Unsupervised Deep Learning for Structured Shape Matching
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We present a novel method for computing correspondences across shapes using unsupervised learning. Our method allows to compute a non-linear transformation of given descriptor functions, while optimizing for global structural properties of the resulting maps, such as their bijectivity or approximate isometry. To this end, we use the functional maps framework, and build upon the recently proposed FMNet architecture for descriptor learning. Unlike the method proposed in that work, however, we show that learning can be done in a purely unsupervised setting, without having access to any ground truth correspondences. This results in a very general shape matching method, which can be used to establish correspondences within shape collections or even just a single shape pair, without any prior information. We demonstrate on a wide range of challenging benchmarks, that our method leads to significant improvement compared to the existing axiomatic methods and achieves comparable, and in some cases superior results to even the supervised learning techniques.
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