The target for this paper is using plain English to explain this paper:

https://openaccess.thecvf.com/content/ICCV2021/papers/Luo_Score-Based_Point_Cloud_Denoising_ICCV_2021_paper.pdf

Motivation

As one can see clearly that the task for this paper is denoising. The data structure to be denoised is point cloud.

Assumption and Intuition

• Point clouds are actually some sampling point from a 2D surface. Even in 3D world, we need to represent this 2D surface using at least 3 coordinates, it is still a 2D surface. However real point cloud always deviate from this surface due to noise and occlusion. As one can see in the following graph:

• Author claim that the real point cloud we get in the real world is actually some signals passing through a noisy channel. Or simply, some real data distribution $p *n$ . That is some real data distribution conv with a noise.
• Author assume that we only have a unique data distribution which. For example, there may be multiple different sofa in the world, the surface of the sofa can alternate. However, author assume that in one point cloud, there is one and only true sofa surface.
• There is a score function (Which I introduced in Yang Song’s tutorial: Yang Song’s Tutorial ) that can describe the difference between the real data distribution and the point around it. As one can see from the graph list above, it shows there is a direction. Those direction means that we can move toward to the real surface we have.

Implementation Details

1. The score estimation network
2. The object function
3. The score based denoising

Lets introduced them one by one.