45,724 research outputs found
SHREC'16: partial matching of deformable shapes
Matching deformable 3D shapes under partiality transformations is a challenging problem that has received limited focus in the computer vision and graphics communities. With this benchmark, we explore and thoroughly investigate the robustness of existing matching methods in this challenging task. Participants are asked to provide a point-to-point correspondence (either sparse or dense) between deformable shapes undergoing different kinds of partiality transformations, resulting in a total of 400 matching problems to be solved for each method - making this benchmark the biggest and most challenging of its kind. Five matching algorithms were evaluated in the contest; this paper presents the details of the dataset, the adopted evaluation measures, and shows thorough comparisons among all competing methods
Inducing a map on homology from a correspondence
We study the homomorphism induced in homology by a closed correspondence
between topological spaces, using projections from the graph of the
correspondence to its domain and codomain. We provide assumptions under which
the homomorphism induced by an outer approximation of a continuous map
coincides with the homomorphism induced in homology by the map. In contrast to
more classical results we do not require that the projection to the domain have
acyclic preimages. Moreover, we show that it is possible to retrieve correct
homological information from a correspondence even if some data is missing or
perturbed. Finally, we describe an application to combinatorial maps that are
either outer approximations of continuous maps or reconstructions of such maps
from a finite set of data points
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