Optimization of Max-Norm Objective Functions in Image Processing and Computer Vision

  • Filip MalmbergEmail author
  • Krzysztof Chris Ciesielski
  • Robin Strand
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11414)


Many fundamental problems in image processing and computer vision, such as image filtering, segmentation, registration, and stereo vision, can naturally be formulated as optimization problems.

We consider binary labeling problems where the objective function is defined as the max-norm over a set of variables. It is well known that for a limited subclass of such problems, globally optimal solutions can be found via watershed cuts, i.e., cuts by optimum spanning forests. Here, we propose a new algorithm for optimizing a broader class of such problems. We prove that the proposed algorithm returns a globally optimal labeling, provided that the objective function satisfies certain given conditions, analogous to the submodularity conditions encountered in min-cut/max-flow optimization. The proposed method is highly efficient, with quasi-linear computational complexity.


Energy minimization Pixel labeling Minimum cut Submodularity 


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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Filip Malmberg
    • 1
    Email author
  • Krzysztof Chris Ciesielski
    • 2
    • 3
  • Robin Strand
    • 1
  1. 1.Centre for Image Analysis, Department of Information TechnologyUppsala UniversityUppsalaSweden
  2. 2.Department of MathematicsWest Virginia UniversityMorgantownUSA
  3. 3.Department of Radiology, MIPGUniversity of PennsylvaniaPhiladelphiaUSA

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