Image segmentation and edge enhancement with stabilized inverse diffusion equations

We introduce a family of first-order multidimensional ordinary differential equations (ODE's) with discontinuous right-hand sides and demonstrate thei r applicability in image processing. An equation belonging to this family i s an inverse diffusion everywhere except at local extrema, where some stabi lization is introduced. For this reason, we call these equations "stabilize d inverse diffusion equations" (SIDE's), Existence and uniqueness of soluti ons, as well as stability, are proven for SIDE's, A SIDE in one spatial dim ension may be interpreted as a limiting case of a semi-discretized Perona-M alik equation [14], [15], In an experimental section, SIDE's are shown to s uppress noise while sharpening edges present in the input signal, Their app lication to image segmentation is also demonstrated.