Graduated nonconvexity by functional focusing

Reconstruction of noise-corrupted surfaces may be stated as a (in general nonconvex) functional minimization problem. For functionals with quadratic data term, this paper addresses the criteria for such functionals to be convex, and the variational approach for minimization. I present two automatic and general methods of approximation with convex functionals based on Gaussian convolution. They are compared to the Blake-Zisserman graduated nonconvexity (GNC) method (1987) and Bilbro et al. (1992) and Geiger and Girosi's (1991) mean field annealing (MFA) of a weak membrane.