Topology matching for fully automatic similarity estimation of 3D shapes

By Masaki Hilaga, Y. Shinagawa, Taku Komura, T. Kunii. 2001

2,281 citations recorded by the source corpus.

Subfields: Computational Mechanics, Computer Vision and Pattern Recognition

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In Computational Mechanics

In Computer Vision and Pattern Recognition

Citations in the corpus

3D shape segmentation via shape fully convolutional networks (2017, methodology): “The three features include: average geodesic distance (AGD) [41], shape context (SC) [42] and spin image (SI) [43].”
Feature-based surface parameterization and texture mapping (2005, methodology): “R induces a Reeb graph rf , which can be used to reveal the topological and skeletal structures of S [Hilaga et al. 2001].”
Shape google: Geometric words and expressions for invariant shape retrieval (2011, methodology): “2003] and Reeb graphs [Hilaga et al. 2001; Biasotti et al. 2003; Tung and Schmitt 2005] are capable of dealing with deformations e.”
Interactive shape co-segmentation via label propagation (2014, background): “These widely recognized descriptors are the Shape Diameter Function (SDF) [31], the Conformal Factor (CF) [32], the Shape Contexts (SCs) [33,34], the Average Geodesic Distance (AGD) [35], and the geodesic distance to the base of the shape (GB) [7].”
Curve skeleton extraction from incomplete point cloud (2009, methodology): “Many algorithms for curve skeleton extraction exist [Cornea et al. 2007], dealing mostly with shapes speciﬁed by closed polygonal meshes [Hilaga et al. 2001; Katz and Tal 2003; Chuang et al. 2004; Dey and Sun 2006; Au et al. 2008].”
Consistent mesh partitioning and skeletonisation using the shape diameter function (2008, background): “Topology-based approaches as in [24] , spectral analysis as in [20], and global attributes such as average geodesic distance (AGD) [11] and Reeb-graphs [2] can support some level of consistency over pose differences of the same shape.”
3D Mesh Labeling via Deep Convolutional Neural Networks (2015, background): “Thus, we ﬁrst extract seven types of geometric features that are widely used in existing studies, including: curvature (CUR) [Gal and Cohen-Or 2006], PCA feature (PCA) [Kalogerakis et al. 2010], shape diameter function (SDF) [Shapira et al. 2010], distance from medial surface (DIS) [Liu et al. 2009]”
3D Shape Matching with 3D Shape Contexts (2003, methodology): “[23] presented a method for general 3D objects utilizing Reeb graphs based on geodesic distances between points on the mesh, which enabled a deformation invariant recognition.”
Tracking deformable objects with point clouds (2013, background): “2) Form the Reeb graph of G based on geodesic distance from an arbitrary point in the graph [9].”
3D Skeletons: A State‐of‐the‐Art Report (2016, methodology): “This gives ﬂexibility in the delineation of a skeletal line, which may be guided to follow speciﬁc characteristics, e.g. , Reeb graphs deﬁned by the integral geodesic distance [HSKK01] or by Laplace-Beltrami eigenfunctions [BMMP03].”
Joint embeddings of shapes and images via CNN image purification (2015, methodology): “Another type of method uses graph representations in order to obtain a topological description of the shape [Hilaga et al. 2001; Chen and Ouhyoung 2002; Sundar et al. 2003].”
Retrieving Articulated 3-D Models Using Medial Surfaces and Their Graph Spectra (2005, methodology): “In the domain of graph theory there have also been attempts to address the problem of 3D shape matching using representations based on Reeb graphs [24, 10].”