Usage of functional maps for extracting partial correspondenses and shape assembly

[ttsesm]

Dear @dongliangcao,

Congratulations for your work and thanks for sharing it with us. I have been following your work regarding the usage of functional maps and I was quite curious to understand whether it could be used for shape assembly.

In brief to understand the problem, you might have two or more pieces of an object which are matching to some part in order to assemble a complete object. So imagine that you have the following pieces of a stone:

These can be assembled together as follows:

So in principle there are specific parts of the objects that should have a bijective matching:

My question now is whether I could use functional maps in order to extract these partial bijective matching parts?

[dongliangcao]

Hi,

Thanks a lot for your interest to this work. Unfortunately, this work cannot solve the assembly problem. From the matching perspective, assembly problem is a very difficult problem, since it is a partial-to-partial matching problem with very little overlap ratio. To best of my knowledge, current functional map methods are not able to handle this problem.

Alternatively, you can search for works designed for shape/point cloud registration, since I assume shape assembly is more about find a rigid transformation to assemble shape parts. For shape/point cloud registration, I think many algorithms are specifically designed to handle partial-to-partial registration with lower overlap ratio.

Hope you can find the proper algorithm to solve this problem.

Best, Dongliang

[ttsesm]

I see, thanks a lot for your time and the feedback ;-)