Shape Modeling with Spline Partitions
- URL: http://arxiv.org/abs/2108.02507v1
- Date: Thu, 5 Aug 2021 10:33:05 GMT
- Title: Shape Modeling with Spline Partitions
- Authors: Shufei Ge, Shijia Wang, Lloyd Elliott
- Abstract summary: 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.
- Score: 3.222802562733787
- License: http://creativecommons.org/licenses/by/4.0/
- 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}.
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