Shape Modeling with Spline Partitions

TL;DR

This paper introduces a novel Bayesian nonparametric method for shape modeling using spline partitions, enabling complex shape representations and applications to biological image data, with an accompanying R package.

Contribution

The work presents a new parallelized Bayesian approach for partitioning domains with curves, extending previous methods to handle complex shapes in higher dimensions.

Findings

Effective shape modeling on biological images

Outperforms traditional classifiers like SVMs and random forests

Provides an accessible R package for implementation

Abstract

Shape modelling (with methods that output shapes) is a new and important task in Bayesian nonparametrics and bioinformatics. In this work, we focus on Bayesian nonparametric methods for capturing shapes by partitioning a space using curves. In related work, the classical Mondrian process is used to partition spaces recursively with axis-aligned cuts, and is widely applied in multi-dimensional and relational data. The Mondrian process outputs hyper-rectangles. Recently, the random tessellation process was introduced as a generalization of the Mondrian process, partitioning a domain with non-axis aligned cuts in an arbitrary dimensional space, and outputting polytopes. Motivated by these processes, in this work, we propose a novel parallelized Bayesian nonparametric approach to partition a domain with curves, enabling complex data-shapes to be acquired. We apply our method to HIV-1-infected human macrophage image dataset, and also simulated datasets sets to illustrate our approach. We compare to support vector machines, random forests and state-of-the-art computer vision methods such as simple linear iterative clustering super pixel image segmentation. We develop an R package that is available at \url{https://github.com/ShufeiGe/Shape-Modeling-with-Spline-Partitions}.