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Register a new userArticulated Shape Matching Using Laplacian Eigenfunctions and Unsupervised Point Registration
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Added by
Radu P Horaud
Publication date
2020
fields
Informatics Engineering
and research's language is
English
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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.
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We propose a self-supervised method for partial point set registration. While recent proposed learning-based methods have achieved impressive registration performance on the full shape observations, these methods mostly suffer from performance degradation when dealing with partial shapes. To bridge the performance gaps between partial point set registration with full point set registration, we proposed to incorporate a shape completion network to benefit the registration process. To achieve this, we design a latent code for each pair of shapes, which can be regarded as a geometric encoding of the target shape. By doing so, our model does need an explicit feature embedding network to learn the feature encodings. More importantly, both our shape completion network and the point set registration network take the shared latent codes as input, which are optimized along with the parameters of two decoder networks in the training process. Therefore, the point set registration process can thus benefit from the joint optimization process of latent codes, which are enforced to represent the information of full shape instead of partial ones. In the inference stage, we fix the network parameter and optimize the latent codes to get the optimal shape completion and registration results. Our proposed method is pure unsupervised and does not need any ground truth supervision. Experiments on the ModelNet40 dataset demonstrate the effectiveness of our model for partial point set registration.
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