Convexity Shape Prior for Binary Segmentation.

Convexity is a known important cue in human vision. We propose shape convexity as a new high-order regularization constraint for binary image segmentation. In the context of discrete optimization, object convexity is represented as a sum of three-clique potentials penalizing any 1- 0- 1 configuration on all straight lines. We show that these non-submodular potentials can be efficiently optimized using an iterative trust region approach. At each iteration the energy is linearly approximated and globally optimized within a small trust region around the current solution. While the quadratic number of all three-cliques is prohibitively high, we design a dynamic programming technique for evaluating and approximating these cliques in linear time. We also derive a second order approximation model that is more accurate but computationally intensive. We discuss limitations of our local optimization and propose gradual non-submodularization scheme that alleviates some limitations. Our experiments demonstrate general usefulness of the proposed convexity shape prior on synthetic and real image segmentation examples. Unlike standard second-order length regularization, our convexity prior does not have shrinking bias, and is robust to changes in scale and parameter selection.

Spatially varying color distributions for interactive multilabel segmentation.

We propose a method for interactive multilabel segmentation which explicitly takes into account the spatial variation of color distributions. To this end, we estimate a joint distribution over color and spatial location using a generalized Parzen density estimator applied to each user scribble. In this way, we obtain a likelihood for observing certain color values at a spatial coordinate. This likelihood is then incorporated in a Bayesian MAP estimation approach to multiregion segmentation which in turn is optimized using recently developed convex relaxation techniques. These guarantee global optimality for the two-region case (foreground/background) and solutions of bounded optimality for the multiregion case. We show results on the GrabCut benchmark, the recently published Graz benchmark, and on the Berkeley segmentation database which exceed previous approaches such as GrabCut, the Random Walker, Santner's approach, TV-Seg, and interactive graph cuts in accuracy. Our results demonstrate that taking into account the spatial variation of color models leads to drastic improvements for interactive image segmentation.