# Improved Laplacian smoothing of noisy surface meshes

I have a question regarding Laplacian Smoothing of meshes and in particular the paper "Improved Laplacian smoothing of noisy surface meshes" by J. Vollmer in the early 2000's.

What is the reason for shrinkage after Laplacian Smoothing on noisy surface meshes?

• Hi Jay. The stack exchange sites are question and answer sites. While it can happen as a side effect, they are not meant for making connections or for having open ended conversations. I would recomend asking a specific question about something you are having trouble understanding, and then if you get an answer, use the site's chat feature to connect with the individual. Voting to close this question as is, since it's off topic, but please feel free to modify it into a specific question about the technique and it will be re-opened! Dec 13, 2016 at 22:51
• Thank you I shall revise as follows. What is the reason of SHRINKAGE after Laplacian Smoothing on noisy surface meshes. But this requires someone who is expert on the techniques, right?
– Jay
Dec 14, 2016 at 18:28

## 1 Answer

This is a quite common property of smoothing in 3D. When you have some data and you smooth it out you get some kind of average of the local variation. And this works fine, and stably, in one dimensional graphs.

But when your entire data set is being smoothed over its coordinates the neighboring coordinates drag your data with them. Those again are dragged by their neighbors. The net effect is that the local variation of the surface as a whole is dragging itself towards an average that is stable in the smoothing operation itself. This will cause shrinkage because a closed object as a whole has a local average that is towards the common center of all the points in operation. Even in cases where you go locally outwards you are eventually caught up with the edges that drag you inwards.

In other words there is no structure to keep the surface locked to its place. The tendency to drag towards the center eventually wins because there is nothing to counteract this. There just simply are more opportunities to go inward than outward.

• Thank you joojaa - you seem to know what you are talking about. If I may ask, have you coded Laplacian Smoothing in C++? How can I reach out to you for technical help?
– Jay
Jan 7, 2017 at 18:02
• Is there a way to contact members privately? I am trying to get some help from "joojaa".
– Jay
Jan 12, 2017 at 18:13
• @Jay i have once done a Laplacian smoothing algorithm but in 2D. But i dont know if im very good at helping you with your code. Jan 12, 2017 at 19:11