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A non-rigid 3D model retrieval method based on scale-invariant heat kernel signature features

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Abstract

The number of non-rigid 3D models increases steadily in various areas. It is imperative to develop efficient retrieval system for 3D non-rigid models. As we know, global features fail to consistently describe the intra-class variability of non-rigid 3D models, the local features are more effective than global features for the retrieval of non-rigid 3D models. In this paper, we use Heat Kernel Signature (HKS) as the local features to represent non-rigid 3D models and further propose the retrieval method based on scale-invariant local features. Firstly, we extract key-points at multiple scales automatically. Then, the HKS local features are computed for each key-point. However, the HKS features are sensitive to scale. In order to solve this problem, we convert the scale problem into the translation problem using the diffusion Wavelets transform. To solve the translation problem, we use a kind of histogram equalization technique. Finally, we use the bipartite graph matching algorithm to compute similarity between the 3D models. Experimental results on two public benchmarks show that our method outperforms state-of-the-art methods for non-rigid 3D models retrieval.

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References

  1. Auo KC, Taic L, Chu HK, Cohen ORD, Lee TY (2008) Skeleton extraction by mesh contraction. ACM SIGGRAPH 1–10

  2. Barra V, Biasotti S (2013) 3D shape retrieval using kernels on extended Reeb graphs. Pattern Recogn 46(11):2985–2999

    Article  MATH  Google Scholar 

  3. Ben-Chen M, Weber O, Gotsman C (2008) Characterizing shape using conformal factors. Eurographics Workshop on 3D Object Retrieval (3DOR)1–8

  4. Bronstein MM, Kokkinos I (2010) Scale-invariant heat kernel signatures for non-rigid shape recognition. In: IEEE International Conference on Computer Vision and Pattern Recognition (CVPR), pp 1704– 1711

  5. Bronstein AM, Bronstein MM, Kimmel R (2006) Generalized multidimensional scaling: a framework for isometry-invariant partial surface matching. Proc Natl Acad Sci (PNAS) 103(5):1168–1172

    Article  MathSciNet  MATH  Google Scholar 

  6. Bronstein AM, Bronstein MM, Kimmel R, Mahmoudi M, Sapiro G (2010) A Gromov-Hausdorff framework with diffusion geometry for topologically-robust non-rigid shape matching. Int J Comput Vis (IJCV) 89(2-3):266–286

    Article  Google Scholar 

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

    Article  Google Scholar 

  8. Bu S, Liu Z, Han J, Wu J, Ji R (2014) Learning high-level feature by deep belief networks for 3-D model retrieval and recognition. IEEE Trans Multimed 16(8):2154–2167

    Article  Google Scholar 

  9. Cao Y, Wang C, Li Z, Zhang L, Zhang L (2010) Spatial-bag-of-features. IEEE Conference on Computer Vision and Pattern Recognition (CVPR)3352–3359

  10. Chazal F, Cohen-Steiner D, Guibas LJ, Memoli F, Oudot SY (2009) Gromov-hausdorff stable signatures for shapes using persistence. Comput Graph Forum 28(5):1393–1403

    Article  Google Scholar 

  11. Dang F, Emad N (2014) Fast iterative method in solving eikonal equations: a multi-level parallel approach. Procedia Comput Sci 29:1859–1869

    Article  Google Scholar 

  12. Detrixhe M, Gibou F, Min C (2013) A parallel fast sweeping method for the eikonal equation. J Comput Phys 237:46–55

    Article  MathSciNet  Google Scholar 

  13. Donoser M, Bischof H (2013) Diffusion processes for retrieval revisited. IEEE Conf Comput Vis Pattern Recognit (CVPR)1320–1327

  14. Gao Y, Wang M, Zha ZJ, Tian Q, et al. (2011) Less is more: efficient 3D object retrieval with query view selection. IEEE Trans Multimed 13(5):1007–1018

    Article  Google Scholar 

  15. Grigor’yan A. (2009) Heat kernel and analysis on manifolds, a textbook. AMS/IP Studies in Advanced Mathematics 47:1–498

