论文标题
早期视觉和神经几何模型的功能结构
The functional architecture of the early vision and neurogeometric models
论文作者
论文摘要
本文的最初部分提供了简洁的演示，专门为以数学为导向的受众设计，内容涉及一些早期视觉功能架构的一些最基本的事实。这些信息通常散布在各种论文和书籍中，非专家不容易访问这些信息。因此，我们的目标是为此主题提供方便而简短的介绍，这可能对愿意进入现代差异几何形状应用的研究人员在视觉系统研究中的应用，J。Petitot受洗的神经几何学。然后，我们对三个最重要的神经几何模型进行了调查：Petitot的主要视觉皮层的接触模型，其扩展到A. Sarti，G。Citti和J. Petitot的Symbletic模型，以及P. C. Bressloff和J. D. Cowan的HyperColumms球形模型。我们最终讨论了超牙的所谓``共形模型''的要点（该模型在[D. V. Alekseevsky中简要介绍，V1 Cortex和Moebius集团的超殖民地的整形模型，在`和A. spiro，一级视觉皮层V1中的超柱的共形模型，ARXIV 2024]），可以将其视为符号和球形模型的合成。
The initial sections of the paper give a concise presentation, specially designed for a mathematically oriented audience, of some of the most basic facts on the functional architecture of early vision. Such information is usually scattered in a variety of papers and books, which are not easily accessible by non-specialists. Our goal is thus to offer a handy and short introduction to this topics, which might be helpful for researchers willing to enter the area of the applications of modern Differential Geometry in studies on the visual systems, baptized neurogeometry by J. Petitot. We then offer a survey of three of the most important neurogeometric models: Petitot's contact model of the primary visual cortex, its extension to A. Sarti, G. Citti and J. Petitot's symplectic model, and P. C. Bressloff and J. D. Cowan's spherical model of hypercolumns. We finally discuss the main points of the so-called ``conformal model'' for hypercolumns (a model that was briefly presented in [D. V. Alekseevsky, Conformal model of hypercolumns in V1 cortex and the Moebius group, in ``Geometric science of information'', pp. 65--72, Springer, 2021] and given in detail in [D. V. Alekseevsky and A. Spiro, Conformal models for hypercolumns in the primary visual cortex V1, arXiv 2024]), which can be considered as a synthesis of the symplectic and the spherical models.
