# Shape Modeling with Spline Partitions

arXiv: https://arxiv.org/abs/2108.02507 · HTML: https://mlsanity.com/paper/2108.02507/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 52 references that are in the map.
- First posted on arXiv 5 Aug 2021.

## Builds on (most cited first, 10 of 10)

- [Artificial Intelligence and Statistics](https://mlsanity.com/paper/1712.03779/) (2017)
- [Mondrian Forests: Efficient Online Random Forests](https://mlsanity.com/paper/1406.2673/) (2014)
- [Canonical Correlation Forests](https://mlsanity.com/paper/1507.05444/) (2015)
- [Extrinsic Gaussian processes for regression and classification on manifolds](https://mlsanity.com/paper/1706.08757/) (2017)
- [Random Tessellation Forests](https://mlsanity.com/paper/1906.05440/) (2019)
- [Rectangular Bounding Process](https://mlsanity.com/paper/1903.03906/) (2019)
- [The Binary Space Partitioning-Tree Process](https://mlsanity.com/paper/1903.09343/) (2019)
- [Particle Gibbs for Bayesian Additive Regression Trees](https://mlsanity.com/paper/1502.04622/) (2015)
- [Binary Space Partitioning Forests](https://mlsanity.com/paper/1903.09348/) (2019)
- [Online Binary Space Partitioning Forests](https://mlsanity.com/paper/2003.00269/) (2020)

## Built on by (most cited first, 1 of 1)

- [BiMotion: B-spline Motion for Text-guided Dynamic 3D Character Generation](https://mlsanity.com/paper/2602.18873/) (2026)

## Abstract (arXiv)

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.