79,375 research outputs found
Learning shape correspondence with anisotropic convolutional neural networks
Establishing correspondence between shapes is a fundamental problem in
geometry processing, arising in a wide variety of applications. The problem is
especially difficult in the setting of non-isometric deformations, as well as
in the presence of topological noise and missing parts, mainly due to the
limited capability to model such deformations axiomatically. Several recent
works showed that invariance to complex shape transformations can be learned
from examples. In this paper, we introduce an intrinsic convolutional neural
network architecture based on anisotropic diffusion kernels, which we term
Anisotropic Convolutional Neural Network (ACNN). In our construction, we
generalize convolutions to non-Euclidean domains by constructing a set of
oriented anisotropic diffusion kernels, creating in this way a local intrinsic
polar representation of the data (`patch'), which is then correlated with a
filter. Several cascades of such filters, linear, and non-linear operators are
stacked to form a deep neural network whose parameters are learned by
minimizing a task-specific cost. We use ACNNs to effectively learn intrinsic
dense correspondences between deformable shapes in very challenging settings,
achieving state-of-the-art results on some of the most difficult recent
correspondence benchmarks
A relaxed approach for curve matching with elastic metrics
In this paper we study a class of Riemannian metrics on the space of
unparametrized curves and develop a method to compute geodesics with given
boundary conditions. It extends previous works on this topic in several
important ways. The model and resulting matching algorithm integrate within one
common setting both the family of -metrics with constant coefficients and
scale-invariant -metrics on both open and closed immersed curves. These
families include as particular cases the class of first-order elastic metrics.
An essential difference with prior approaches is the way that boundary
constraints are dealt with. By leveraging varifold-based similarity metrics we
propose a relaxed variational formulation for the matching problem that avoids
the necessity of optimizing over the reparametrization group. Furthermore, we
show that we can also quotient out finite-dimensional similarity groups such as
translation, rotation and scaling groups. The different properties and
advantages are illustrated through numerical examples in which we also provide
a comparison with related diffeomorphic methods used in shape registration.Comment: 27 page
Influence of general convective motions on the exterior of isolated rotating bodies in equilibrium
The problem of describing isolated rotating bodies in equilibrium in General
Relativity has so far been treated under the assumption of the circularity
condition in the interior of the body. For a fluid without energy flux, this
condition implies that the fluid flow moves only along the angular direction,
i.e. there is no convection. Using this simplification, some recent studies
have provided us with uniqueness and existence results for asymptotically flat
vacuum exterior fields given the interior sources. Here, the generalisation of
the problem to include general sources is studied. It is proven that the
convective motions have no direct influence on the exterior field, and hence,
that the aforementioned results on uniqueness and existence of exterior fields
apply equally in the general case.Comment: 8 pages, LaTex, uses iopart style files. To appear in Class. Quatum
Gra
A Low-Dimensional Representation for Robust Partial Isometric Correspondences Computation
Intrinsic isometric shape matching has become the standard approach for pose
invariant correspondence estimation among deformable shapes. Most existing
approaches assume global consistency, i.e., the metric structure of the whole
manifold must not change significantly. While global isometric matching is well
understood, only a few heuristic solutions are known for partial matching.
Partial matching is particularly important for robustness to topological noise
(incomplete data and contacts), which is a common problem in real-world 3D
scanner data. In this paper, we introduce a new approach to partial, intrinsic
isometric matching. Our method is based on the observation that isometries are
fully determined by purely local information: a map of a single point and its
tangent space fixes an isometry for both global and the partial maps. From this
idea, we develop a new representation for partial isometric maps based on
equivalence classes of correspondences between pairs of points and their
tangent spaces. From this, we derive a local propagation algorithm that find
such mappings efficiently. In contrast to previous heuristics based on RANSAC
or expectation maximization, our method is based on a simple and sound
theoretical model and fully deterministic. We apply our approach to register
partial point clouds and compare it to the state-of-the-art methods, where we
obtain significant improvements over global methods for real-world data and
stronger guarantees than previous heuristic partial matching algorithms.Comment: 17 pages, 12 figure
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