Spectral analysis on a triangle mesh gained its popularity in shape retrieval due to the success of shape-DNA, which is easy to compute yet can achieve an accuracy of over 90 percent in some tests. The idea of bringing wavelet transforms into this area is straightforward, but requires careful design to outperform its precedents. One consideration would be similar to cshape-DNA, that is, a compact version of shape-DNA where the Fourier transformation of the shape-DNA is used to further reduce redundancy of the original shape signature. However, the authors take a second approach by directly building wavelets on the mesh to obtain dense descriptors per vertex (from here we can see the algorithm also only works on manifolds just like the shape-DNA). Nevertheless, this is only one third of the story.

The wavelet features were further grouped into clusters using a k-means algorithm (nothing fancy here) to reduce the number. A geodesic-aware bags-of-features approach was adopted to build the final global descriptor from the clusters before feeding to a support vector machine (SVM) for classification. Although I am concerned about the time performance of the proposed pipeline compared to others, all of the hard work paid off by contributing to an accuracy of greater than 95 percent on public SHREC datasets by tuning just a couple of parameters.

The paper has a very concrete introduction to spectral-based approaches for shape recognition. Besides, it is good to see some engineering work like this while many researchers are moving toward data-driven approaches. Although the authors do not say how they would improve the algorithm in the future, I think it is worthwhile to try mesh segmentation using the wavelet descriptors or the mid-level features after clustering. Using the geodesic-aware bags-of-features approach, directly building a graph of the mid-level features for shape retrieval would also be feasible.