  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}.
