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Link to original content: https://doi.org/10.1007/s10044-017-0610-2
Biharmonic density estimate: a scale-space descriptor for 3-D deformable surfaces | Pattern Analysis and Applications Skip to main content
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Biharmonic density estimate: a scale-space descriptor for 3-D deformable surfaces

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Abstract

The wide variability in deformable three-dimensional (3-D) shapes calls for the formulation of a multiscale surface signature for effective characterization and analysis of the underlying 3-D intrinsic geometry. To this end, a novel intrinsic geometric scale-space descriptor for 3-D deformable surfaces, termed as the biharmonic density estimate (BDE), is proposed. The BDE, derived from the biharmonic distance measure, is shown to provide an intrinsic geometric scale-space signature for multiscale surface feature-based representation of deformable 3-D shapes that is both effective and useful for practical applications. The proposed BDE signature provides a theoretical framework for the concept of intrinsic geometric scale space, resulting in a highly descriptive characterization of both the local surface structure and the global metric of the underlying 3-D shape. The compactness and robustness of the BDE are experimentally demonstrated on two standard benchmark datasets. The applications of the BDE in the detection of key components on a deformable 3-D surface and determination of sparse point correspondences between two deformable 3-D shapes are also demonstrated.

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References

  1. Aubry M, Schlickewei U, Cremers D (2011) The wave kernel signature: a quantum mechanical approach to shape analysis. In: Proceedings of the IEEE conference computer vision pattern recognition (CVPR)

  2. Bansal M, Daniilidis K (2013) Joint spectral correspondence for disparate image matching. In: Proceedings of the IEEE conference computer vision pattern recognition (CVPR), pp 2802–2809

  3. Belkin MM, Sun J, Wang Y (2008) Laplace operator on meshed surface. In: Proceedings of the symposium on computational geometry (SCG), pp 278–287

  4. Belongie S, Malik J, Puzicha J (2000) Shape context: a new descriptor for shape matching and object recognition. In: Proceedings of the neural information processing systems (NIPS)

  5. Boscaini D, Castellani U (2014) A sparse coding approach for local-to-global 3D shape description. Vis Comput 30(11):1233–1245

    Article  Google Scholar 

  6. Bronstein AM, Bronstein MM, Kimmel R (2007) Calculus of non-rigid surfaces for geometry and texture manipulation. IEEE Trans Vis Comput Graph 13(5):902–913

    Article  Google Scholar 

  7. Bronstein AM, Bronstein MM, Kimmel R (2008) Numerical geometry of non-rigid shapes. Springer, Berlin

    MATH  Google Scholar 

  8. Bronstein AM, Bronstein MM, Castellani U, Falcidieno B, Fusiello A, Godil A, Guibas LJ, Kokkinos I, Lian Z, Ovsjanikov M, Patane G, Spagnuolo M, Toldo R (2010) SHREC 2010: robust large-scale shape retrieval benchmark. In: Proceedings of the eurographics workshop 3D object retrieval (3DOR)

  9. Bronstein MM, Bronstein AM (2011) Shape recognition with spectral distances. IEEE Trans Pattern Anal Mach Intell 33(5):1065–1071

    Article  Google Scholar 

  10. Bronstein AM, Bronstein MM, Guibas LJ, Ovsjanikov M (2011) Shape Google: geometric words and expressions for invariant shape retrieval. ACM Trans Graph 30(1):1–20

    Article  Google Scholar 

  11. Fang Y, Sun M, Ramani K (2012) Temperature distribution descriptor for robust 3D shape retrieval. In: Proceedings of the IEEE conference computer vision and pattern recognition (CVPR), pp 9–16

  12. Johnson A, Hebert M (2002) Using spin images for efficient object recognition in cluttered 3D scenes. IEEE Trans Pattern Anal Mach Intell 21(5):433–449

    Article  Google Scholar 

  13. Karni Z, Gotsman C (2000) Spectral compression of mesh geometry. In: Proceedings of the ACM SIGGRAPH

  14. Levy B (2006) Laplace–Beltrami eigenfunctions: towards an algorithm that understands geometry. In: Proceedings of the IEEE international conference on shape modeling and applications, p 13

  15. Li X, Guskov I (2005) Multi-scale features for approximate alignment of point-based surfaces. In: Proceedings of the eurographics symposium on geometry processing (SGP), p 217

  16. Li B, Godil A, Johan H (2014) Hybrid shape descriptor and meta similarity generation for non-rigid and partial 3D model retrieval. Multimed Tools Appl 72(2):1531–1560

    Article  Google Scholar 

  17. Ling H, Okada K (2006) Diffusion distance for histogram comparison. In: Proceedings of the IEEE conference computer vision pattern recognition (CVPR), vol 1

