Also appears in collection : 2019 - T1 - WS1 - Variational methods and optimization in imaging

Recent works have indicated the potential of using curvature as a regularizer in image segmentation, in particular for the class of thin and elongated objects. These are ubiquitous in bio-medical imaging (e.g. vascular networks), in which length regularization can sometime performs badly, as well as in texture identication. However, curvature is a second-order dierential measure, and so its estimators are sensitive to noise. The straightforward extentions to Total Variation are not convex, making it a challenge to optimize. State-of-art techniques make use of a coarse approximation of curvature that limit practical applications. We argue that curvature must instead be computed using a multigrid convergent estimator, and we propose in this paper a new digital curvature ow which mimicks continuous curvature flow. We illustrate its potential as a post-processing step to a variational segmentation framework.