Parallel tempering strategies for model-based landmark detection on shapes

Abstract

In the field of shape analysis, landmarks are defined as a low-dimensional, representative set of important features of an object’s shape that can be used to identify regions of interest along its outline. An important problem is to infer the number and arrangement of landmarks, given a set of shapes drawn from a population. One proposed approach defines a posterior distribution over landmark locations by associating each landmark configuration with a linear reconstruction of the shape. In practice, sampling from the resulting posterior density is challenging using standard Markov chain Monte Carlo (MCMC) methods because multiple configurations of landmarks can describe a complex shape similarly well, manifesting in a multi-modal posterior with well-separated modes. Standard MCMC methods traverse multi-modal posteriors poorly and, even when multiple modes are identified, the relative amount of time spent in each one can be misleading. We apply new advances in the parallel tempering literature to the problem of landmark detection, providing guidance on implementation generalized to other applications within shape analysis. Proposal adaptation is used during burn-in to ensure efficient traversal of the parameter space while maintaining computational efficiency. We demonstrate this algorithm on simulated data and common shapes obtained from computer vision scenes.

Keywords:

• shape analysis
• parallel tempering
• landmarks
• Markov chain Monte Carlo
• elastic metric

Additional information

Funding

This work was partially supported by the following grants (SK): NSF (DMS 1613054), NSF (CCF 1740761), NSF (CCF 1839252) and NIH (R37 CA214955).