maximum smooth 3d surface

Question

I have following question and I am not able to solve it (even after a lot of research).

Problem: I have a 3d point cloud and want to estimate a smooth 3d surface lying on top of my points (like throwing a thick blanket on my data-set). First of all, I estimated the maximum margins of the data-set. Now I want to estimate the smooth surface.

Currently, what I have tried either gives me a regression surface (not approximating my maximal points) or a maximum surface that is not smooth at all.

Therefore, I tried using bezier splines, the cobs package, alphashape, and interp. The best results I got so far, was by applying the transformation 1/x to my dataset and estimating the convex hull (Smooth 3d surface after transforming with 1/x, applying convex hull and retransforming). But since the data-set might change, it is not clear to me why this transformation should work in general for such kind of a problem.

I uploaded the maximal margins data-set as .Rdata file at my cloud: https://www.magentacloud.de/lnk/Q0lgRwba

I would really appreciate any help since I am looking for a solution for multiple months now :(

Best regards, sschu

Answer 1

okay, after some time I got one possible solution. It is not the best since the surface is above the point cloud and not "on top" - but at least it is something.

One can sequentially apply cobs multiple time with different conditions and different parameters for lambda (-1, or 0). Additionally, I chose the degree to be 1 since the L1 conditions is sufficient enough.

If someone got another idea, I would really appreciate this!