  18. Lipman Y, Rustamov RM, Funkhouser TA (2010) Biharmonic distance. ACM Trans Graph 29(3):27:1–27:11

    Article  Google Scholar 

  19. Litman R, Bronstein AM (2014) Learning spectral descriptors for deformable shape correspondence. IEEE Trans Pattern Anal Mach Intell 36(1):171–180

    Article  Google Scholar 

  20. Manay S, Cremers D, Hong BW, Yezzi AJ, Soatto S (2006) Integral invariants for shape matching. IEEE Trans Pattern Anal Mach Intell 28(10):1602–1618

    Article  MATH  Google Scholar 

  21. Moenning C, Dodgson NA (2003) Fast marching farthest point sampling. In: Proceedings of the Eurographics

  22. Mukhopadhyay A, Bhandarkar SM (2014) Biharmonic density estimate—a scale space signature for deformable surfaces. In: Proceedings of the IEEE international conference on image processing (ICIP)

  23. Mukhopadhyay A, Arun Kumar CS, Bhandarkar SM (2016) Joint geometric graph embedding for partial shape matching in images. In: Proceedings of the IEEE Winter conference on applications of computer vision (WACV)

  24. New AT, Mukhopadhyay A, Arabnia HR, Bhandarkar SM (2012) Non-rigid shape correspondence and description using geodesic field estimate distribution. In: Proceedings of the ACM SIGGRAPH, poster

  25. Osada R, Funkhouser T, Chazelle B, Dobkin D (2002) Shape distributions. ACM Trans Graph 21(4):807–832

    Article  MATH  MathSciNet  Google Scholar 

  26. Ovsjanikov M, Merigot Q, Memoli F, Guibas L (2010) One point isometric matching with the heat kernel. In: Proceedings of the Eurographics symposium on geometry processing (SGP)

  27. Peyre G (2009) Toolbox Graph - A toolbox to process graph and triangulated meshes. In: Matlab Central. http://www.mathworks.com/matlabcentral/fileexchange/loadFile.do?objectId=5355&objectType=FILE

  28. Pinkall U, Polthier K (1993) Computing discrete minimal surfaces and their conjugates. Exp Maths 2(1):15–36

    Article  MATH  MathSciNet  Google Scholar 

  29. Reuter M, Wolter F-E, Peinecke N (2006) Laplace–Beltrami spectra as “Shape-DNA” of surfaces and solids. Comput-Aided Des 38(4):342–366

    Article  Google Scholar 

  30. Rustamov R (2007) Laplace–Beltrami eigenfunctions for deformation invariant shape representation. In: Proceedings of the eurographics symposium on geometry processing (SGP), pp 225–233

  31. Sipiran I, Bustos B (2012) Key-component detection on 3D meshes using local features. In: Proceedings of the 5th Eurographics conference 3D Object Retrieval (3DOR)

  32. Sun J, Ovsjanikov M, Guibas L (2009) A concise and provably informative multi-scale signature based on heat diffusion. Comput Graph Forum 28(5):1383–1392

    Article  Google Scholar 

  33. Taubin G (1995) A signal processing approach to fair surface design. In: Proceedings of the ACM SIGGRAPH

  34. Wardetzkey M (2005) Convergence of the cotangent formula: an overview. In: Discrete differential geometry. Birkhäuser Basel, pp 89–112

  35. Xu G (2004) Discrete Laplace–Beltrami operators and their convergence. Comput Aided Geom Des 21(8):767–784

    Article  MATH  MathSciNet  Google Scholar 

  36. Yen L, Fouss F, Decaestecker C, Francq P, Saerens M (2007) Graph nodes clustering based on the commute-time kernel. In: Proceedings of the 11th Pacific-Asia conference knowledge discovery and data mining (PAKDD)

  37. Zaharescu A, Boyer E, Horaud R (2012) Keypoints and local descriptors of scalar functions on 2D manifolds. Int J Comput Vis 100(1):78–98

    Article  MATH  Google Scholar 

  38. Zou G, Hua J, Lai Z, Gu X, Dong M (2009) Intrinsic geometric scale space by shape diffusion. IEEE Trans Vis Comput Graph 15(6):1193–1200

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Computer Science, The University of Georgia, 415 Boyd GSRC Building, Athens, GA, 30602-7404, USA

    Anirban Mukhopadhyay & Suchendra M. Bhandarkar

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  1. Anirban Mukhopadhyay
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  2. Suchendra M. Bhandarkar
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Correspondence to Suchendra M. Bhandarkar.

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Mukhopadhyay, A., Bhandarkar, S.M. Biharmonic density estimate: a scale-space descriptor for 3-D deformable surfaces. Pattern Anal Applic 20, 1261–1273 (2017). https://doi.org/10.1007/s10044-017-0610-2

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  • DOI: https://doi.org/10.1007/s10044-017-0610-2

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