2021/08/05 by Shufei Ge, Ge, Shufei, Shijia Wang +3
Computer Science · Mathematics · #FOS: Computer and information sciences #Image Retrieval and Classification Techniques #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Medical Image Segmentation Techniques #Morphological variations and asymmetry
paper · pdf · doi:10.48550/arxiv.2108.02507
openalex publication_date 2021/08/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 \urlhttps://github.com/ShufeiGe/Shape-Modeling-with-Spline-Partitions.