Point cloud denoising based on tensor Tucker decomposition
This addresses noise reduction in 3D point clouds for applications like computer vision, but it is incremental as it builds on existing tensor methods with mixed performance gains.
The paper tackles point cloud denoising by representing local patches as a tensor and applying Tucker decomposition with hard thresholding to remove noise, showing it outperforms a graph Laplacian regularized algorithm at high Gaussian noise levels (σ=0.1) but is worse at lower noise levels (σ=0.04, 0.05, 0.08).
In this paper, we propose a new algorithm for point cloud denoising based on the tensor Tucker decomposition. We first represent the local surface patches of a noisy point cloud to be matrices by their distances to a reference point, and stack the similar patch matrices to be a 3rd order tensor. Then we use the Tucker decomposition to compress this patch tensor to be a core tensor of smaller size. We consider this core tensor as the frequency domain and remove the noise by manipulating the hard thresholding. Finally, all the fibers of the denoised patch tensor are placed back, and the average is taken if there are more than one estimators overlapped. The experimental evaluation shows that the proposed algorithm outperforms the state-of-the-art graph Laplacian regularized (GLR) algorithm when the Gaussian noise is high ($σ=0.1$), and the GLR algorithm is better in lower noise cases ($σ=0.04, 0.05, 0.08$).