characterize, which makes models based on linear Hebbian learning, or principal components analysis, inappropriate for finding efficient codes for natural images. We suggest that a good objective for an efficient coding of natural scenes is to maximize the sparseness of the representation, and we show that a network that learns sparse codes of natural scenes succeeds in developing localized, oriented, bandpass receptive fields similar to those in the mammalian striate cortex.

Abstract—Receptive � elds of simple cells in the primate visual cortex were well � t in the space and time domains by the Gaussian Derivative (GD) model for spatio-temporal vision. All 23 � elds in the data sample could be � t by one equation, varying only a single shape number and nine geometric transformation parameters. A difference-of-offset-Gaussians (DOOG) mechanism for the GD model also � t the data well. Other models tested did not � t the data as well as or as succinctly, or failed to converge on a unique solution, indicatingover-parameterization.An ef � cient computationalalgorithm was found for the GD model which produced robust estimates of the direction and speed of moving objects in real scenes. 1.

This thesis focuses on the statistics of natural images. The first question that is to be answered is: what are natural images and why do we study them. We start with our definition, and then discuss the properties and uses of natural images. An image is a projection of an environment, and natural images are those that are taken from a natural environment, i.e., an environment that is commonly encountered by a particular organism. This means that these images represent the natural visual input (natural stimulus) of an eye. In general, images may include optical information extending over space, time (time-varying images), as well as wavelength (colour images). In this thesis, however, we restrict ourselves to images of light intensity (black and white images) that either extend exclusively over space (still images) or exclusively over time (time series). The motivation for investigating natural images is to gain a better understanding of neural processing in visual systems. Natural images and visual processing in biological systems are linked by the hypothesis that evolution has optimised visual systems to process natural stimuli. The analysis of the optimal performance of biological visual systems may inspire the building of artificial visual systems.

A neural model is presented of how cortical areas V1, V2, and V4 interact to convert a textured 2D image into a representation of curved 3D shape. Two basic problems are solved to achieve this: (1) Patterns of spatially discrete 2D texture elements are transformed into a spatially smooth surface representation of 3D shape. (2) Changes in the statistical properties of texture elements across space induce the perceived 3D shape of this surface representation. This is achieved in the model through multiple-scale filtering of a 2D image, followed by a cooperative-competitive grouping network that coherently binds texture elements into boundary webs at the appropriate depths using a scale-to-depth map and a subsequent depth competition stage. These boundary webs then gate filling-in of surface lightness signals in order to form a smooth 3D surface percept. The model quantitatively simulates challenging psychophysical data about perception of prolate ellipsoids [Todd, J., & Akerstrom, R. (1987). Perception of three-dimensional form from patterns of optical texture. Journal of Experimental Psychology: Human Perception and Performance, 13(2), 242–255]. In particular, the model represents a high degree of 3D curvature for a certain class of images, all of whose texture elements have the same degree of optical compression, in accordance with percepts of human observers. Simulations of 3D percepts of an elliptical cylinder, a slanted plane, and a photo of a golf ball are also presented.

The selectivities of neurons in primary visual cortex are often considered to be adapted to the statistics of natural images. Accordingly, simple cell-like tuning emerges when unsupervised learning models that seek sparse representations of input probabilities are trained on natural scenes. However, orientation tuning develops before structured vision starts, rendering these previous results moot as models of activity-dependent development. A more stringent examination of such models comes from experiments demonstrating altered neural response properties in goggle-reared kittens. We show that an unsupervised learning model of cortical responsivity accounts well for the dramatic effects of stimulus driven development during goggle-rearing.

Stereoscopic vision is extremely precise in detecting minute differences between adjacent depth planes, but quite imprecise in estimating absolute depth. In this paper, we address the issue of the spatial acuity (and not the stereo acuity) of stereopsis. Static RDS (random dot stereograms) stimuli were used to find the spatial grain in which human stereoscopic vision operates.

The paper discusses the potentialities and feasibility of a vision system to be implemented as a neuromorphic microsystem, thus satisfying the physical and economical constraints of low-end components. The paper presents methods and approaches to the design of micropower collective computational systems based on an appropriate cooperative organization of building blocks. First, to characterize the essence of recurrent lattice networks, a basic cooperative block (the "perceptual engine") is introduced, and its practical realization, performance and limitations are described. Secondly, its application in the hardware implementation of an important class of perceptual problems, such edge detection, texture analysis, stereo disparity estimation, and motion analysis, is considered. 1 Introduction In recent years, many new approaches have been taken to perform tasks based on the responses to visual information. They are motivated by a need to react to visual stimuli in appropriate ways, re...

The contribution of interocular orientation differences to depth perception, at either the neuronal or the psychophysical level, is unclear. To understand the responses of binocular neurons to orientation disparity, we extended the energy model of Ohzawa et al. (1990) to incorporate binocular differences in receptive-field orientation. The responses of the model to grating stimuli with interocular orientation differences were examined, along with the responses to random dot stereograms (RDS) depicting slanted surfaces. The responses to combinations of stimulus orientations in the two eyes were left–right separable, which means there was no consistent response to the binocular orientation difference. All existing neuronal data concerning orientation disparity can be well described by this type of model (even a version with no disparity selectivity). The disparity sensitive model is nonetheless sensitive to changes in RDS slant, although it requires narrow orientation bandwidth to produce substantial modulation. The disparity-insensitive model shows no selectivity to slant in this stimulus. Several modifications to the model were attempted to improve its selectivity for orientation disparity and0or slant. A model built by summing several disparity-sensitive models showed left–right inseparable responses, responding maximally to a consistent orientation difference. Despite this property, the selectivity for slant in RDS stimuli was no better than the simple disparity-selective model. The range of models evaluated here demonstrate that interocular orientation differences are neither necessary nor sufficient for signaling slant. In contrast, within the framework of the energy model, positional disparity sensitivity appears to be both necessary and sufficient.