Pose Invariant Shape Prior Segmentation Using Continuous Cuts and Gradient Descent on Lie Groups

摘要

This paper proposes a novel formulation of the Chan-Vese model for pose invariant shape prior segmentation as a continuous cut problem. The model is based on the classic L~2 shape dissimilarity measure and with pose invariance under the full (Lie-) group of similarity transforms in the plane. To overcome the common numerical problems associated with step size control for translation, rotation and scaling in the discretization of the pose model, a new gradient descent procedure for the pose estimation is introduced. This procedure is based on the construction of a Riemannian structure on the group of transformations and a derivation of the corresponding pose energy gradient. Numerically, this amounts to an adaptive step size selection in the discretization of the gradient descent equations. Together with efficient numerics for TV-minimization we get a fast and reliable implementation of the model. Moreover, the theory introduced is generic and reliable enough for application to more general segmentation- and shape-models.