Journal of Mathematical Imaging and Vision

, Volume 61, Issue 1, pp 71–83 | Cite as

Morphological Decomposition and Compression of Binary Images via a Minimum Set Cover Algorithm

  • Davod Farazmanesh
  • Ali TavakoliEmail author


In this paper, by a novel morphological decomposition method, we propose an efficient compression approach. Our presented decomposition arises from solving a minimum set cover problem (MSCP) obtained from the image skeleton data. We first use the skeleton pixels to create a collection of blocks which cover the foreground. The given blocks are both overlapped and too many. Hence, in order to find the minimum number of the blocks that cover the foreground, we form an MCSP. To solve this problem, we present a new algorithm of which accuracy is better than those of the known methods in the literatures. Also, its error analysis is studied to obtain an error bound. In the sequel, we present a fast algorithm which include an extra parameter by which the relation between the accuracy and CPU time can be controlled. Finally, several examples are given to confirm the efficiency of our approach.


Decomposition Compression Minimum set cover algorithm 

Mathematics Subject Classification

68U10 94A08 



We thank the anonymous reviewers for their careful reading of our manuscript and their many insightful comments and suggestions.


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Authors and Affiliations

  1. 1.Mathematics DepartmentVali-e-Asr University of RafsanjanRafsanjanIran
  2. 2.Mathematics DepartmentUniversity of MazandaranBabolsarIran

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