Modelling shapes with uncertainties: higher order polynomials, variable bandwidth kernels and non parametric density estimation

In this paper, we introduce a new technique for shape modelling in the space of implicit polynomials. Registration consists of recovering an optimal one-to-one transformation of a higher order polynomial along with uncertainties measures that are determined according to the covariance matrix of the correspondences at the zero isosurface. In the modelling phase, these measures are used to weight the importance of the training samples phase according to a variable bandwidth non-parametric density estimation process. The selection of the most appropriate kernels to represent the training set is done through the maximum likelihood criterion. Excellent results for patterns of digits, related with the registration and the modelling aspects of our approach demonstrate the potentials of our method