Nonlinear diffusion for early vision

We derive the fundamental constraints of using nonlinear diffusion in early vision. The deformed images from continuous nonlinear diffusion form nonlinear scale space. We first formularize some criteria of this space, and then, to obey these criteria, we derive the constraints on diffusion coefficient. We show that the "positive coefficient", which was considered as the only constraint in most of the literature, is not sufficient because it may introduce spurious edges. We propose diffusing the derivatives of the image, and prove that in these cases, the "positive coefficient" guarantees that no new extreme nor edge will be generated.