Advanced perceptual systems are faced with the problem of securing a principled relationship between the world and its internal representation. I propose a unified approach to visual representation, based on Shepard's (1968) notion of second-order isomorphism. According to the proposed theory, a shape is represented internally by the responses of a few tuned modules, each of which is broadly selective for some reference shape, whose similarity to the stimulus it measures. The result is a philosophically appealing, computationally feasible, biologically credible, and formally veridical representation of a distal shape space. This approach supports representation of and discrimination among shapes radically different from the reference ones, while bypassing the need for the computationally problematic decomposition into parts; it also addresses the needs of shape categorization, and can be used to derive a range of models of perceived similarity. Representation is Representation of Sim...

This paper introduces two new coding schemes, the probabilistic reasoning models (PRM) and the enhanced FLD (Fisher linear discrimimant) models (EFM), for indexing and retrieval from large image databases with applications to face recognition. The unifying theme of the new schemes is that of lowering the space dimension ("data compression") subject to increased fitness for the discrimination index.

The problem of dimension reduction is introduced as a way to overcome the curse of the dimensionality when dealing with vector data in high-dimensional spaces and as a modelling tool for such data. It is defined as the search for a low-dimensional manifold that embeds the high-dimensional data. A classification of dimension reduction problems is proposed. A survey of several techniques for dimension reduction is given, including principal component analysis, projection pursuit and projection pursuit regression, principal curves and methods based on topologically continuous maps, such as Kohonen’s maps or the generalised topographic mapping. Neural network implementations for several of these techniques are also reviewed, such as the projection pursuit learning network and the BCM neuron with an objective function. Several appendices complement the mathematical treatment of the main text.

Psychophysical findings accumulated over the past several decades indicate that perceptual tasks such as similarity judgment tend to be performed on a low-dimensional representation of the sensory data. Low dimensionality is especially important for learning, as the number of examples required for attaining a given level of performance grows exponentially with the dimensionality of the underlying representation space. In this chapter, we argue that, whereas many perceptual problems are tractable precisely because their intrinsic dimensionality is low, the raw dimensionality of the sensory data is normally high, and must be reduced by a nontrivial computational process, which, in itself, may involve learning. Following a survey of computational techniques for dimensionality reduction, we show that it is possible to learn a low-dimensional representation that captures the intrinsic low-dimensional nature of certain classes of visual objects, thereby facilitating further learning of tasks...

We introduce in this paper two probabilistic reasoning models (PRM-1 and PRM-2) which combine the Principal Component Analysis (PCA) technique and the Bayes classifier and show their feasibility on the face recognition problem. The conditional probability density function for each class is modeled using the within class scatter and the Maximum A Posteriori (MAP) classification rule is implemented in the reduced PCA subspace. Experiments carried out using 1107 facial images corresponding to 369 subjects (with 169 subjects having duplicate images) from the FERET database show that the PRM approach compares favorably against the two well-known methods for face recognition --- the Eigenfaces and Fisherfaces.

No finite sample is sufficient to determine the density, and therefore the entropy, of a signal directly. Some assumption about either the functional form of the density or about its smoothness is necessary. Both amount to a prior over the space of possible density functions. By far the most common approach is to assume that the density has a parametric form. By contrast we derive a differential learning rule called EMMA that optimizes entropy by way of kernel density estimation. Entropy and its derivative can then be calculated by sampling from this density estimate. The resulting parameter update rule is surprisingly simple and efficient. We will show how EMMA can be used to detect and correct corruption in magnetic resonance images (MRI). This application is beyond the scope of existing parametric entropy models. 1 Introduction Information theory is playing an increasing role in unsupervised learning and visual processing. For example, Linsker has used the concept of information ma...

The formation of ocular dominance and orientation columns in the mammalian visual cortex is briefly reviewed. Correlation-based models for their development are then discussed, beginning with the models of Von der Malsburg. For the case of semi-linear models, model behavior is well understood: correlations determine receptive field structure, intracortical interactions determine projective field structure, and the "knitting together" of the two determines the cortical map. This provides a basis for simple but powerful models of ocular dominance and orientation column formation: ocular dominance columns form through a correlationbased competition between left-eye and right-eye inputs, while orientation columns can form through a competition between ON-center and OFF-center inputs. These models account well for receptive field structure, but are not completely adequate to account for the details of cortical map structure. Alternative approaches to map structure, including the...

. It has been proposed that the receptive fields of neurons in V1 are optimised to generate "sparse", Kurtotic, or "interesting" output probability distributions (Barlow & Tolhurst, 1992; Barlow, 1994; Field, 1994; Intrator & Cooper, 1991; Intrator, 1992). We investigate the empirical evidence for this further and argue that filters can produce "interesting" output distributions simply because natural images have variable local intensity variance. If the proposed filters have zero D.C., then the probability distribution of filter outputs (and hence the output Kurtosis) is well predicted simply from these effects of variable local variance. This suggests that finding filters with high output Kurtosis does not necessarily signal interesting image structure. It is then argued that finding filters that maximise output Kurtosis generates filters that are incompatible with observed physiology. In particular the optimal difference--of--Gaussian (DOG) filter should have the smallest possible s...

A system for automatic face recognition is presented. It consists of several steps; Automatic detection of the eyes and mouth is followed by a spatial normalization of the images. The classification of the normalized images is carried out by a hybrid (supervised and unsupervised) Neural Network. Two methods for reducing the overfitting -- a common problem in high dimensional classification schemes -- are presented, and the superiority of their combination is demonstrated. Key words: Face recognition, Neural Networks, Interest points, Symmetry operator. To appear: Pattern Recognition Letters 17 (1996) 67-76 1 Introduction Automatic face recognition has gained much attention in recent years, due to the variety of potential applications, and the increase in computational power which enables effective implementation of algorithms. Traditionally, face recognition was based on extracting certain features (e.g. spatial location of facial features and their geometrical relations) [4, 20]....

ed on visual and speech data. The ability of the network to automatically generate wavelet codes from natural images is demonstrated. These bear a close resemblance to 2-D Gabor functions, which have previously been used to describe physiological receptive fields, and as a means of producing compact image representations. Keywords: neural networks, unsupervised learning, self-organisation, feature extraction, information theory, redundancy reduction, sparse coding, imaging models, occlusion, image coding, speech coding. Declaration This dissertation is the result of my own original work, except where reference is made to the work of others. No part of it has been submitted for any other university degree or diploma. Its length, including captions, footnotes, appendix and bibliography, is approximately 58000 words. Acknowledgements I would like first and foremost to thank Richard Prager, my supervisor, fo