149 research outputs found
On Nonrigid Shape Similarity and Correspondence
An important operation in geometry processing is finding the correspondences
between pairs of shapes. The Gromov-Hausdorff distance, a measure of
dissimilarity between metric spaces, has been found to be highly useful for
nonrigid shape comparison. Here, we explore the applicability of related shape
similarity measures to the problem of shape correspondence, adopting spectral
type distances. We propose to evaluate the spectral kernel distance, the
spectral embedding distance and the novel spectral quasi-conformal distance,
comparing the manifolds from different viewpoints. By matching the shapes in
the spectral domain, important attributes of surface structure are being
aligned. For the purpose of testing our ideas, we introduce a fully automatic
framework for finding intrinsic correspondence between two shapes. The proposed
method achieves state-of-the-art results on the Princeton isometric shape
matching protocol applied, as usual, to the TOSCA and SCAPE benchmarks
Learning Generative Models across Incomparable Spaces
Generative Adversarial Networks have shown remarkable success in learning a
distribution that faithfully recovers a reference distribution in its entirety.
However, in some cases, we may want to only learn some aspects (e.g., cluster
or manifold structure), while modifying others (e.g., style, orientation or
dimension). In this work, we propose an approach to learn generative models
across such incomparable spaces, and demonstrate how to steer the learned
distribution towards target properties. A key component of our model is the
Gromov-Wasserstein distance, a notion of discrepancy that compares
distributions relationally rather than absolutely. While this framework
subsumes current generative models in identically reproducing distributions,
its inherent flexibility allows application to tasks in manifold learning,
relational learning and cross-domain learning.Comment: International Conference on Machine Learning (ICML
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
Gromov-Wasserstein Transfer Operators
Gromov-Wasserstein (GW) transport is inherently invariant under isometric
transformations of the data. Having this property in mind, we propose to
estimate dynamical systems by transfer operators derived from GW transport
plans, when merely the initial and final states are known. We focus on entropy
regularized GW transport, which allows to utilize the fast Sinkhorn algorithm
and a spectral clustering procedure to extract coherent structures. Moreover,
the GW framework provides a natural quantitative assessment on the
shape-coherence of the extracted structures. We discuss fused and unbalanced
variants of GW transport for labelled and noisy data, respectively. Our models
are verified by three numerical examples of dynamical systems with governing
rotational forces
Comparing Morse Complexes Using Optimal Transport: An Experimental Study
Morse complexes and Morse-Smale complexes are topological descriptors popular
in topology-based visualization. Comparing these complexes plays an important
role in their applications in feature correspondences, feature tracking,
symmetry detection, and uncertainty visualization. Leveraging recent advances
in optimal transport, we apply a class of optimal transport distances to the
comparative analysis of Morse complexes. Contrasting with existing comparative
measures, such distances are easy and efficient to compute, and naturally
provide structural matching between Morse complexes. We perform an experimental
study involving scientific simulation datasets and discuss the effectiveness of
these distances as comparative measures for Morse complexes. We also provide an
initial guideline for choosing the optimal transport distances under various
data assumptions.Comment: IEEE Visualization Conference (IEEE VIS) Short Paper, accepted, 2023;
supplementary materials:
http://www.sci.utah.edu/~beiwang/publications/GWMC_VIS_Short_BeiWang_2023_Supplement.pd
NetLSD: Hearing the Shape of a Graph
Comparison among graphs is ubiquitous in graph analytics. However, it is a
hard task in terms of the expressiveness of the employed similarity measure and
the efficiency of its computation. Ideally, graph comparison should be
invariant to the order of nodes and the sizes of compared graphs, adaptive to
the scale of graph patterns, and scalable. Unfortunately, these properties have
not been addressed together. Graph comparisons still rely on direct approaches,
graph kernels, or representation-based methods, which are all inefficient and
impractical for large graph collections.
In this paper, we propose the Network Laplacian Spectral Descriptor (NetLSD):
the first, to our knowledge, permutation- and size-invariant, scale-adaptive,
and efficiently computable graph representation method that allows for
straightforward comparisons of large graphs. NetLSD extracts a compact
signature that inherits the formal properties of the Laplacian spectrum,
specifically its heat or wave kernel; thus, it hears the shape of a graph. Our
evaluation on a variety of real-world graphs demonstrates that it outperforms
previous works in both expressiveness and efficiency.Comment: KDD '18: The 24th ACM SIGKDD International Conference on Knowledge
Discovery & Data Mining, August 19--23, 2018, London, United Kingdo
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