Anisotropic continuous-scale morphology

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. © Springer-Verlag Berlin Heidelberg 2007.