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foundations of COmputational similarity geoMETtry

Final Report Summary - COMET (foundations of COmputational similarity geoMETtry)

COMET has developed into a unifying framework of computational similarity geometry that extends the theoretical metric model and provides efficient numerical and computational tools for the representation and computation of generic similarity models. These include:

- a framework for multimodal similarity models, which has been successfully applied to different fields such as data clustering, biomedical imaging, shape analysis, and colormap conversions;

- efficient similarity-preserving and multimodal hashing algorithms;

- a general method for robust multidimensional scaling based on non-smooth manifold optimisation;

- algorithms for robust image descriptors and video copy detection, as well as multimedia search.

We pioneered the use of neural networks for hashing, multi-modal similarity-sensitive hashing (that is currently used as a reference in the field), the use of joint diagonalization for spectral analysis of multimodal data, and the concept of geometric deep learning and intrinsic convolutional neural networks, that achieve state-of-the-art results in several challenging shape analysis applications.

Results have been published in several journal/conference papers as well as a book chapter and one patent. Furthermore, our algorithms have been adopted for several industrial applications; in particular, the similarity-sensitive hashing method is used by the company Videocites for detection of illegal video copies on the web; the same technology is currently brought into a commercial prototype as ERC PoC grant VideoPlus. The works on geometric deep learning (first formulation of intrinsic convolutional network architectures on manifolds) opened a new research field in computer graphics and vision and resulted in a following ERC Consolidator grant LEMAN.