In this paper, we propose a new shape decomposition method, called convex shape decomposition. We formalize the convex decomposition problem as an integer linear programming problem, and obtain approximate optimal solution by minimizing the total cost of decomposition under some concavity

Abstract. Convexity is known as an 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 3-clique potentials penal-izing any 1

Given points in convex position in three dimensions, we want to find an approximating convex surface consisting of spherical patches, such that all points are within some specified tolerance bound ε of the approximating surface. We describe a greedy algorithm which constructs an approximating

Shape decomposition is a fundamental problem for part-based shape representation. We propose the Minimum Near-Convex Decomposition (MNCD) to decompose arbitrary shapes into minimum number of “near-convex ” parts. The near-convex shape decomposition is formulated as a discrete optimization problem

Visibility methods are often based on the existence of large convex occluders. We present an algorithm that for a given simple non-convex polygon P finds an approximate inner-cover by large convex polygons. The algorithm is based on an initial partitioning of P into a set C of disjoint convex

Motivated by a long-standing conjecture of Pólya and Szegö about the Newtonian capacity of convex bodies, we discuss the role of concavity inequalities in shape optimization, and we provide several counterexamples to the Blaschke-concavity of variational functionals, including capacity. We

sums of rotating convex polyhedra. We show that DYMSUM is significantly more efficient than the traditional approach, in particular when the size of the input polyhedra are large and when the rotation is small between frames. From our experimental results, we show that the computation time

in naturally looking skins. Due to the simplicity of our algorithm, it can be generalised to branched skins, to skinning simple convex shapes in the plane, and to sphere skinning in 3D. The functionality of the designed algorithm is presented and discussed on several examples.

Abstract. We propose a novel method to find approximate convex 3D shapes from single RGBD images. Convex shapes are more general than cuboids, cylinders, cones and spheres. Many real-world objects are near-convex and every non-convex object can be represented using convex parts. By finding

studies the multigrid convergence of tangent estimators based on maximal digital straight segment recognition. We show that such estimators are multigrid convergent for some family of convex shapes and that their speed of convergence is on average O(h 2 3). Experiments confirm this result and suggest