Convex Cardinal Shape Composition

TL;DR

This paper introduces a convex relaxation approach for shape composition in imaging, enabling efficient selection and combination of shape priors for various applications like object recognition and tracking.

Contribution

It presents a novel convex formulation for combinatorial shape composition, facilitating tractable solutions and analysis of minimizers.

Findings

Convex relaxation makes the shape composition problem computationally feasible.

The method effectively characterizes desired image regions using shape dictionaries.

Applications include shape recognition, object tracking, and occlusion recovery.

Abstract

We propose a new shape-based modeling technique for applications in imaging problems. Given a collection of shape priors (a shape dictionary), we define our problem as choosing the right dictionary elements and geometrically composing them through basic set operations to characterize desired regions in an image. This is a combinatorial problem solving which requires an exhaustive search among a large number of possibilities. We propose a convex relaxation to the problem to make it computationally tractable. We take some major steps towards the analysis of the proposed convex program and characterizing its minimizers. Applications vary from shape-based characterization, object tracking, optical character recognition, and shape recovery in occlusion, to other disciplines such as the geometric packing problem.