Esedoglu, Selim2007-08-162007-08-162001-07https://hdl.handle.net/11299/3714The Perona-Malik scheme is a numerical technique for de-noising digital images without blurring object boundaries (edges). In general, solutions generated by this scheme do not satisfy a comparison principle. We identify conditions under which two solutions initially ordered remain ordered, and state (restricted) comparison principles. These allow us to study stability properties of the scheme. We also explore what these results say in the limit as the discretization size goes to 0.