Elastic Net Constraints for Shape Matching

@article{Rodol2013ElasticNC,
  title={Elastic Net Constraints for Shape Matching},
  author={E. Rodol{\`a} and A. Torsello and T. Harada and Y. Kuniyoshi and D. Cremers},
  journal={2013 IEEE International Conference on Computer Vision},
  year={2013},
  pages={1169-1176}
}
We consider a parametrized relaxation of the widely adopted quadratic assignment problem (QAP) formulation for minimum distortion correspondence between deformable shapes. In order to control the accuracy/sparsity trade-off we introduce a weighting parameter on the combination of two existing relaxations, namely spectral and game-theoretic. This leads to the introduction of the elastic net penalty function into shape matching problems. In combination with an efficient algorithm to project onto… Expand
Relaxations for Minimizing Metric Distortion and Elastic Energies for 3D Shape Matching
We present two methods for non-rigid shape matching. Both methods formulate shape matching as an energy minimization problem, where the energy measures distortion of the metric defined on the shapesExpand
Partial Matching of Deformable Shapes
TLDR
This paper presents the details of the dataset, the adopted evaluation measures, and shows thorough comparisons among all competing methods in this benchmark, the biggest and most challenging of its kind. Expand
Matching of Deformable Shapes with Topological Noise
TLDR
This track of the SHREC'16 contest evaluates shape matching algorithms that operate on 3D shapes under synthetically produced topological changes and describes the different methods and the contest results. Expand
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, weExpand
Consistent Partial Matching of Shape Collections via Sparse Modeling
TLDR
A novel approach to obtain consistent matches without requiring initial pairwise solutions to be given as input is introduced by optimizing a joint measure of metric distortion directly over the space of cycle‐consistent maps. Expand
Applying Random Forests to the Problem of Dense Non-rigid Shape Correspondence
TLDR
This work introduces a novel dense shape matching method for deformable, three-dimensional shapes which achieves significant improvements over the baseline approach and obtains state-of-the-art results while keeping a low computational cost. Expand
Matching Deformable Objects in Clutter
TLDR
This work considers the problem of deformable object detection and dense correspondence in cluttered 3D scenes using the functional maps framework, and seeks for the most regular nearly-isometric parts in the model and the scene that minimize correspondence error. Expand
Fully Spectral Partial Shape Matching
TLDR
An efficient procedure for calculating partial dense intrinsic correspondence between deformable shapes performed entirely in the spectral domain is proposed and a variant of the JAD problem with an appropriately modified coupling term allows to construct quasi‐harmonic bases localized on the latent corresponding parts. Expand
Partial Functional Correspondence
TLDR
P perturbation analysis is used to show how removal of shape parts changes the Laplace–Beltrami eigenfunctions, and exploit it as a prior on the spectral representation of the correspondence. Expand
Dense Non-rigid Shape Correspondence Using Random Forests
TLDR
A shape matching method that produces dense correspondences tuned to a specific class of shapes and deformations that achieves significant improvements over the baseline approach and obtains state-of-the-art results while keeping short computation times. Expand
...
1
2
3
4
5
...

References

SHOWING 1-10 OF 20 REFERENCES
A game-theoretic approach to deformable shape matching
TLDR
This paper adopts the recently introduced alternative L1 relaxation of the QAP based on the principles of game theory and relates it to the Gromov and Lipschitz metrics between metric spaces and demonstrates on state-of-the-art benchmarks that the proposed approach is capable of finding very accurate sparse correspondences between deformable shapes. Expand
Geometrically consistent elastic matching of 3D shapes: A linear programming solution
TLDR
Experimental results demonstrate that the proposed LP relaxation allows to compute highquality matchings which reliably put into correspondence articulated 3D shapes, and a quantitative evaluation shows improvements over existing works. Expand
A Condition Number for Non‐Rigid Shape Matching
TLDR
The notion of the shape condition number is introduced, which captures the intuition that some shapes are inherently more difficult to match against than others and makes a connection between the symmetry of a given shape and the stability of any method used to match it while optimizing a given distortion measure. Expand
Dense non-rigid surface registration using high-order graph matching
TLDR
The novelty of this paper includes casting 3D surface registration into a graph matching problem that combines both geometric and appearance similarities and intrinsic embedding information, the first implementation of high-order graph matching algorithm that solves a non-convex optimization problem, and an efficient two-stage optimization approach to constrain the search space for dense surface registration. Expand
Efficient Learning of Label Ranking by Soft Projections onto Polyhedra
TLDR
This work discusses the problem of learning to rank labels from a real valued feedback associated with each label and describes an efficient algorithm, called SOPOPO, for solving the reduced problem by employing a soft projection onto the polyhedron defined by a reduced set of constraints. Expand
SHREC 2010: robust correspondence benchmark
TLDR
The SHREC’10 robust correspondence benchmark results are reported, which allow evaluating how correspondence algorithms cope with certain classes of transformations and what is the strength of the transformations that can be dealt with. Expand
Convex Optimization & Euclidean Distance Geometry
Optimization is the science of making a best choice in the face of conflicting requirements. Any convex optimization problem has geometric interpretation. If a given optimization problem can beExpand
Möbius voting for surface correspondence
TLDR
A Möbius Voting algorithm that iteratively produces "votes" for predicted correspondences between the mutually closest points with magnitude representing their estimated deviation from isometry, which is converted to a permutation matrix with simple matrix operations and output as a discrete set of point correspondences with confidence values. Expand
A spectral technique for correspondence problems using pairwise constraints
  • M. Leordeanu, M. Hebert
  • Mathematics, Computer Science
  • Tenth IEEE International Conference on Computer Vision (ICCV'05) Volume 1
  • 2005
TLDR
An efficient spectral method for finding consistent correspondences between two sets of features by using the principal eigenvector of M and imposing the mapping constraints required by the overall correspondence mapping. Expand
Generalized multidimensional scaling: A framework for isometry-invariant partial surface matching
TLDR
The generalized multidimensional scaling algorithm is introduced, a computationally efficient continuous optimization algorithm for finding the least distortion embedding of one surface into another that allows for both full and partial surface matching. Expand
...
1
2
...