早期视觉的功能架构与神经几何模型
摘要
本文开篇为面向数学背景读者简明呈现早期视觉功能架构的一些最基本事实。此类信息通常散见于各类论文与著作中，非专业人士不易获取。因此，我们的目标是以简明扼要的方式介绍该主题，以助于愿意进入现代微分几何在视觉系统研究中应用（由 J. Petitot 命名为神经几何）领域的研究者。随后，我们综述三个最重要的神经几何模型：Petitot 的初级视觉皮层接触模型、其推广至 A. Sarti、G. Citti 与 J. Petitot 的辛模型，以及 P. C. Bressloff 与 J. D. Cowan 的超柱球面模型。最后，我们讨论所谓超柱“共形模型”的要点（该模型曾在 [D. V. Alekseevsky, Conformal model of hypercolumns in V1 cortex and the Moebius group, in “Geometric science of information”, pp. 65–72, Springer, 2021] 中简要提出，并在 [D. V. Alekseevsky and A. Spiro, Conformal models for hypercolumns in the primary visual cortex V1, arXiv 2024] 中详述），该模型可视为辛模型与球面模型的综合。
引用
@article{arxiv.2202.10157,
title = {The functional architecture of the early vision and neurogeometric models},
author = {Dmitri V. Alekseevsky and Andrea Spiro},
journal= {arXiv preprint arXiv:2202.10157},
year = {2024}
}
备注
39 pages, 2 figures -- The previous version v.2 has been split into two separate papers, corresponding to previous Part I and Part II. This v.3 is the first, the second is posted with the title "Conformal models for hypercolumns in the primary visual cortex V1''. The contents are basically unchanged, but the presentations is improved in many aspects. Many references are added