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.

翻译：在形状数据中建模随机性，例如生物学中生物体形状的演化，需要形状的随机模型。本文提出了一种新的随机形状模型，该模型基于将形状描述为Sobolev空间中的函数。通过使用显式的标准正交基作为噪声的参考框架，该模型独立于网格的参数化。我们定义了该随机模型，探究了其性质，并利用所得的数值框架展示了随机形状演化的示例。