Matching articulated shapes represented by voxel-sets reduces to maximal
sub-graph isomorphism when each set is described by a weighted graph. Spectral
graph theory can be used to map these graphs onto lower dimensional spaces and
match shapes by aligning their embeddings in virtue of their invariance to
change of pose. Classical graph isomorphism schemes relying on the ordering of
the eigenvalues to align the eigenspaces fail when handling large data-sets or
noisy data. We derive a new formulation that finds the best alignment between
two congruent $K$-dimensional sets of points by selecting the best subset of
eigenfunctions of the Laplacian matrix. The selection is done by matching
eigenfunction signatures built with histograms, and the retained set provides a
smart initialization for the alignment problem with a considerable impact on
the overall performance. Dense shape matching casted into graph matching
reduces then, to point registration of embeddings under orthogonal
transformations; the registration is solved using the framework of unsupervised
clustering and the EM algorithm. Maximal subset matching of non identical
shapes is handled by defining an appropriate outlier class. Experimental
results on challenging examples show how the algorithm naturally treats changes
of topology, shape variations and different sampling densities.

该研究论文提出了一种基于图形而非基于点的匹配算法，通过使用谱图理论将图形映射到低维空间来对齐形状和避免姿态变化带来的不变性问题，该算法通过直方图匹配来选择拉普拉斯矩阵的最佳特征函数子集以提高性能，并将形状匹配转化为点注册的问题。