Efficient Topology-Controlled Sampling of Implicit Shapes

TL;DR

This paper introduces an improved sampling method for implicit shapes that accelerates convergence by accepting samples at each iteration and incorporates topological constraints, enhancing efficiency and control.

Contribution

It extends existing Metropolis-Hastings sampling for implicit shapes by enabling sample acceptance at every iteration and integrating topological constraints.

Findings

Achieves an order of magnitude faster convergence.

Allows incorporation of topological constraints.

Provides a more efficient sampling framework for shape analysis.

Abstract

Sampling from distributions of implicitly defined shapes enables analysis of various energy functionals used for image segmentation. Recent work describes a computationally efficient Metropolis-Hastings method for accomplishing this task. Here, we extend that framework so that samples are accepted at every iteration of the sampler, achieving an order of magnitude speed up in convergence. Additionally, we show how to incorporate topological constraints.