194 research outputs found
Discrete schemes for Gaussian curvature and their convergence
In this paper, several discrete schemes for Gaussian curvature are surveyed.
The convergence property of a modified discrete scheme for the Gaussian
curvature is considered. Furthermore, a new discrete scheme for Gaussian
curvature is resented. We prove that the new scheme converges at the regular
vertex with valence not less than 5. By constructing a counterexample, we also
show that it is impossible for building a discrete scheme for Gaussian
curvature which converges over the regular vertex with valence 4. Finally,
asymptotic errors of several discrete scheme for Gaussian curvature are
compared
Point-wise Map Recovery and Refinement from Functional Correspondence
Since their introduction in the shape analysis community, functional maps
have met with considerable success due to their ability to compactly represent
dense correspondences between deformable shapes, with applications ranging from
shape matching and image segmentation, to exploration of large shape
collections. Despite the numerous advantages of such representation, however,
the problem of converting a given functional map back to a point-to-point map
has received a surprisingly limited interest. In this paper we analyze the
general problem of point-wise map recovery from arbitrary functional maps. In
doing so, we rule out many of the assumptions required by the currently
established approach -- most notably, the limiting requirement of the input
shapes being nearly-isometric. We devise an efficient recovery process based on
a simple probabilistic model. Experiments confirm that this approach achieves
remarkable accuracy improvements in very challenging cases
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