{"title":"A Cortical-Inspired Contour Completion Model Based on Contour Orientation and Thickness.","authors":"Ivan Galyaev, Alexey Mashtakov","doi":"10.3390/jimaging10080185","DOIUrl":null,"url":null,"abstract":"<p><p>An extended four-dimensional version of the traditional Petitot-Citti-Sarti model on contour completion in the visual cortex is examined. The neural configuration space is considered as the group of similarity transformations, denoted as M=SIM(2). The left-invariant subbundle of the tangent bundle models possible directions for establishing neural communication. The sub-Riemannian distance is proportional to the energy expended in interneuron activation between two excited border neurons. According to the model, the damaged image contours are restored via sub-Riemannian geodesics in the space <i>M</i> of positions, orientations and thicknesses (scales). We study the geodesic problem in <i>M</i> using geometric control theory techniques. We prove the existence of a minimal geodesic between arbitrary specified boundary conditions. We apply the Pontryagin maximum principle and derive the geodesic equations. In the special cases, we find explicit solutions. In the general case, we provide a qualitative analysis. Finally, we support our model with a simulation of the association field.</p>","PeriodicalId":37035,"journal":{"name":"Journal of Imaging","volume":null,"pages":null},"PeriodicalIF":2.7000,"publicationDate":"2024-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11355450/pdf/","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Imaging","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.3390/jimaging10080185","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"IMAGING SCIENCE & PHOTOGRAPHIC TECHNOLOGY","Score":null,"Total":0}
引用次数: 0
Abstract
An extended four-dimensional version of the traditional Petitot-Citti-Sarti model on contour completion in the visual cortex is examined. The neural configuration space is considered as the group of similarity transformations, denoted as M=SIM(2). The left-invariant subbundle of the tangent bundle models possible directions for establishing neural communication. The sub-Riemannian distance is proportional to the energy expended in interneuron activation between two excited border neurons. According to the model, the damaged image contours are restored via sub-Riemannian geodesics in the space M of positions, orientations and thicknesses (scales). We study the geodesic problem in M using geometric control theory techniques. We prove the existence of a minimal geodesic between arbitrary specified boundary conditions. We apply the Pontryagin maximum principle and derive the geodesic equations. In the special cases, we find explicit solutions. In the general case, we provide a qualitative analysis. Finally, we support our model with a simulation of the association field.
本文研究了传统的 Petitot-Citti-Sarti 模型在视觉皮层中轮廓完成的扩展四维版本。神经配置空间被视为相似性变换组,表示为 M=SIM(2)。切线束的左不变子束模拟了建立神经通信的可能方向。子黎曼距离与两个兴奋边界神经元之间的神经元间激活所消耗的能量成正比。根据该模型,受损的图像轮廓是通过位置、方向和厚度(尺度)空间 M 中的亚黎曼大地线恢复的。我们利用几何控制理论技术研究了 M 空间中的大地线问题。我们证明了在任意指定的边界条件之间存在一条最小的大地线。我们应用庞特里亚金最大原则,推导出大地方程。在特殊情况下,我们找到了显式解。在一般情况下,我们提供了定性分析。最后,我们通过模拟关联场来支持我们的模型。