MDL Spline Models: Gradient and Polynomial Reparameterisations

The major problem when building shape models by minimising the description length (DL) is the computationally demanding optimisation in a highdimensional space. To speed up the convergence when dealing with discretised contours, Ericsson and Åström [6] have shown how to approximate and how to exploit the gradient of the DL. We derive the gradient of the DL for differentiable training sets. Additionally, we propose a class of polynomial reparameterisations that allows us to avoid numerical approximation of the functions and integrals involved in computation of the model and of its DL’s gradient, making the whole process exact and more efficient.