Möbius voting for surface correspondence

@article{Lipman2009MbiusVF,
  title={M{\"o}bius voting for surface correspondence},
  author={Yaron Lipman and Thomas A. Funkhouser},
  journal={ACM Trans. Graph.},
  year={2009},
  volume={28},
  pages={72}
}
The goal of our work is to develop an efficient, automatic algorithm for discovering point correspondences between surfaces that are approximately and/or partially isometric. Our approach is based on three observations. First, isometries are a subset of the Möbius group, which has low-dimensionality -- six degrees of freedom for topological spheres, and three for topological discs. Second, computing the Möbius transformation that interpolates any three points can be computed in closed-form… 

3D Shape correspondence by isometry-driven greedy optimization

  • Y. SahilliogluY. Yemez
  • Computer Science, Mathematics
    2010 IEEE Computer Society Conference on Computer Vision and Pattern Recognition
  • 2010
An automatic method is presented that establishes 3D correspondence between isometric shapes in a fast and robust manner at a relatively coarse level as imposed by the patch radius and explicitly minimize the isometry cost via an iterative greedy algorithm in the original 3D Euclidean space.

Möbius Transformations For Global Intrinsic Symmetry Analysis

The algorithm is able to find intrinsic symmetries for a wide variety of object types with moderate deviations from perfect symmetry and the main advantages stem from the stability of the AGD in predicting potential symmetric point features and the low dimensionality of the Möbius group for enumerating potential self‐mappings.

Automatic Alignment of Genus-Zero Surfaces

  • P. KoehlJ. Hass
  • Computer Science
    IEEE Transactions on Pattern Analysis and Machine Intelligence
  • 2014
A new algorithm is presented that provides a constructive way to conformally warp a triangular mesh of genus zero to a destination surface with minimal metric deformation, as well as a means to

Finding Surface Correspondences Using Symmetry Axis Curves

An automatic algorithm for finding a correspondence map between two 3D surfaces is proposed, finding that it is superior to previous methods in cases where two surfaces have different overall shapes but similar reflective symmetry axes, a common case in computer graphics.

Stable Region Correspondences Between Non‐Isometric Shapes

This paper considers the problem of finding meaningful correspondences between 3D models that are related but not necessarily very similar, and provides an algorithm to solve this problem that mimics the power method.

Isometric Shape Correspondence Based on the Geodesic Structure

A novel approach to find the correspondence between two nearly isometric shapes by solving the correspondence problem as some minimum cost max flow problems MCFP with shortest path faster algorithm SPFA, and combining the results of these MCFP as the last correspondence result.

One Point Isometric Matching with the Heat Kernel

It is shown that under mild genericity conditions, a single correspondence can be used to recover an isometry defined on entire shapes, and thus the space of all isometries can be parameterized by one correspondence between a pair of points.

Inter-surface maps via constant-curvature metrics

A novel approach to represent maps between two discrete surfaces of the same genus and to minimize intrinsic mapping distortion, built upon the fact that such metrics exist on surfaces of arbitrary topology, without the need for any cuts or cones.

Compatible intrinsic triangulations

This work proposes a simple method utilizing intrinsic triangulations, operating directly on the original surfaces without going through any intermediate domains such as a plane or a sphere, which is robust enough to be used within a similar second-order optimization framework as was used previously in the literature.

Semantic isometry for 3-D shape correspondence

The semantic isometry to three-dimensional shape correspondence is introduced and a new framework called detection–recognition–correspondence is proposed that can greatly improve the corresponding accuracy over the existing state-of-the-art algorithms.
...

References

SHOWING 1-10 OF 51 REFERENCES

A Method for Registration of 3-D Shapes

A general-purpose, representation-independent method for the accurate and computationally efficient registration of 3-D shapes including free-form curves and surfaces based on the iterative closest point (ICP) algorithm.

The Correlated Correspondence Algorithm for Unsupervised Registration of Nonrigid Surfaces

An unsupervised algorithm for registering 3D surface scans of an object undergoing significant deformations that can be used for compelling computer graphics tasks such as interpolation between two scans of a non-rigid object and automatic recovery of articulated object models.

Robust global registration

This work presents an algorithm for the automatic alignment of two 3D shapes ( data and model), without any assumptions about their initial positions, and develops a fast branch-and-bound algorithm based on distance matrix comparisons to select the optimal correspondence set and bring the two shapes into a coarse alignment.

3D Non-rigid Surface Matching and Registration Based on Holomorphic Differentials

A novel approach for generating an efficient and optimal combined matching from multiple boundary-constrained conformal parameterizations for multiply connected domains, especially for 3D non-rigid surfaces with significantly inconsistent boundaries is described.

Shape matching and object recognition using low distortion correspondences

This work approaches recognition in the framework of deformable shape matching, relying on a new algorithm for finding correspondences between feature points, and shows results for localizing frontal and profile faces that are comparable to special purpose approaches tuned to faces.

A new point matching algorithm for non-rigid registration

On Bending Invariant Signatures for Surfaces

This work presents a method to construct a bending invariant signature for isometric surfaces, an embedding of the geometric structure of the surface in a small dimensional Euclidesan space in which geodesic distances are approximated by Euclidean ones.

Generalizing the Hough transform to detect arbitrary shapes

Non-Rigid Spectral Correspondence of Triangle Meshes

An algorithm for finding a meaningful vertex-to-vertex correspondence between two triangle meshes, which is designed to handle general non-rigid transformations, outperforms previous spectral methods, as well as schemes that compute correspondence in the spatial domain via non- Rigid iterative closest points or the use of local shape descriptors.

Conformal Geometry and Its Applications on 3D Shape Matching, Recognition, and Stitching

A novel and computationally efficient shape matching framework by using least-squares conformal maps is proposed by comparing the resulting 2D parametric maps, which are stable, insensitive to resolution changes and robust to occlusion, and noise.
...