Convex cardinal shape composition and object recognition in computer vision

This work mainly focuses on the segmentation and identification of objects present in an image, where the geometry sought is composed of given prototype shapes. Given a dictionary of prototype shapes, we define our problem as selecting a limited number of dictionary elements and geometrically composing them through basic set operations to characterize desired regions in an image. Aside from imaging applications such as shape-based characterization and optical character recognition, this problem is closely linked to the geometric packing problem. A recent work proposes a convex relaxation to this combinatorial problem [1], and the main focus of this paper is to computationally address the proposed convex program. We consider an alternating direction method of multipliers (ADMM) scheme, which suits a parallel processing framework and supports large-scale problems.