3D non-rigid shape similarity measure based on Fréchet distance between spectral distance distribution curve

Dan Zhang; Zhongke Wu; Xingce Wang; Chenlei Lv; Mingquan Zhou

doi:10.1007/s11042-020-09420-5

journal article Sep 03, 2020

3D non-rigid shape similarity measure based on Fréchet distance between spectral distance distribution curve

Dan Zhang

Zhongke Wu

Xingce Wang Chenlei Lv

Mingquan Zhou

Multimedia Tools and Applications Vol. 80 No. 1 pp. 615-640 · Springer Science and Business Media LLC

View at Publisher Save 10.1007/s11042-020-09420-5

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References

50

[1]

Alt H, Knauer C, Wenk C (2001) Matching polygonal curves with respect to the fréchet distance. In: Symposium on theoretical aspects of computer science, pp 63–74 10.1007/3-540-44693-1_6

[2]

Point Set Registration: Coherent Point Drift

Andriy Myronenko, Xubo Song

IEEE Transactions on Pattern Analysis and Machine... 2010 10.1109/tpami.2010.46

[3]

Anguelov D, Srinivasan P, Koller D, Thrun S, Rodgers J, Davis J (2005) SCAPE: Shape completion and animation of people. ACM Trans Graph 24(3):408–416 10.1145/1073204.1073207

[4]

Aspert N, Santa-Cruz D, Ebrahimi T (2002) MESH: Measuring errors between surfaces using the hausdorff distance. In: IEEE international conference on multimedia and expo, vol 1, pp 705–708 10.1109/icme.2002.1035879

[5]

Aubry M, Schlickewei U, Cremers D (2011) The wave kernel signature: A quantum mechanical approach to shape analysis. In: IEEE international conference on computer vision workshops, pp 1626–1633 10.1109/iccvw.2011.6130444

[6]

Axenopoulos A, Rafailidis D, Papadopoulos G, Houstis EN, Daras P (2016) Similarity search of flexible 3d molecules combining local and global shape descriptors. IEEE/ACM Trans Comput Bio Bioinforma 13(5):954–970 10.1109/tcbb.2015.2498553

[7]

Belongie S, Malik J, Puzicha J (2010) Shape matching and object recognition using shape contexts. In: IEEE international conference on computer science and information technology, pp 483–507

[8]

Ben HA, Krim H (2006) Geodesic matching of triangulated surfaces. IEEE Trans Image Process 15(8):2249–2258 10.1109/tip.2006.875250

[9]

A method for registration of 3-D shapes

P.J. Besl, Neil D. McKay

IEEE Transactions on Pattern Analysis and Machine... 1992 10.1109/34.121791

[10]

Biasotti S, Cerri A, Bronstein A, Bronstein M (2016) Recent trends, applications, and perspectives in 3D shape similarity assessment. Computer Graphics Forum 35(6):87–119 10.1111/cgf.12734

[11]

Bronstein MM, Bronstein AM (2011) Shape recognition with spectral distances. IEEE Trans Patt Anal Mach Intel 33(5):1065 10.1109/tpami.2010.210

[12]

Bronstein MM, Kokkinos I (2010) Scale-invariant heat kernel signatures for non-rigid shape recognition. In: Computer vision and pattern recognition, pp 1704–1711 10.1109/cvpr.2010.5539838

[13]

Bronstein AM, Bronstein MM, Kimmel R (2009) Monographs in computer science, Numerical geometry of non-rigid shapes. Multidimensional Scaling[J] (Chapter 7):137–167, https://doi.org/10.1007/978-0-387-73301-2 10.1007/978-0-387-73301-2

[14]

Castellani U, Cristani M, Fantoni S, Murino V (2010) Sparse points matching by combining 3D mesh saliency with statistical descriptors. Computer Graphics Forum 27(2):643–652 10.1111/j.1467-8659.2008.01162.x

[15]

Chui H, Rangarajan A (2003) A new point matching algorithm for non-rigid registration. Comput Vis Image Underst 89(2):114–141 10.1016/s1077-3142(03)00009-2

[16]

Eiter T, Mannila H (1994) Computing discrete fréchet distance. Tech. rep., Citeseer

