Surface reconstruction: GNCs and MFA

The reconstruction of noise corrupted surfaces can be inferred by methodologies such as Bayesian estimation and minimum description length. Both of these imply a formulation where the reconstruction minimizes a functional. Often this functional is non convex and the minimum cannot be found by simple gradient methods. The paper concerns functionals with quadratic data term, criteria for such functionals to be convex, and the variational approach of minimizing non convex functionals. Initial convexity of the approximating functional is considered to be a critical point. Two fully automatic methods of generating convex functionals are presented. They are based on Gaussian convolution and are compared to the Blake-Zisserman graduated non convexity (GNC) (A. Blake, A. Zisserman, 1987) and G.L. Bilbro et al. (1992) and D. Geiger and F. Girosi´s (1991) mean field annealing (MFA) of the weak membrane