A function space perspective on stochastic shape evolution

2023/02/10 by Elizabeth Baker, Baker, Elizabeth, Thomas Besnier +3 · 1 citation
Mathematics · #Computer Vision and Pattern Recognition (cs.CV) #FOS: Computer and information sciences #FOS: Mathematics #Morphological variations and asymmetry #Probability (math.PR)

paper · pdf · doi:10.48550/arxiv.2302.05382

openalex publication_date 2023/02/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

Modelling randomness in shape data, for example, the evolution of shapes of organisms in biology, requires stochastic models of shapes. This paper presents a new stochastic shape model based on a description of shapes as functions in a Sobolev space. Using an explicit orthonormal basis as a reference frame for the noise, the model is independent of the parameterisation of the mesh. We define the stochastic model, explore its properties, and illustrate examples of stochastic shape evolutions using the resulting numerical framework.

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