[17]

Fang Y, Liu YS, Ramani K (2009) Three dimensional shape comparison of flexible proteins using the local-diameter descriptor. Bmc Structural Bio 9(1):29–29 10.1186/1472-6807-9-29

[18]

Ghorpade VK, Checchin P, Malaterre L, Trassoudaine L (2017) 3D Shape representation with spatial probabilistic distribution of intrinsic shape keypoints. Eurasip J Advances Signal Process 2017(1):52 10.1186/s13634-017-0483-y

[19]

Hamza AB (2016) A graph-theoretic approach to 3d shape classification. Neurocomputing 211:11–21 10.1016/j.neucom.2015.12.130

[20]

Havens TC, Bezdek JC, Keller JM, Popescu M (2009) Dunn’s cluster validity index as a contrast measure of vat images. In: International conference on pattern recognition, pp 1–4 10.1109/icpr.2008.4761772

[21]

He S, Choi YK, Guo Y, Guo X, Wang W (2015) A 3D shape descriptor based on spectral analysis of medial axis. Computer Aided Geometric Design 39 (C):50–66 10.1016/j.cagd.2015.08.004

[22]

Ion A, Artner NM, Peyre G, Marmol SBL (2009) 3D shape matching by geodesic eccentricity. In: IEEE computer society conference on computer vision and pattern recognition workshops, pp 1–8 10.1109/cvprw.2008.4563032

[23]

Levy B (2006) Laplace-Beltrami eigenfunctions towards an algorithm that understands geometry. In: IEEE international conference on shape modeling and applications, pp 13–13 10.1109/smi.2006.21

[24]

Lian Z, Godil A, Bustos B, Daoudi Mea (2011) SHREC’11 track: shape retrieval on non-rigid 3d watertight meshes. In: Proceedings of the 4th Eurographics conference on 3D object retrieval, EG 3DOR’11, Eurographics Association, pp 79–88

[25]

Lian Z, Godil A, Sun X, Xiao J (2013) CM-BOF: Visual similarity-based 3D shape retrieval using Clock Matching and Bag-of-Features. Mach Vis Appl 24(8):1685–1704 10.1007/s00138-013-0501-5

[26]

Ling H, Jacobs DW (2007) Shape classification using the inner-distance. IEEE Trans Patt Anal Mach Intel 29(2):286 10.1109/tpami.2007.41

[27]

Ling H, Okada K (2006) Diffusion distance for histogram comparison. In: IEEE computer society conference on computer vision and pattern recognition, pp 246–253

[28]

Lipman Y, Rustamov RM, Funkhouser TA (2010) Biharmonic distance. ACM Trans Graph 29(3):27 10.1145/1805964.1805971

[29]

Object recognition from local scale-invariant features

D.G. Lowe

Proceedings of the Seventh IEEE International Conf... 10.1109/iccv.1999.790410

[30]

Mahmoudi M, Sapiro G (2009) Three-dimensional point cloud recognition via distributions of geometric distances. Graph Model 71(1):22–31 10.1016/j.gmod.2008.10.002

[31]

Marcolin F, Vezzetti E (2017) Novel descriptors for geometrical 3d face analysis. Multimedia Tools and Applications 76(12):13805–13834 10.1007/s11042-016-3741-3

[32]

Osada R, Funkhouser TA, Chazelle B, Dobkin DP (2002) Shape distributions. ACM Trans Graph 21(4):807–832 10.1145/571647.571648

[33]

Ovsjanikov M, Sun J, Guibas L (2008) Global intrinsic symmetries of shapes. In: Computer graphics forum, vol 27, pp 1341–1348 10.1111/j.1467-8659.2008.01273.x

[34]

Patané G, Barsky BA (2017) An introduction to Laplacian spectral distances and kernels: Theory, computation, and applications. In: ACM SIGGRAPH, pp 3 10.1145/3084873.3084919

[35]

Pickup D, Sun Xea (2015) Canonical forms for non-rigid 3d shape retrieval. In: Eurographics workshop on 3d object retrieval 10.1007/s41095-016-0045-5

[36]

