Imperial College London


Faculty of EngineeringDepartment of Computing

Chair in Machine Learning and Pattern Recognition



m.bronstein Website




569Huxley BuildingSouth Kensington Campus






BibTex format

author = {Gasparetto, A and Cosmo, L and Rodola, E and Bronstein, M and Torsello, A},
doi = {10.1109/3DV.2017.00061},
pages = {477--485},
title = {Spatial Maps: From low rank spectral to sparse spatial functional representations},
url = {},
year = {2018}

RIS format (EndNote, RefMan)

AB - © 2017 IEEE. Functional representation is a well-established approach to represent dense correspondences between deformable shapes. The approach provides an efficient low rank representation of a continuous mapping between two shapes, however under that framework the correspondences are only intrinsically captured, which implies that the induced map is not guaranteed to map the whole surface, much less to form a continuous mapping. In this work, we define a novel approach to the computation of a continuous bijective map between two surfaces moving from the low rank spectral representation to a sparse spatial representation. Key to this is the observation that continuity and smoothness of the optimal map induces structure both on the spectral and the spatial domain, the former providing effective low rank approximations, while the latter exhibiting strong sparsity and locality that can be used in the solution of large-scale problems. We cast our approach in terms of the functional transfer through a fuzzy map between shapes satisfying infinitesimal mass transportation at each point. The result is that, not only the spatial map induces a sub-vertex correspondence between the surfaces, but also the transportation of the whole surface, and thus the bijectivity of the induced map is assured. The performance of the proposed method is assessed on several popular benchmarks.
AU - Gasparetto,A
AU - Cosmo,L
AU - Rodola,E
AU - Bronstein,M
AU - Torsello,A
DO - 10.1109/3DV.2017.00061
EP - 485
PY - 2018///
SP - 477
TI - Spatial Maps: From low rank spectral to sparse spatial functional representations
UR -
ER -