Abstract

The aim of this paper is to study an optimal opening in the sense of minimize the relationship perimeter over area. We analyze theoretical properties of this opening by means of classical results from variational calculus. Firstly, we explore the optimal radius as attribute in morphological attribute filtering for grey scale images. Secondly, an application of this optimal opening that yields a decomposition into meaningful parts in the case of binary image is explored. We provide different examples of 2D, 3D images and mesh-points datasets.

Keywords

Attribute filter 3D Shape 2D Shape Cheeger Set 

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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Centre of Mathematical MorphologyMines Paris TechParisFrance

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