Computational geometry: an introduction
Computational geometry: an introduction
A sweepline algorithm for Voronoi diagrams
SCG '86 Proceedings of the second annual symposium on Computational geometry
IEEE Transactions on Pattern Analysis and Machine Intelligence
A Numerical Solution to the Generalized Mapmaker's Problem: Flattening Nonconvex Polyhedral Surfaces
IEEE Transactions on Pattern Analysis and Machine Intelligence
IEEE Transactions on Pattern Analysis and Machine Intelligence
Neural mapping and space-variant image processing
Neural Networks
Digital Image Warping
IEEE Computer Graphics and Applications
Vision: Conformal Image Warping
IEEE Computer Graphics and Applications
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Neo-cortical sensory areas of the vertebrate brain are organized in terms of sensory (topographic) maps of peripheral sense organs. Known for over 40 years, cortical topography has been generally modeled in terms of a continuous map of a peripheral sensory surface onto a cortical surface. However, the details of cortical architecture do not conform to this concept: most, if not all cortical areas are represented by an interlacing of multiple featural or peripheral maps in the form of columns consisting of distinct classes of neural input to the cortex. Since such an architecture is at best piecewise continuous, it is useful to introduce a new term which focuses attention on the many-to-one interlaced nature of neo-cortex. We use the term ''polymap'' to refer to a cortical area which consists of more than one input system, interlaced in a globally topographic, but locally columnar fashion. The best known example of a cortical polymap is provided by the ocular dominance column system in layer IV of primate striate cortex, but the puff/extra-puff and orientation systems of surrounding layers also illustrate this concept, as do the thick-thin-interstripe columns of V-2, and the direction columns of MT. Since polymap architecture seems to be a common architectural pattern in neo-cortex, we have addressed the problem of computational modeling of polymap systems. In the present paper, we present an algorithm, based on the computational geometric constructs of Generalized Voronoi Polygon and Medial Axis, along with related image warps, which is capable of providing a general method for simulating polymap systems. We illustrate this idea with the ocular dominance column system of V-1, and show computer simulations of the structure of binocular stimuli, as they would appear at the level of layer IV in V-1. Comparison of these results to recent binocular 2DG experiments is presented, and methods of generalizing these techniques to other common polymap cortical areas are outlined. This work provides a demonstration of computational neuroscience. The basic anatomical structure of many neo-cortical areas cannot be understood even on a qualitative level, and certainly cannot be modeled, without the development of a detailed set of geometric structures and algorithms which make clear the relationship of an experimentally observed polymap to its afferent inputs.