Improved Recursive Geodesic Distance Computation for Edge Preserving Filter

All known recursive filters based on the geodesic distance affinity are realized by two 1D recursions applied in two orthogonal directions of the image plane. The 2D extension of the filter is not valid and has theoretically drawbacks, which lead to known artifacts. In this paper, a maximum influence propagation method is proposed to approximate the 2D extension for the geodesic distance-based recursive filter. The method allows to partially overcome the drawbacks of the 1D recursion approach. We show that our improved recursion better approximates the true geodesic distance filter, and the application of this improved filter for image denoising outperforms the existing recursive implementation of the geodesic distance. As an application, we consider a geodesic distance-based filter for image denoising. Experimental evaluation of our denoising method demonstrates comparable and for several test images better results, than state-of-the-art approaches, while our algorithm is considerably faster with computational complexity O(8P).