On Simulation of Shape Diffusions

Sampling-based computational methods are essential elements of the most practical researches in statistics. In both theoretical and applied fields of statistics one needs to draw samples to make inference, to justify an assertion or to simply plot a complicated distribution. One of the new fields of research emerging in statistics is the shape analysis. It deals with geometrical aspect of an object whose location, scale and orientation is not of interest. To study diffusion of shapes evolving through a time period, the simulation based sampling is required in order to visualize, to generate sample and to forecast the new shape generation. We illustrate an implementation of the popular simulation based sampling algorithm, through approximation of a stochastic differential equation by its discrete counterpart to model shape diffusions.

Keywords:

Simulation , Shape analysis , Shape diffusions , Stochastic differential equations