Parameterisation invariant statistical shape models

Abstract

In this paper novel theory to automate shape modelling is described. The main idea is to develop a theory that is intrinsically defined for curves as opposed to a finite sample of points along the curves. The major problem here is to define shape variation in a way that is invariant to curve parameterisations. Instead of representing continous curves using landmarks, the problem is treated analytically and numerical approximations are introduced at the latest stage. The problem is solved by calculating the covariance matrix of the shapes using a scalar product that is invariant to global reparameterisations. An algorithm for implementing the ideas is proposed and it is compared to a state of the art algorithm of automatic shape modelling. The problems with stability in former formulations are solved and the resulting models are of higher quality.