5,790 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
Mechanics of Systems of Affine Bodies. Geometric Foundations and Applications in Dynamics of Structured Media
In the present paper we investigate the mechanics of systems of
affinely-rigid bodies, i.e., bodies rigid in the sense of affine geometry.
Certain physical applications are possible in modelling of molecular crystals,
granular media, and other physical objects. Particularly interesting are
dynamical models invariant under the group underlying geometry of degrees of
freedom. In contrary to the single body case there exist nontrivial potentials
invariant under this group (left and right acting). The concept of relative
(mutual) deformation tensors of pairs of affine bodies is discussed. Scalar
invariants built of such tensors are constructed. There is an essential novelty
in comparison to deformation scalars of single affine bodies, i.e., there exist
affinely-invariant scalars of mutual deformations. Hence, the hierarchy of
interaction models according to their invariance group, from Euclidean to
affine ones, can be considered.Comment: 50 pages, 4 figure
Quantifying the Evolutionary Self Structuring of Embodied Cognitive Networks
We outline a possible theoretical framework for the quantitative modeling of
networked embodied cognitive systems. We notice that: 1) information self
structuring through sensory-motor coordination does not deterministically occur
in Rn vector space, a generic multivariable space, but in SE(3), the group
structure of the possible motions of a body in space; 2) it happens in a
stochastic open ended environment. These observations may simplify, at the
price of a certain abstraction, the modeling and the design of self
organization processes based on the maximization of some informational
measures, such as mutual information. Furthermore, by providing closed form or
computationally lighter algorithms, it may significantly reduce the
computational burden of their implementation. We propose a modeling framework
which aims to give new tools for the design of networks of new artificial self
organizing, embodied and intelligent agents and the reverse engineering of
natural ones. At this point, it represents much a theoretical conjecture and it
has still to be experimentally verified whether this model will be useful in
practice.
Deformation of Hypersurfaces Preserving the Moebius Metric and a Reduction Theorem
A hypersurface without umbilics in the n+1 dimensional Euclidean space is
known to be determined by the Moebius metric and the Moebius second fundamental
form up to a Moebius transformation when n>2. In this paper we consider Moebius
rigidity for hypersurfaces and deformations of a hypersurface preserving the
Moebius metric in the high dimensional case n>3. When the highest multiplicity
of principal curvatures is less than n-2, the hypersurface is Moebius rigid.
Deformable hypersurfaces and the possible deformations are also classified
completely. In addition, we establish a Reduction Theorem characterizing the
classical construction of cylinders, cones, and rotational hypersurfaces, which
helps to find all the non-trivial deformable examples in our classification
with wider application in the future.Comment: 51 pages. A mistake in the proof to Theorem 9.2 has been fixed.
Accepted by Adv. in Mat
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