This text deals with a fast growing research area. The development of the subject springs from two factors: the great expansion of nonlinear methods applied to problems in imaging and vision, and the degree to which nonlinear approaches are both using and fostering new developments in diverse areas of mathematics. It should be of interest to people working in areas of applied mathematics, as well as researchers in computer vision. It is an edited volume of original research, and has been published as a special issue of "The Journal of Mathematical Imaging and Vision" (Vol 2, Issue 2/3)