In this paper, the problem of denoising and occlusion restoration of 3-D range data based on dictionary learning and sparse representation methods is explored. We apply these techniques after converting the noisy 3-D surface into one or more images. We present experimental results on the proposed approaches.

In this paper, we focus on the use of random projections as a dimensionality reduction tool for sampled manifolds in high- dimensional Euclidean spaces. We show that geodesic paths approximations from nearest neighbors Euclidean distances are well-preserved by Gaussian projections and we characterize the distribution of geodesic lengths in the reduced dimensional point cloud. A stylized application to a real-world data set of human faces is presented to validate our theoretical findings.

In this letter, improvements to the nonlocal means image denoising method introduced by Buades et al. are presented. The original nonlocal means method replaces a noisy pixel by the weighted average of pixels with related surrounding neighborhoods. While producing state-of-the-art denoising results, this method is computationally impractical. In order to accelerate the algorithm, we introduce filters that eliminate unrelated neighborhoods from the weighted average. These filters are based on local average gray values and gradients, preclassifying neighborhoods and thereby reducing the original quadratic complexity to a linear one and reducing the influence of less-related areas in the denoising of a given pixel. We present the underlying framework and experimental results for gray level and color images as well as for video.