Optimal mesh signal transforms

We describe a simple autoregressive model for 3D mesh geometry based on linear prediction. Assuming a Gaussian error term, we show that the resulting probabilistic distribution is a multivariate Gaussian, which may be singular. Furthermore, if the prediction operator is symmetric positive semi-definite, then its eigenvectors coincide with that of the covariance matrix for the distribution. This implies that the mesh signal transform induced by the prediction operator is optimal, with respect to a specific class of mesh distributions and in the sense of basis restriction errors.