Kernel Averaging Filter

Nonparametric kernel estimation techniques have been widely used in many computer vision and pattern recognition problems. Among them, the mean shift iterative procedure is a highly successful one. In this paper, we first theoretically prove that the mean shift method is identical to the least-square error reconstruction of the result of averaging filter performed in the nonlinear feature space. We then combine this idea with the kernel principal component analysis (KPCA) algorithm, and derive the kernel averaging filter (KAF). KAF is much less sensitive to the noise and can largely keep the sharpness of the image. Image filtering experiments demonstrate the excellent performance of KAF.