Guaranteeing Convergence of Iterative Skewed Voting Algorithms for Image Segmentation

Authors

Doru C. Balcan, Georgia Institute of Technology
Gowri Srinivasa, PES School of Engineering - Bangalore
Matthew C. Fickus, Air Force Institute of TechnologyFollow
Jelena Kovacevic, Carnegie Mellon University

Document Type

Article

Publication Date

9-2012

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.

Comments

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Reviewed at MR2927463

Previous version (Pre-print): arXiv:1102.2615 [math.FA].

DOI

10.1016/j.acha.2012.03.008

Source Publication

Applied and Computational Harmonic Analysis

Recommended Citation

Balcan, D. C., Srinivasa, G., Fickus, M., & Kovačević, J. (2012). Guaranteeing convergence of iterative skewed voting algorithms for image segmentation. Applied and Computational Harmonic Analysis, 33(2), 300–308.