Neural networks. Learning from your neighbour.
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Brain↗
Biomedical subjects
G Mitchison
Publications and source records attributed to G Mitchison.
Axonal trees and cortical architecture.
In modern computer design considerable care is taken to arrange the components in such a way that wiring is kept to a minimum. Certain features of cortical structure--the mappings, stripes and blobs within areas, and areas themselves--are somewhat reminiscent of the layout of computer components, and suggest that the cortex may also be organized so as to economize on neuronal 'wiring'. One important difference between the brain and a computer is that the wiring in the brain takes the form of elaborate branched structures, namely axonal trees. In this article, it is argued that an assessment of the efficiency of cortical wiring must take account of the branching rules of these trees.
Animals↗
Neuronal branching patterns and the economy of cortical wiring.
Keeping the volume of connections in the cortex as low as possible may be an important evolutionary constraint on the design of the brain. Much as an engineer tries to arrange the components of a computer in such a way as to give efficient wiring, so the brain may have evolved a layout of neuronal types which gives an economical use of axonal 'wiring'. One key difference between computer and brain is that connections in the brain take the form of elaborate branching structures. It is argued here that certain features of cortical mapping, such as the stripes and patches seen within cortical areas, may be adaptations which allow efficient wiring by such structures. Some simple calculations are given to support this, using as models for axonal arbors certain branching patterns which give a low volume of wiring. In particular, it is shown that a pattern of stripes can give economical wiring when axon diameters follow a law dp = dp1 + dp2 with p greater than 4, where d1 and d2 are the diameters of the daughter branches and d that of the parent.
Animals↗
A dimension reduction framework for understanding cortical maps.
We argue that cortical maps, such as those for ocular dominance, orientation and retinotopic position in primary visual cortex, can be understood in terms of dimension-reducing mappings from many-dimensional parameter spaces to the surface of the cortex. The goal of these mappings is to preserve as far as possible neighbourhood relations in parameter space so that local computations in parameter space can be performed locally in the cortex. We have found that, in a simple case, certain self-organizing models generate maps that are near-optimally local, in the sense that they come close to minimizing the neuronal wiring required for local operations. When these self-organizing models are applied to the task of simultaneously mapping retinotopic position and orientation, they produce maps with orientation vortices resembling those produced in primary visual cortex. This approach also yields a new prediction, which is that the mapping of position in visual cortex will be distorted in the orientation fracture zones.
Animals↗
The enigma of the cortical code.
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Animals↗
Planarity and segmentation in stereoscopic matching.
The matching of stereograms which contain periodic patterns suggests ways in which the stereo correspondence problem may be solved in human vision. The stereograms seem to be segmented by coarse-scale features. Within each segment a set of matches approximating a plane is chosen. In regions with periodic patterns there may be many such planar sets, and the disparity of coarse-scale features seems to guide the choice of a particular set. This emphasis on planarity may reflect the occurrence of correlation-like operations in cortical neurons. An attractive possibility is that segmentation effectively delimits areas of the visual field within which disparities are likely to be slow changing (eg local tangent planes to surfaces) so that the correlation sums evaluated in a segment can give the best estimate of depth. A mechanism of this kind cannot account for all of stereo matching, since not all visual objects are well described by ensembles of planes. But it is likely to be a component of the matching system which is particularly important where images are 'noisy' and averaging is needed to extract reliable disparities.
Algorithms↗