Permutohedral lattice in 3D point cloud processing

Noise is inherent in digital systems. To smooth a point cloud while preserving sharp edges, a new 3D bilateral filter is proposed. It uses the point cloud normal vector in addition to color as a position vector for preserving sharp edges while smoothing the color. The bilateral blurs data while preserving strong edges. In 2D images, the concept of edge is defined by an abrupt change in color. In this paper, the 3D edge is defined as a change in color or point cloud normal vector. The 3D difference of Gaussians (3D DoG) is presented by subtracting two bilateral filters with different standard deviations in color and normal space. The new 3D normal-non-local means (NNM) filter is proposed for denoising the unstructured point cloud. In the proposed NNM filter, in the kd-tree nearest neighbor search in position vector, the normal vector is considered instead of the point color. Since it needs high dimensional Gaussian filtering, the time complexity is high. Therefore, the Permutohedral lattice is used for Gaussian processing. For high dimensional filtering of n values in d dimensions it has a time complexity of 0(d²n) and space complexity of(dn).