Regularization of Discrete Contour by Willmore Energy

Abstract

We propose a novel approach to reconstruct shapes from digital data. Contrarily to most methods, reconstructed shapes are smooth with a well-defined curvature field and have the same digitization as the input data: the range of application we have in mind is especially postprocessing to image segmentation where labelled regions are digital objects. For this purpose, we introduce three new algorithms to regularize digital contours based on the minimization of Willmore energy: our first algorithm is based on tools coming from discrete geometry, the second is related to convex geometry while the third approach is a constrained phase field minimization. The three algorithms are described in details and the convergence of the phase field approach is investigated. We present a comparative evaluation of all three methods, in terms of the accuracy of curvature estimators and computation time.

Jacques-Olivier Lachaud

Professor of Computer Science

My research interests include digital geometry, geometry processing, image analysis, variational models and discrete calculus.