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：在形状数据中模拟随机性,例如生物生物形状的演变,需要有形状的随机性模型。本文根据对形状作为Sobolev空间函数的描述,展示了新的形状模型。使用明确的正态基础作为噪音的参考框架,该模型独立于网格的参数化。我们定义了随机模型,探索了它的特性,并用由此产生的数字框架来说明形状进化实例。