Guaranteeing convergence of iterative skewed voting algorithms for image segmentation

Doru C. Balcan, Gowri Srinivasa, Matthew Fickus, Jelena Kovaĉević

Research output: Contribution to journalLetter

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.

Original languageEnglish (US)
Pages (from-to)300-308
Number of pages9
JournalApplied and Computational Harmonic Analysis
Volume33
Issue number2
DOIs
StatePublished - Sep 2012

Keywords

  • Active Masks
  • Cellular automata
  • Convergence
  • Segmentation

ASJC Scopus subject areas

  • Applied Mathematics

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