Sparse Shape Reconstruction

TL;DR

This paper presents a novel sparse shape reconstruction method that uses shape priors and basis functions called 'knolls' to efficiently solve variational imaging problems like segmentation and tomography.

Contribution

It introduces a new sparse nonlinear reconstruction technique based on shape dictionaries and basis expansion with knolls, applicable to various imaging tasks.

Findings

Effective in image segmentation, X-ray tomography, and diffusive tomography.

Achieves accurate shape reconstruction with sparse basis representation.

Demonstrates competitive performance on standard imaging problems.

Abstract

This paper introduces a new shape-based image reconstruction technique applicable to a large class of imaging problems formulated in a variational sense. Given a collection of shape priors (a shape dictionary), we define our problem as choosing the right elements and geometrically composing them through basic set operations to characterize desired regions in the image. This combinatorial problem can be relaxed and then solved using classical descent methods. The main component of this relaxation is forming certain compactly supported functions which we call "knolls", and reformulating the shape representation as a basis expansion in terms of such functions. To select suitable elements of the dictionary, our problem ultimately reduces to solving a nonlinear program with sparsity constraints. We provide a new sparse nonlinear reconstruction technique to approach this problem. The performance of proposed technique is demonstrated with some standard imaging problems including image segmentation, X-ray tomography and diffusive tomography.