论文标题
在旋转翻译组中通过亚里曼尼亚测量学的几何光学幻觉
Geometrical Optical Illusion via Sub-Riemannian Geodesics in the Roto-Translation Group
论文作者
论文摘要
我们提出了一个用于几何光盘（GOIS）的神经数学模型，这是一种虚幻现象，包括视觉刺激的几何特性及其相关的感知。它们发生在视觉区域V1/V2的视觉区域，其功能架构是在Citti和Sarti以前的作品中建模的，作为配备了子里曼（SR）度量的谎言组。在这里，我们扩展了他们的模型，建议负责皮质连通性的度量是由简单细胞对视觉刺激的建模神经生理响应调节的，因此提供了一个更具生物学上可行的模型，该模型考虑了视觉刺激的存在。在我们的模型中，虚幻的轮廓被描述为新指标中的大地测量学。该模型通过数值模拟确认，在该模拟中，我们通过SR-FAST行进来计算大地测量学。
We present a neuro-mathematical model for geometrical optical illusions (GOIs), a class of illusory phenomena that consists in a mismatch of geometrical properties of the visual stimulus and its associated percept. They take place in the visual areas V1/V2 whose functional architecture have been modelled in previous works by Citti and Sarti as a Lie group equipped with a sub-Riemannian (SR) metric. Here we extend their model proposing that the metric responsible for the cortical connectivity is modulated by the modelled neuro-physiological response of simple cells to the visual stimulus, hence providing a more biologically plausible model that takes into account a presence of visual stimulus. Illusory contours in our model are described as geodesics in the new metric. The model is confirmed by numerical simulations, where we compute the geodesics via SR-Fast Marching.
