Shock filters based on implicit cluster separation

One of the classic problems in low level vision is image restoration. An important contribution toward this effort has been the development of shock filters by Osher and Rudin (1990). It performs image deblurring using hyperbolic partial differential equations. In this paper we relate the notion of cluster separation from the field of pattern recognition to the shock filter formulation. A kind of shock filter is proposed based on the idea of gradient based separation of clusters. The proposed formulation is general enough as it can allow various models of density functions in the cluster separation process. The efficacy of the method is demonstrated through various examples.