Tracking of Lines in Spherical Images via Sub-Riemannian Geodesics in \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$
Tracking of Lines in Spherical Images via Sub-Riemannian Geodesics in \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$
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DOI：
10.1007/s10851-017-0705-9
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发表时间：
2016-04
影响因子：
2
通讯作者：
Alexey Pavlovich Mashtakov;R. Duits;Y. Sachkov;E. Bekkers
中科院分区：
文献类型：
--
作者：
Alexey Pavlovich Mashtakov;R. Duits;Y. Sachkov;E. Bekkers
为了检测球面图像中的显著直线，我们考虑了球面上具有固定边界点和方向的曲线的泛函最小化问题。总长度是自由的，s表示球面弧长，和表示的测地曲率。这里光滑的外部成本是从球面数据得到的。我们解除这个问题的子黎曼（SR）李群的问题，并表明球面投影的某些SR测地线提供了一个解决方案，我们的曲线优化问题。事实上，这只适用于球面投影不显示尖点的测地线。这个问题是一个著名的轮廓感知模型，在那里我们扩展了Boscain和Rossi的模型的一般情况下的球形扩展。对于，我们推导了SR测地线并计算了第一个尖点时间。我们表明，这些曲线有一个更简单的表达式时，他们被参数化的球面弧长，而不是由亚黎曼弧长。对于数据驱动的SR测地线，我们通过SR快速推进方法求解。最后，我们展示了一个实验的血管跟踪在一个球面图像的视网膜和研究的效果，包括球面几何形状的血管曲率分析。
In order to detect salient lines in spherical images, we consider the problem of minimizing the functionalfor a curveon a sphere with fixed boundary points and directions. The total lengthlis free,sdenotes the spherical arclength, anddenotes the geodesic curvature of. Here the smooth external costis obtained from spherical data. We lift this problem to the sub-Riemannian (SR) problem in Lie groupand show that the spherical projection of certain SR geodesics provides a solution to our curve optimization problem. In fact, this holds only for the geodesics whose spherical projection does not exhibit a cusp. The problem is a spherical extension of a well-known contour perception model, where we extend the model by Boscain and Rossi to the general case. For, we derive SR geodesics and evaluate the first cusp time. We show that these curves have a simpler expression when they are parameterized by spherical arclength rather than by sub-Riemannian arclength. For case(data-driven SR geodesics), we solve via a SR Fast Marching method. Finally, we show an experiment of vessel tracking in a spherical image of the retina and study the effect of including the spherical geometry in analysis of vessels curvature.