Is perception of the whole based on perception of its parts? There is psychological and physiological evidence for parts-based representations in the brain, and certain computational theories of object recognition rely on such representations. But little is known about how brains or computers might learn the parts of objects. Here we demonstrate an algorithm for non-negative matrix factorization that is able to learn parts of faces and semantic features of text. This is in contrast to other methods, such as principal components analysis and vector quantization, that learn holistic, not parts-based, representations. Non-negative matrix factorization is distinguished from the other methods by its use of non-negativity constraints. These constraints lead to a parts-based representation because they allow only additive, not subtractive, combinations. When non-negative matrix factorization is implemented as a neural network, parts-based representations emerge by virtue of two properties: the firing rates of neurons are never negative and synaptic strengths do not change sign.

Learning parts of objects by non-negative matrix factorization

Using a differential-geometric treatment of planar shapes, we present tools for: 1) hierarchical clustering of imaged objects according to the shapes of their boundaries, 2) learning of probability models for clusters of shapes, and 3) testing of newly observed shapes under competing probability models. Clustering at any level of hierarchy is performed using a minimum variance type criterion and a Markov process. Statistical means of clusters provide shapes to be clustered at the next higher level, thus building a hierarchy of shapes. Using finite-dimensional approximations of spaces tangent to the shape space at sample means, we (implicitly) impose probability models on the shape space, and results are illustrated via random sampling and classification (hypothesis testing). Together, hierarchical clustering and hypothesis testing provide an efficient framework for shape retrieval. Examples are presented using shapes and images from ETH, Surrey, and AMCOM databases.

Statistical shape analysis: clustering, learning, and testing

A Common Network of Functional Areas for Attention and Eye Movements

We perceive the shapes and material properties of objects quickly and reliably despite the complexity and objective ambiguities of natural images. Typical images are highly complex because they consist of many objects embedded in background clutter. Moreover, the image features of an object are extremely variable and ambiguous owing to the effects of projection, occlusion, background clutter, and illumination. The very success of everyday vision implies neural mechanisms, yet to be understood, that discount irrelevant information and organize ambiguous or noisy local image features into objects and surfaces. Recent work in Bayesian theories of visual perception has shown how complexity may be managed and ambiguity resolved through the task-dependent, probabilistic integration of prior object knowledge with image features.

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Dominic Ffytche

Papers

High-Level Vision: Object Recognition and Visual Cognition