Alternating direction optimization for image segmentation using hidden Markov measure field models

José Bioucas-Dias, Filipe Condessa, Jelena Kovačević

Research output: Chapter in Book/Report/Conference proceedingConference contribution


Image segmentation is fundamentally a discrete problem. It consists of finding a partition of the image domain such that the pixels in each element of the partition exhibit some kind of similarity. The solution is often obtained by minimizing an objective function containing terms measuring the consistency of the candidate partition with respect to the observed image, and regularization terms promoting solutions with desired properties. This formulation ends up being an integer optimization problem that, apart from a few exceptions, is NP-hard and thus impossible to solve exactly. This roadblock has stimulated active research aimed at computing agood†approximations to the solutions of those integer optimization problems. Relevant lines of attack have focused on the representation of the regions (i.e., the partition elements) in terms of functions, instead of subsets, and on convex relaxations which can be solved in polynomial time. In this paper, inspired by the “ hidden Markov measure field†introduced by Marroquin et al. in 2003, we sidestep the discrete nature of image segmentation by formulating the problem in the Bayesian framework and introducing a hidden set of real-valued random fields determining the probability of a given partition. Armed with this model, the original discrete optimization is converted into a convex program. To infer the hidden fields, we introduce the Segmentation via the Constrained Split Augmented Lagrangian Shrinkage Algorithm (SegSALSA). The effectiveness of the proposed methodology is illustrated with simulated and real hyperspectral and medical images.

Original languageEnglish (US)
Title of host publicationProceedings of SPIE-IS and T Electronic Imaging - Image Processing
Subtitle of host publicationAlgorithms and Systems XII
ISBN (Print)9780819499363
StatePublished - 2014
EventImage Processing: Algorithms and Systems XII - San Francisco, CA, United States
Duration: Feb 3 2014Feb 5 2014

Publication series

NameProceedings of SPIE - The International Society for Optical Engineering
ISSN (Print)0277-786X
ISSN (Electronic)1996-756X


OtherImage Processing: Algorithms and Systems XII
Country/TerritoryUnited States
CitySan Francisco, CA


  • Alternating optimization
  • Constrained Split Augmented Lagrangian Shrinkage Algorithm (SALSA)
  • Hidden Markov measure fields
  • Image segmentation
  • Integer optimization
  • Markov random fields
  • Semi-supervised segmentation
  • hidden fields

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics
  • Computer Science Applications
  • Applied Mathematics
  • Electrical and Electronic Engineering


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