图像分割迭代斜投票算法的收敛性保证
Guaranteeing Convergence of Iterative Skewed Voting Algorithms for Image Segmentation
摘要：
在本文中，我们提供了严格的收敛性证明的迭代投票为基础的图像分割算法称为主动面具。主动掩模（AM）被提出来解决从荧光显微镜图像中描绘细胞点状图案的挑战性任务。AM的每次迭代都由一个线性卷积和一个非线性阈值组成;在我们的例子中，这个过程的特殊之处在于附加项的存在，其作用是在先验信息可用时“扭曲”投票。在现实世界的实现中，AM算法总是收敛到一个不动点。我们研究的行为AM严格，并提出了这种收敛的证明。其关键思想是制定AM作为一个广义（并行）多数元胞自动机，从离散动力系统适应证明技术。
英文摘要：
In this paper we provide rigorous proof for the convergence of an iterative voting-based image segmentation algorithm called Active Masks. Active Masks (AM) was proposed to solve the challenging task of delineating punctate patterns of cells from fluorescence microscope images. Each iteration of AM consists of a linear convolution composed with a nonlinear thresholding; what makes this process special in our case is the presence of additive terms whose role is to "skew" the voting when prior information is available. In real-world implementation, the AM algorithm always converges to a fixed point. We study the behavior of AM rigorously and present a proof of this convergence. The key idea is to formulate AM as a generalized (parallel) majority cellular automaton, adapting proof techniques from discrete dynamical systems.
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