Template-Based Statistical Shape Modelling on Deformation Space

A statistical model for shapes in $\mathbb{R}^2$ or $\mathbb{R}^3$ is proposed. Shape modelling is a difficult problem mainly due to the non-linear nature of its space. Our approach considers curves as shape contours, and models their deformations with respect to a deformable template shape. Contours are uniformly sampled into a discrete sequence of points. Hence, the deformation of a shape is formulated as an action of transformation matrices on each of these points. A parametrized stochastic model based on Markov process is proposed to model shape variability in the deformation space. The model's parameters are estimated from a labeled training dataset. Moreover, a similarity metric based on the Mahalanobis distance is proposed. Subsequently, the model has been successfully tested for shape recognition, synthesis, and retrieval.