A widely used approach to image segmentation is to define corresponding segmentation energies and to compute shapes that are minimizers of these energies. In this work, we introduce a flexible and efficient numerical framework for minimization of such energies. The framework enables use of various gradient descent flows, including H1 flows that are fast and stable. For this, we model the geometry explicitly and make use of shape differential calculus. We discretize the resulting partial differential equations using finite elements and obtain linear systems that can be solved efficiently. Incorporating spatial adaptivity, time step controls, topological changes results in a robust practical method.
Conference Dates: August 22-23, 2010
Conference Location: Istanbul, -1
Conference Title: Workshop on Applications of Digital Geometry and Mathematical Morphology
Pub Type: Conferences
image segmentation, gradient descent flows, finite elements, adaptivity