P(x) Harmonic Surface and Its Projection for Noise Removal

Over the last two decades, many image processing problems have been modeled by partial differential equations (PDEs), such as restoration and segmentation. Due to good performance at controlling the trade-off between noise removal and edge-preserving, second-order PDEs play leading role in image restoration. The dilemma for second-order PDEs is the so-called staircasing effect. One remedy for this issue is the fourth-order PDEs, but the fourth-order PDEs suffer from the problem of oversmoothing the edges. In this paper, a novel PDE is proposed based on minimal surface and p(x) harmonic maps. The proposed model behaves like TV model at edge regions while like heat transfer equation within homogeneous regions. The proposed model is further projected to the normal direction of a smoothed version of the original image for the purpose of edge preserving. Several experiments have been conducted and promising results are observed.