Geometry and Geodesy on the Primary Visual Cortex as a Surface of Revolution

被引:1
作者
Resca, Lorenzo G. [1 ]
Mecholsky, Nicholas A.
机构
[1] Catholic Univ Amer, Dept Phys, 620 Michigan Ave NE, Washington, DC 20064 USA
关键词
geodesy; vision; primary visual cortex; differential geometry; OCULAR DOMINANCE COLUMNS; CORTICAL MAGNIFICATION; FUNCTIONAL ARCHITECTURE; STRIATE CORTEX; RECEPTIVE-FIELDS; EYE-MOVEMENTS; PATTERN; REPRESENTATION; ATTENTION; GUIDANCE;
D O I
10.3390/mca25040064
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
Biological mapping of the visual field from the eye retina to the primary visual cortex, also known as occipital area V1, is central to vision and eye movement phenomena and research. That mapping is critically dependent on the existence of cortical magnification factors. Once unfolded, V1 has a convex three-dimensional shape, which can be mathematically modeled as a surface of revolution embedded in three-dimensional Euclidean space. Thus, we solve the problem of differential geometry and geodesy for the mapping of the visual field to V1, involving both isotropic and non-isotropic cortical magnification factors of a most general form. We provide illustrations of our technique and results that apply to V1 surfaces with curve profiles relevant to vision research in general and to visual phenomena such as 'crowding' effects and eye movement guidance in particular. From a mathematical perspective, we also find intriguing and unexpected differential geometry properties of V1 surfaces, discovering that geodesic orbits have alternative prograde and retrograde characteristics, depending on the interplay between local curvature and global topology.
引用
收藏
页数:29
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