SIAM Journal on Applied Mathematics, Volume 80, Issue 2, Page 1057-1081, January 2020.
The purpose of this work is to construct a model for the functional architecture of the primary visual cortex (V1), based on a structure of metric measure space induced by the underlying organization of receptive profiles (RPs) of visual cells. In order to account for the horizontal connectivity of V1 in such a context, a diffusion process compatible with the geometry of the space is defined following the classical approach of K.-T. Sturm [Ann. Probab., 26 (1998), pp. 1--55]. The construction of our distance function neither requires any group parameterization of the family of RPs nor involves any differential structure. As such, it adapts to nonparameterized sets of RPs, possibly obtained through numerical procedures; it also allows us to model the lateral connectivity arising from nondifferential metrics such as the one induced on a pinwheel surface by a family of filters of vanishing scale. On the other hand, when applied to the classical framework of Gabor filters, this construction yields a distance approximating the sub-Riemannian structure proposed as a model for V1 by Citti and Sarti [J. Math. Imaging Vision Archive, 24 (2006), pp. 307--326], thus showing itself to be consistent with existing cortex models.

中文翻译：

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视觉皮层功能架构的度量模型

SIAM应用数学杂志，第80卷，第2期，第1057-1081页，2020年1月。
这项工作的目的是基于由视觉细胞的接受轮廓（RP）的潜在组织引起的度量度量空间的结构，为主要视觉皮层（V1）的功能体系结构构建模型。为了在这种情况下考虑V1的水平连通性，按照K.-T的经典方法定义了与空间几何形状兼容的扩散过程。Sturm [Ann。Probab。，26（1998），第1--55页]。距离函数的构造既不需要RP系列的任何组参数化，也不需要任何差分结构。因此，它适用于可能通过数值程序获得的非参数化RP集。它还允许我们对由非差分量度引起的横向连通性建模，例如由一系列消失的过滤器在风车表面上引起的横向连通性。另一方面，当将其应用于经典的Gabor滤波器框架时，这种构造产生的距离近似于Citti和Sarti [1]建议的V1模型所用的次黎曼结构。数学。《影像视觉档案》，第24期（2006），第307--326页]，因此显示出其与现有皮质模型的一致性。