Pickup D, Sun X, Rosin PL, Martin RRea (2014) SHREC’14 track: Shape retrieval of non-rigid 3d human models. In: Proceedings of the 7th eurographics workshop on 3D object retrieval, EG 3DOR’14, Eurographics Association

[37]

Pickup D, Sun X, Rosin PL, Martin RR (2016) Skeleton-based canonical forms for non-rigid 3d shape retrieval. Comput Vis Med 2(3):231–243 10.1007/s41095-016-0045-5

[38]

Roman-Rangel E, Wang C, Marchand-Maillet S (2016) Simmap: Similarity maps for scale invariant local shape descriptors. Neurocomputing 175:888–898 10.1016/j.neucom.2015.06.093

[39]

Rustamov RM (2007) Laplace-Beltrami eigenfunctions for deformation invariant shape representation. In: Eurographics symposium on geometry processing, pp 225–233

[40]

Shinagawa Y, Kunii TL (1991) Constructing a reeb graph automatically from cross sections. IEEE Comput Graph Appl 11(6):44–51 10.1109/38.103393

[41]

Smeets D, Hermans J, Vandermeulen D, Suetens P (2012) Isometric deformation invariant 3D shape recognition. Pattern Recogn 45 (7):2817–2831 10.1016/j.patcog.2012.01.020

[42]

Sun J, Ovsjanikov M, Guibas L (2009) A concise and provably informative multi-scale signature based on heat diffusion. In: Computer fraphics forum, vol 28, pp 1383–1392 10.1111/j.1467-8659.2009.01515.x

[43]

Sundar H, Silver D, Gagvani N, Dickinson S (2003) Skeleton based shape matching and retrieval. In: Shape modeling international, pp 130–139 10.1109/smi.2003.1199609

[44]

Tatsuma A, Koyanagi H, Aono M (2012) A large-scale shape benchmark for 3d object retrieval: Toyohashi shape benchmark

[45]

Tierny J, Vandeborre JP, Daoudi M (2010) Partial 3D shape retrieval by reeb pattern unfolding. Computer Graphics Forum 28(1):41–55 10.1111/j.1467-8659.2008.01190.x

[46]

Vezzetti E, Marcolin F, Tornincasa S, Ulrich L, Dagnes N (2018) 3D geometry-based automatic landmark localization in presence of facial occlusions. Multimedia Tools and Applications 77(11):14177–14205 10.1007/s11042-017-5025-y

[47]

Wang H, Li Y, Jin H, Yin C, Su X, Chen W (2003) Three-dimensional visualization of shape measurement data based on a computer generated hologram. J Opt A Pure Appl Opt 5(5):S195—S199

[48]

Xu G (2004) Discrete laplace–beltrami operators and their convergence. Computer Aided Geometric Design 21(8):767–784 10.1016/j.cagd.2004.07.007

[49]

Yao B, Li Z, Ding M, Chen M (2016) Three-dimensional protein model similarity analysis based on salient shape index. BMC Bioinforma 17 (1):131–131 10.1186/s12859-016-0983-z

[50]

ÇeliktutanBerk GökberkBülent SankurLale Akarun ASAD (2008) Bosphorus database for 3d face analysis. Biomet Ident Manage 1:47–56

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Improved biharmonic kernel signature for 3D non-rigid shape matching and retrieval

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Citations

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References

Details

Published: Sep 03, 2020
Vol/Issue: 80(1)
Pages: 615-640
License: View

Authors

Donghua University

College of Computer Science and Software Engineering, Shenzhen University, Shenzhen, China

M

Mingquan Zhou

Funding

National Key R&D Program of China Award: 2017YFB1002604

the National Key Cooperation between the BRICS of China Award: 2017YFE0100500

Beijing Natural Science Foundation of China Award: 4172033

Cite This Article

Dan Zhang, Zhongke Wu, Xingce Wang, et al. (2020). 3D non-rigid shape similarity measure based on Fréchet distance between spectral distance distribution curve. Multimedia Tools and Applications, 80(1), 615-640. https://doi.org/10.1007/s11042-020-09420-5

3D non-rigid shape similarity measure based on Fréchet distance between spectral distance distribution curve

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