视觉皮层功能结构的度量模型
A metric model for the functional architecture of the visual cortex
摘要：
本工作的目的是构建一个模型的初级视觉皮层（V1）的功能架构，基于一个结构的度量测度空间诱导的视觉细胞的接受配置文件（RP）的潜在组织。为了说明V1在这样的上下文中的水平连通性，遵循K.-K.的经典方法定义了与空间几何相容的扩散过程。T.斯特姆我们的距离函数的构造既不需要RP族的任何群参数化，也不涉及任何微分结构。因此，它适应于非参数化的RP集，可能通过数值程序获得;它还允许模拟横向连接所产生的非差分度量，如一个由一个家庭的过滤器消失的规模上引起的风车表面。另一方面，当应用于经典的Gabor滤波器框架时，这种构造产生了一个近似于G. Citti和A. Sarti [J Math Imaging Vis 24：307（2006）]，从而表明其本身与现有的皮质模型一致。
英文摘要：
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. The construction of our distance function does neither require any group parameterization of the family of RPs, nor involve any differential structure. As such, it adapts to non-parameterized sets of RPs, possibly obtained through numerical procedures; it also allows to model the lateral connectivity arising from non-differential 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 G. Citti and A. Sarti [J Math Imaging Vis 24: 307 (2006)], thus showing itself to be consistent with existing cortex models.
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