Combining Curvature Motion and Edge-Preserving Denoising

In this paper we investigate a family of partial di erential equations (PDEs) for image processing which can be regarded as isotropic nonlinear di usion with an additional factor on the right-hand side. The one-dimensional analogues to this lter class have been motivated as scaling limits of one-dimensional adaptive averaging schemes. In 2-D, mean curvature motion is one of the most prominent examples of this family of PDEs. Other representatives of the lter class combine properties of curvature motion with the enhanced edge preservation of Perona-Malik di usion. It becomes appearent that these PDEs require a careful discretisation. Numerical experiments display the di erences between Perona-Malik di usion, classical mean curvature motion and the proposed extensions. We consider, for example, enhanced edge sharpness, the question of morphological invariance, and the behaviour with respect to noise.