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?
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.