MapTree: Recovering Multiple Solutions in the Space of Maps

@article{Ren2020MapTreeRM,
  title={MapTree: Recovering Multiple Solutions in the Space of Maps},
  author={Jing Ren and Simone Melzi and Maks Ovsjanikov and Peter Wonka},
  journal={ACM Trans. Graph.},
  year={2020},
  volume={39},
  pages={264:1-264:17}
}
In this paper we propose an approach for computing multiple high-quality near-isometric maps between a pair of 3D shapes. Our method is fully automatic and does not rely on user-provided landmarks or descriptors. This allows us to analyze the full space of maps and extract multiple diverse and accurate solutions, rather than optimizing for a single optimal correspondence as done in previous approaches. To achieve this, we propose a compact tree structure based on the spectral map representation… Expand
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References

SHOWING 1-10 OF 91 REFERENCES
Continuous and orientation-preserving correspondences via functional maps
TLDR
This work shows how orientation preservation can be formulated directly in the functional (spectral) domain without using landmark or region correspondences and without relying on external symmetry information to obtain functional maps that promote orientation preservation, even when using descriptors that are invariant to orientation changes. Expand
Functional maps
TLDR
A novel representation of maps between pairs of shapes that allows for efficient inference and manipulation and supports certain algebraic operations such as map sum, difference and composition, and enables a number of applications, such as function or annotation transfer without establishing point-to-point correspondences. Expand
Unsupervised Deep Learning for Structured Shape Matching
We present a novel method for computing correspondences across 3D shapes using unsupervised learning. Our method computes a non-linear transformation of given descriptor functions, while optimizingExpand
ZoomOut: Spectral Upsampling for Efficient Shape Correspondence
TLDR
It is shown that high quality maps can be obtained even if the input correspondences are noisy or are encoded by a small number of coefficients in a spectral basis, and the method is both robust to noisy input and scalable with respect to shape complexity. Expand
Consistent Shape Matching via Coupled Optimization
TLDR
This work proposes a new method for computing accurate point‐to‐point mappings between a pair of triangle meshes given imperfect initial correspondences, and provides quantitative and qualitative comparison of the method with several existing techniques, showing that it provides a powerful matching tool when accurate and consistent correspondences are required. Expand
Point-wise Map Recovery and Refinement from Functional Correspondence
TLDR
This paper analyzes the general problem of point-wise map recovery from arbitrary functional maps and devise an efficient recovery process based on a simple probabilistic model that achieves remarkable accuracy improvements in very challenging cases. Expand
Blended intrinsic maps
TLDR
This approach enables algorithms that leverage efficient search procedures, yet can provide the flexibility to handle large deformations, and solves a global optimization problem that selects candidate maps based both on their area preservation and consistency with other selected maps. Expand
Finding the M-best consistent correspondences between 3D symmetric objects
TLDR
A novel algorithm is proposed that finds multiple probable solutions for consistent shape correspondences between two 3D symmetric objects and lets the user select one of them for an application-specific purpose. Expand
Informative Descriptor Preservation via Commutativity for Shape Matching
TLDR
This paper shows that considering descriptors as linear operators acting on functions through multiplication, rather than as simple scalar‐valued signals, allows to extract significantly more information from a given descriptor and ultimately results in a more accurate functional map estimation. Expand
Entropic metric alignment for correspondence problems
TLDR
This work presents an algorithm for probabilistic correspondence that optimizes an entropy-regularized Gromov-Wasserstein (GW) objective that is compact, provably convergent, and applicable to any geometric domain expressible as a metric measure matrix. Expand
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