We present new continuous variants of the Geman-McClure model and the Hebert-Leahy model for image restoration, where the energy is given by the nonconvex function x bar right arrow x(2)/(1+x(2)) or x bar right arrow log(1+x(2)), respectively. In addition to studying these models' Gamma-convergence, we consider their point-wise behaviour when the scale of convolution tends to zero. In both cases the limit is the Mumford-Shah functional.