Disjunctive Normal Level Set: An Efficient Parametric Implicit Method

Level set methods are widely used for image segmentation because of their capability to handle topological changes. In this paper, we propose a novel parametric level set method called Disjunctive Normal Level Set (DNLS), and apply it to both two phase (single object) and multiphase (multi-object) image segmentations. The DNLS is formed by union of polytopes which themselves are formed by intersections of half-spaces. The proposed level set framework has the following major advantages compared to other level set methods available in the literature. First, segmentation using DNLS converges much faster. Second, the DNLS level set function remains regular throughout its evolution. Third, the proposed multiphase version of the DNLS is less sensitive to initialization, and its computational cost and memory requirement remains almost constant as the number of objects to be simultaneously segmented grows. The experimental results show the potential of the proposed method.

Convex Decomposition And Efficient Shape Representation Using Deformable Convex Polytopes

Decomposition of shapes into (approximate) convex parts is essential for applications such as part-based shape representation, shape matching, and collision detection. In this paper, we propose a novel convex decomposition using a parametric implicit shape model called Disjunctive Normal Shape Model (DNSM). The DNSM is formed as a union of polytopes which themselves are formed by intersections of halfspaces. The key idea is by deforming the polytopes, which naturally remain convex during the evolution, the polytopes capture convex parts without the need to compute convexity. The major contributions of this paper include a robust convex decomposition which also results in an efficient part-based shape representation, and a novel shape convexity measure. The experimental results show the potential of the proposed method.