一种用于检测线段的变分算法
A variational algorithm for the detection of line segments
AI总结：
本文提出一种基于拓扑渐近分析的图像边缘检测算法，通过变分功能惩罚近似边缘集外的振荡，采用薄条带表示边缘，通过渐近展开定义梯度下降法，提升边缘检测精度与效率。
摘要：
在本文中，我们提出了一种基于拓扑渐近分析的图像边缘检测算法。受Mumford-Shah函数启发，我们考虑一个变分函数，该函数惩罚某些近似边缘集外的振荡，这些边缘集表示为有限数量的薄条带的并集，其宽度比长度小多个数量级。为了找到这些条带的近似最优布置，我们计算了该函数关于条带尺寸的渐近展开。此展开随后用于定义一种类似于拓扑梯度下降的最小化方法。与一些作者最近提出的方法不同，该方法使用球覆盖，而条带的使用包含了一些方向信息，可用于获得更精细的边缘，并可能减少计算时间。
英文摘要：
In this paper we propose an algorithm for the detection of edges in images that is based on topological asymptotic analysis. Motivated from the Mumford--Shah functional, we consider a variational functional that penalizes oscillations outside some approximate edge set, which we represent as the union of a finite number of thin strips, the width of which is an order of magnitude smaller than their length. In order to find a near optimal placement of these strips, we compute an asymptotic expansion of the functional with respect to the strip size. This expansion is then employed for defining a (topological) gradient descent like minimization method. As opposed to a recently proposed method by some of the authors, which uses coverings with balls, the usage of strips includes some directional information into the method, which can be used for obtaining finer edges and can also result in a reduction of computation times.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