    Google Scholar 

  16. Hilaga M, Shinagawa Y, Kohmura T, Kunii TL (2001) Topology matching for fully automatic similarity estimation of 3D shapes. ACM SIGGRAPH203–212

  17. Hu M, Wu T, Weir JD (2013) An adaptive particle swarm optimization with multiple adaptive methods. IEEE Trans Evol Comput 17(5):705–720

    Article  Google Scholar 

  18. Jain V, Zhang H, Kaick OV (2007) Non-rigid spectral correspondence of triangle meshes. Int J Shape Model 13(1):101–124

    Article  MathSciNet  MATH  Google Scholar 

  19. Jia Y, Huang C, Darrell T (2012) Beyond spatial pyramids: receptive field learning for pooled image features. IEEE Conference on Computer Vision and Pattern Recognition (CVPR)3370–3377

  20. Jiang L, Tong W, Meng D, Hauptmann A (2014) Towards efficient learning of optimal spatial bag-of-words representations. ACM International Conference on Multimedia Retrieval1–8

  21. Kuang Z, Li Z, Jiang X, Liu Y, Li H (2015) Retrieval of non-rigid 3D shapes from multiple aspects. Comput Aided Des 58(1):13–23

    Article  Google Scholar 

  22. Lafon S (2004) Diffusion maps and geometric harmonics. Ph.D.thesis, Yale

  23. Leng B, Zeng J, Yao M, Xiong Z (2015) 3D object retrieval with multitopic model combining relevance feedback and LDA model. IEEE Trans Image Process 24 (1):94–105

    Article  MathSciNet  Google Scholar 

  24. Li C (2013) Spectral geometric methods for deformable 3D shape retrieval. Master’s thesis, Concordia University

  25. Li B, Johan H (2013) 3D model retrieval using hybrid features and class information. Multimed Tools Appl 62(3):821–846

    Article  Google Scholar 

  26. Li P, Ma H, Ming A (2011) Non-rigid 3D model retrieval using multi-scale local features. ACM Multimed1425–1428

  27. Lian Z, Godil A (2011) A feature-preserved canonical form for non-rigid 3D mesh. In: IEEE International Conference on 3D Imaging, Modeling, Processing, Visualization and Transmission (3DIMPVT), pp 116–123

  28. Lian Z, Godil A, Bustos B, et al. (2013) A comparison of methods for non-rigid 3D shape retrieval. Pattern Recognit 46(1):449–461

    Article  Google Scholar 

  29. Lipman Y, Funkhouser T (2009) Mobius voting for surface correspondence. ACM Trans Graph (TOG) 28(3):1–12

    Article  Google Scholar 

  30. Liu Z, Bu S, Han J (2015) Locality-constrained sparse patch coding for 3D model retrieval. Neurocomputing 151:583–592

    Article  Google Scholar 

  31. Lu K, Ji R, Tang J, Gao Y (2014) Learning based bipartite graph matching for view-based 3D model retrieval. IEEE Trans Image Process 23(10):4553–4563

    Article  MathSciNet  Google Scholar 

  32. Lyu S, Simoncelli EP (2009) Modeling multiscale subbands of photographic images with fields of gaussian scale mixtures. IEEE Transactions on Pattern Analysis and Machine Intelligence 31(4):693–706

    Article  Google Scholar 

  33. Maggioni M, Bremer Jr JC, Coifman RR, Szlam AD (2005) Biorthogonal diffusion wavelets for multiscale representations on manifolds and graphs. Proc SPIE Wavelet XI 5914(1):59141M

    Article  Google Scholar 

  34. Makadia A, Daniilidis K (2010) Spherical correlation of visual representations for 3D model retrieval. Int J Comput Vis 89(2):193–210

    Article  Google Scholar 

  35. Memoli F (2007) On the use of Gromov-Hausdorff Distances for Shape Comparison. International Symposium on Point Based Graphics81–90

  36. Mian A, Bennamoun M, Owens R (2010) On the repeatability and quality of keypoints for local feature-based 3D object retrieval from cluttered scenes. Int J Comput Vis (IJCV) 89(2–3):348–361

