Guaranteeing Convergence of Iterative Skewed Voting Algorithms for Image Segmentation

TL;DR

This paper rigorously proves the convergence of the Active Masks iterative voting algorithm used for image segmentation, especially in delineating cellular patterns in microscopy images, by modeling it as a generalized cellular automaton.

Contribution

The paper provides the first rigorous proof of convergence for the Active Masks image segmentation algorithm, incorporating prior information through skewed voting.

Findings

Active Masks always converges to a fixed point in practice.

The convergence is proven by modeling the algorithm as a majority cellular automaton.

The proof adapts techniques from discrete dynamical systems.

Abstract

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.