# Point cloud denoising based on tensor Tucker decomposition

## TL;DR

This paper introduces a novel point cloud denoising method using tensor Tucker decomposition, which effectively reduces noise in high Gaussian noise scenarios by leveraging local surface patch representations and frequency domain manipulation.

## Contribution

The paper presents a new tensor Tucker decomposition-based algorithm for point cloud denoising that outperforms existing methods in high noise conditions.

## Key findings

- Outperforms state-of-the-art in high Gaussian noise ($\sigma=0.1$)
- Effective noise removal through frequency domain manipulation
- Competitive with existing methods in lower noise scenarios

## Abstract

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 ($\sigma=0.1$), and the GLR algorithm is better in lower noise cases ($\sigma=0.04, 0.05, 0.08$).