    Article  Google Scholar 

  37. Novotni M, Klein R (2003) 3D Zernike descriptors for content based shape retrieval. ACM Symposium on Solid Modeling and Applications216–225

  38. Ovsjanikov M, Bronstein AM, Bronstein MM, Guibas LJ (2009) Shape Google: a computer vision approach to invariant shape retrieval. In: IEEE International Conference on Computer Vision Workshops (ICCV), pp 320–327

  39. Ovsjanikov M, Mrigot Q, Mmoli F, Guibas L (2010) One point isometric matching with the heat kernel. Comput Graph Forum 29(5):1555–1564

    Article  Google Scholar 

  40. Peternell M, Steiner T (2005) A geometric idea to solve the eikonal equation. Spring Conference on Computer Graphics43–48

  41. Raviv D, Bronstein AM, Bronstein MM, Kimmel R, Sapiro G (2010) Diffusion symmetries of non-rigid shapes international symposium on 3D data processing. Visualization and Transmission (3DPVT)1–8

  42. Reuter M, Biasotti S, Giorgi D, Patane G, Spaggnuolo M (2009) Discrete Laplace-Beltrami operators for shape analysis and segmentation. Comput Graph 33 (3):381–390

    Article  Google Scholar 

  43. Rustamov RM (2007) Laplace-beltrami eigenfunctions for deformation invariant shape representation. ACM SIGGRAPH Symposium on Geometry processing (SGP)225–233

  44. Rusur B, Martonz C, Blodow N, Beetz M (2008) Persistent point feature histograms for 3D point clouds. International Conference on Intelligent Autonomous Systems

  45. Sun J, Ovsjanikov M, Guibas L (2009) A concise and provably informative multi-scale signature based on heat diffusion. Eurographics Symposium on Geometry Processing (SGP)1383–1392

  46. Tabia H, Laga H, Picard D, Gosselin PH (2014) Covariance descriptors for 3D shape matching and retrieval. IEEE Conference on Computer Vision and Pattern Recognition (CVPR)4185–4192

  47. Tam GKL, Lau RWH (2007) Deformable model retrieval based on topological and geometric signatures. IEEE Trans Vis Comput Graph 13(3):470–482

    Article  Google Scholar 

  48. Wu HY, Zha H, Luo T, Wang X-L, Ma S (2010) Global and local isometry-invariant descriptor for 3D shape comparison and partial matching. IEEE Conf Comput Vis Pattern Recognit (CVPR)438–445

  49. Ye J, Yan Z, Yu Y (2013) Fast nonrigid 3d retrieval using modal space transform. ACM Conference on International Conference on Multimedia Retrieval121–126

  50. Zhang J, Kaplow R, Chen R (2005) The McGill shape benchmark

  51. Zou G, Hua J, Dong M, Qin H (2008) Surface matching with salient keypoints in geodesic scale space. Comput Animat Virtual Worlds 19:399–410

    Article  Google Scholar 

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Acknowledgments

This work is supported by the National Natural Science Foundation for Distinguished Young Scholars under Grant No. 60925010; the Funds for Creative Research Groups of China under Grant No.61121001; the Research Fund for the Doctoral Program of Higher Education of China under Grant No.20120005130002; the Program for the Jiangsu Provincial Naural Science Fundation of China under Grant No.BK2011170.

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Authors and Affiliations

  1. Institute of Sensing Technology and Business, Beijing, University of Posts and Telecommunications, Beijing, 100876, China

    Pengjie Li

  2. Beijing Key Laboratory of Intelligent Telecommunications Software and Multimedia, Beijing University of Posts and Telecommunications, Beijing, 100876, China

    Huadong Ma & Anlong Ming

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  1. Pengjie Li
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  2. Huadong Ma
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Correspondence to Pengjie Li.

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Li, P., Ma, H. & Ming, A. A non-rigid 3D model retrieval method based on scale-invariant heat kernel signature features. Multimed Tools Appl 76, 10207–10230 (2017). https://doi.org/10.1007/s11042-016-3606-9

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  • DOI: https://doi.org/10.1007/s11042-016-3606-9

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