Analytical Solutions for the Minkowski Addition Equation

  • Joel Edu Sánchez Castro
  • Ronaldo Fumio Hashimoto
  • Junior Barrera
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7883)


This paper presents the formulation of a discrete equation whose solutions have a strong combinatory nature. More formally, given two subsets Y and C, we are interested in finding all subsets X that satisfy the equation (called Minkowski Addition Equation) X ⊕ C = Y. One direct application of the solutions of this equation is that they can be used to find best representations for fast computation of erosions and dilations. The main (and original) result presented in this paper (which is a theoretical result) is an analytical solution formula for this equation. One important characteristic of this analytical formula is that all solutions (which can be in worst case exponential) are expressed in a compact representation.


Minkowski Addition Minkowski Subtraction Estructuring Element Decomposition Dilation Erosion 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Joel Edu Sánchez Castro
    • 1
  • Ronaldo Fumio Hashimoto
    • 1
  • Junior Barrera
    • 1
  1. 1.Institute of Mathematics and StatisticsUniversity of Sao PauloBrazil

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