THE PERONA-MALIK PARADOX

The Perona-Malik equation is a formally ill-posed parabolic equation f or which simple discretizations are nevertheless numerically found to be stable. After discussing the background of this paradox in computer vision, this paper shows the nonexistence of weak solutions even in t hose cases where computations are successful, and introduces a notion of generalized solutions for this equation, which do evolve smoothly a nd possess many of the features of numerical calculations.