Convergence speed of deformable models

We propose a formal framework, based upon statistical results about empirical processes, to study the asymptotic behavior of snakes (or other deformable models) when precision increases. First results include sufficient conditions for ensuring weak O(1/√n) convergence to the asymptotic value, suggesting modifications of curvature-based regularization. Strong assumptions of our work are perfectness of gradient descent (at least for some results) and independence of noise among pixels. We show that classical tools based upon shattering coefficients only conclude to convergence in 1/(⁴ √n)