Anisotropic Continuous-Scale Morphology

Authors:
Michael Breuß;Bernhard Burgeth;Joachim Weickert
Affiliations:
Mathematical Image Analysis Group, Faculty for Mathematics and Computer Science, Building E11, Saarland University, 66041 Saarbrücken, Germany;Mathematical Image Analysis Group, Faculty for Mathematics and Computer Science, Building E11, Saarland University, 66041 Saarbrücken, Germany;Mathematical Image Analysis Group, Faculty for Mathematics and Computer Science, Building E11, Saarland University, 66041 Saarbrücken, Germany
Venue:
IbPRIA '07 Proceedings of the 3rd Iberian conference on Pattern Recognition and Image Analysis, Part II
Year:
2007

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Abstract

We describe a new approach to incorporate adaptivity into the partial differential equations (PDEs) of morphological dilation and erosion. By multiplication of the image gradient with a space-variant matrix, the speed of the evolution is locally adapted to the data. This is used to create anisotropic morphological evolutions that enhance coherent, flow-like image structures. We show that our adaptive method can be implemented by means of a simple modification of the classical Rouy-Tourin finite difference scheme. Numerical experiments confirm that the proposed dilations and erosions are capable of real anisotropic behaviour that can be used for closing interrupted lines.