Bayesian hierarchical modeling of simply connected 2D shapes

TL;DR

This paper introduces a fully Bayesian hierarchical model for analyzing simply connected 2D shapes in images, enabling automatic alignment, uncertainty quantification, and borrowing information across objects, with applications in biomedical imaging.

Contribution

It develops a novel multiscale deformation-based Bayesian model for 2D shapes that avoids landmark dependence and allows for flexible, nonparametric shape analysis.

Findings

Model effectively captures shape variability in simulations.

Applied successfully to yeast cell imaging data.

Provides a scalable MCMC framework for multiple objects.

Abstract

Models for distributions of shapes contained within images can be widely used in biomedical applications ranging from tumor tracking for targeted radiation therapy to classifying cells in a blood sample. Our focus is on hierarchical probability models for the shape and size of simply connected 2D closed curves, avoiding the need to specify landmarks through modeling the entire curve while borrowing information across curves for related objects. Prevalent approaches follow a fundamentally different strategy in providing an initial point estimate of the curve and/or locations of landmarks, which are then fed into subsequent statistical analyses. Such two-stage methods ignore uncertainty in the first stage, and do not allow borrowing of information across objects in estimating object shapes and sizes. Our fully Bayesian hierarchical model is based on multiscale deformations within a linear combination of cyclic basis characterization, which facilitates automatic alignment of the different curves accounting for uncertainty. The characterization is shown to be highly flexible in representing 2D closed curves, leading to a nonparametric Bayesian prior with large support. Efficient Markov chain Monte Carlo methods are developed for simultaneous analysis of many objects. The methods are evaluated through simulation examples and applied to yeast cell imaging data.