A function space perspective on stochastic shape evolution
This work addresses the need for stochastic models in shape analysis, particularly for applications like biology, but it appears incremental as it builds on existing functional space approaches.
The paper tackles the problem of modeling randomness in shape data, such as biological shape evolution, by introducing a new stochastic shape model based on Sobolev spaces, resulting in a parameterization-independent framework with demonstrated examples.
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.