A convex framework for image segmentation with moment constraints

Convex relaxation techniques have become a popular approach to image segmentation as they allow to compute solutions independent of initialization to a variety of image segmentation problems. In this paper, we will show that shape priors in terms of moment constraints can be imposed within the convex optimization framework, since they give rise to convex constraints. In particular, the lowerorder moments correspond to the overall volume, the centroid, and the variance or covariance of the shape and can be easily imposed in interactive segmentation methods. Respective constraints can be imposed as hard constraints or soft constraints. Quantitative segmentation studies on a variety of images demonstrate that the user can easily impose such constraints with a few mouse clicks, giving rise to substantial improvements of the resulting segmentation, and reducing the average segmentation error from 12 % to 0.35%. GPU-based computation times of around 1 second allow for interactive segmentation

Propagated photoconsistency and convexity in variational multiview 3D reconstruction

In this paper, we make two contributions. Firstly, we replace the generic balloon constraints widely used in 3D reconstruction by a more sophisticated data-dependent regional term. The key idea is to propagate classical photoconsistency along visual rays into regional values describing voxel probabilities for being inside or outside the observed object. Secondly, we cast the optimization as one of minimizing a convex functional. Therefore (up to visibility) the reconstruction problem can be solved in a globally optimal manner in a spatially continuous setting. Compared to graph cut methods, this approach does not suffer from discretization artifacts and exhibits considerable reduction in memory requirements. Experimental comparisons clearly show the advantages of the proposed technique