SUMMARY1. A detailed theory of cerebellar cortex is proposed whose consequence is that the cerebellum learns to perform motor skills. Two forms of inputoutput relation are described, both consistent with the cortical theory. One is suitable for learning movements (actions), and the other for learning to maintain posture and balance (maintenance reflexes).2. It is known that the cells of the inferior olive and the cerebellar Purkinje cells have a special one-to-one relationship induced by the climbing fibre input. For learning actions, it is assumed that:(a) each olivary cell responds to a cerebral instruction for an elemental movement. Any action has a defining representation in ferms of elemental movements, and this representation has a neural expression as a sequence of firing patterns in the inferior olive; and (b) in the correct state of the nervous system, a Purkinje cell can initiate the elemental movement to which its corresponding olivary cell responds.3. Whenever an olivary cell fires, it sends an impulse (via the climbing fibre input) to its corresponding Purkinje cell. This Purkinje cell is also exposed (via the mossy fibre input) to information about the context in which its olivary cell fired; and it is shown how, during rehearsal of an action, each Purkinje cell can learn to recognize such contexts. Later, when the action has been learnt, occurrence of the context alone is enough to fire the Purkinje cell, which then causes the next elemental movement. The action thus progresses as it did during rehearsal.4. It is shown that an interpretation of cerebellar cortex as a structure which allows each Purkinje cell to learn a number of cQntexts is consistent both with the distributions of the various types of cell, and with their known excitatory or inhibitory natures. It is demonstrated that the mossy fibre-granule cell arrangement provides the required pattern discrimination capability.5. The following predictions are made.(a) The synapses from parallel fibres to Purkinje cells are facilitated by the conjunction ofpresynaptic and climbing fibre (or post-synaptic) activity.

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It is proposed that the most important characteristic of archicortex is its ability to perform a simple kind of memorizing task. It is shown that rather general numerical constraints roughly determine the dimensions of memorizing models for the mammalian brain, and from these is derived a general model for archicortex. The addition of further constraints leads to the notion of a simple representation, which is a way of translating a great deal of information into the firing of about 200 out of a population of 105 cells. It is shown that if about 10 5 simple representations are stored in such a population of cells, very little information about a single learnt event is necessary to provoke its recall. A detailed numerical examination is made of a particular example of this kind of memory, and various general conclusions are drawn from the analysis. The insight gained from these models is used to derive theories for various archicortical areas. A functional interpretation is given of the cells and synapses of the area entorhinalis, the presubiculum, the prosubiculum, the cornu ammonis and the fascia dentata. Many predictions are made, a substantial number of which must be true if the theory is correct. A general functional classification of typical archicortical cells is proposed.

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 a t a given scale is found to be the second derivative of a Gaussian, and it is shown th a t, provided some simple conditions are satisfied, these prim ary filters need not be orientation-dependent. Thus, intensity changes a t a given scale are best detected by finding the zero values of V2G(x, y)* I(x, y) for image I, where G(x, y) is a two-dimen sional Gaussian distribution and V2 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 th a t this representation is complete. (2) Intensity changes in images arise from surface discontinuities or from reflectance or illumination bound aries, and these all have the property th a t they are spatially localized. 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 opera tion of forming oriented zero-crossing segments from the output of centre-surround V2G filters acting on the image forms the basis for a physiological model of simple cells (see .

The extraction of stereo-disparity information from two images depends upon establishing a correspondence between them. In this article we analyze the nature of the correspondence computation and derive a cooperative algorithm that implements it. We show that this algorithm successfully extracts information from random-dot stereograms, and its implications for the psychophysics and neurophysiology of the visual system are briefly discussed.

The human visual process can be studied by examining the computational problems associated with deriving useful information from retinal images. In this paper, we apply this approach to the problem of representing three-dimensional shapes for the purpose of recognition. 1. Three criteria, accessibility, scope and uniqueness , and stability and sensitivity , are presented for judging the usefulness of a representation for shape recognition. 2. Three aspects of a representation’s design are considered, (i) the representation’s coordinate system, (ii) its primitives, which are the primary units of shape information used in the representation, and (iii) the organization the representation imposes on the information in its descriptions. 3. In terms of these design issues and the criteria presented, a shape representation for recognition should: (i) use an object-centred coordinate system, (ii) include volumetric primitives of varied sizes, and (iii) have a modular organization. A representation based on a shape’s natural axes (for example the axes identified by a stick figure) follows directly from these choices. 4. The basic process for deriving a shape description in this representation must involve: (i) a means for identifying the natural axes of a shape in its image and (ii) a mechanism for transforming viewer-centred axis specifications to specifications in an object-centred coordinate system. 5. Shape recognition involves: (i) a collection of stored shape descriptions, and (ii) various indexes into the collection that allow a newly derived description to be associated with an appropriate stored description. The most important of these indexes allows shape recognition to proceed conservatively from the general to the specific based on the specificity of the information available from the image. 6. New constraints supplied by a conservative recognition process can be used to extract more information from the image. A relaxation process for carrying out this constraint analysis is described.

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