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Optimized multi-scale affine shape registration based on an unsupervised Bayesian classification

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Abstract

Here, we intend to introduce an efficient, robust curve alignment algorithm with respect to the group of special affine transformations of the plane denoted by SA(2,R). Such a group of transformations is known to be well model the pose of 3D scene when objects are far from the visual sensor relatively to their seizes. Its numerical robustness lies in its multi-scale approach and its precision comes from the automatic and unsupervised Bayesian selection of the efficient scales in the sens of L2 metric. In this work, We prove its high alignment performance on the most studied image databases such as MPEG-7, MCD, Kimia-99, Kimia216, ETH-80, and the Swedish leaf experimentally. The unsupervised Bayesian classification is based on the well-known multiclass Expectation-Maximization algorithm.

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Data sharing not applicable to this article as no datasets were generated or analyzed during the current study.

References

  1. Adamek T, O’Connor NE (2004) A multiscale representation method for nonrigid shapes with a single closed contour. IEEE Trans Circuits Syst Video Technol 14(5):742–753

    Google Scholar 

  2. Arbter K, Snyder WE, Burkhardt H, Hirzinger G (1990) Application of affine-invariant fourier descriptors to recognition of 3-d objects. IEEE Trans Pattern Anal Mach Intell 12(7):640–647

    Google Scholar 

  3. Bachelder IA, Ullman S (1992) Contour matching using local affine transformations. Technical report Massachusetts Inst of Tech Cambridge Artificial Intelligence Lab

  4. Belongie S, Malik J, Puzicha J (2002) Shape matching and object recognition using shape contexts. IEEE Trans Pattern Anal Mach Intell 24(4):509–522

    Google Scholar 

  5. BenKhlifa A, Ghorbel F (2019) An almost complete curvature scale space representation: Euclidean case. Signal Process Image Commun 75:32–43

    Google Scholar 

  6. Besl PJ, McKay ND (1992) Method for registration of 3-d shapes. In: Sensor fusion IV: control paradigms and data structures, vol 1611. International Society for Optics and Photonics, pp 586–606

  7. Bryner D, Srivastava A, Klassen E (2012) Affine-invariant, elastic shape analysis of planar contours. In: 2012 IEEE conference on computer vision and pattern recognition, IEEE, pp 390–397

  8. Bryner D, Srivastava A (2014) Bayesian active contours with affine-invariant, elastic shape prior. In: Proceedings of the IEEE conference on computer vision and pattern recognition, pp 312–319

  9. Chui H, Rangarajan A (2000) A feature registration framework using mixture models. In: Proceedings IEEE workshop on mathematical methods in biomedical image analysis. MMBIA-2000 (Cat. No. PR00737), IEEE, pp 190–197

  10. Chui H, Rangarajan A (2003) A new point matching algorithm for non-rigid registration. Comput Vis Image Underst 89(2-3):114–141

    Google Scholar 

  11. Cyganski D, Vaz RF (1992) Linear signal decomposition approach to affine-invariant contour identification. In: Intelligent robots and computer vision x: algorithms and techniques, vol 1607, International Society for Optics and Photonics, pp 98–109

  12. Cyganski D, Cott TA, Orr JA, Dodson RJ (1988) Object identification and orientation estimation from contours based on an affine invariant curvature. In: Intelligent robots and computer vision VI, vol 848, International Society for Optics and Photonics, pp 33–39

  13. Daliri MR, Torre V (2008) Robust symbolic representation for shape recognition and retrieval. Pattern Recognit 41(5):1782–1798

    Google Scholar 

  14. Dempster AP, Laird NM, Rubin DB (1977) Maximum likelihood from incomplete data via the em algorithm. J R Stat Soc Ser B Stat (Methodol) 39(1):1–22

    MathSciNet  Google Scholar 

  15. Egozi A, Keller Y, Guterman H (2010) Improving shape retrieval by spectral matching and meta similarity. IEEE Trans Image Process 19(5):1319–1327

    MathSciNet  Google Scholar 

  16. El Rube I, Ahmed M, Kamel M (2005) Wavelet approximation-based affine invariant shape representation functions. IEEE Trans Pattern Anal Mach Intell 28(2):323–327

    Google Scholar 

  17. El-ghazal A, Basir O, Belkasim S (2009) Farthest point distance: a new shape signature for fourier descriptors. Signal Process Image Commun 24 (7):572–586

    Google Scholar 

  18. El-ghazal A, Basir O, Belkasim S (2012) Invariant curvature-based fourier shape descriptors. J Vis Commun Image Represent 23(4):622–633

    Google Scholar 

  19. Elghoul S, Ghorbel F (2021) A fast and robust affine-invariant method for shape registration under partial occlusion. Int J Multimed Inf Retr 1–21

  20. Elghoul S, Ghorbel F (2021) Fast global sa (2, r) shape registration based on invertible invariant descriptor. Signal Process Image Commun 90:116058

    Google Scholar 

  21. Elghoul S, Ghorbel F (2021) Partial contour matching based on affine curvature scale space descriptors. In: New approaches for multidimensional signal processing: proceedings of international workshop, NAMSP 2020, vol 216, Springer, p 73

  22. Ersi EF, Zelek JS (2006) Local feature matching for face recognition. In: The 3rd Canadian conference on computer and robot vision (CRV’06), IEEE, pp 4–4

  23. Felzenszwalb PF, Schwartz JD (2007) Hierarchical matching of deformable shapes. In: 2007 IEEE Conference on computer vision and pattern recognition, IEEE, pp 1–8

  24. Fu H, Tian Z, Ran M, Fan M (2013) Novel affine-invariant curve descriptor for curve matching and occluded object recognition. IET Comput Vis 7 (4):279–292

    Google Scholar 

  25. Genovese A, Piuri V, Scotti F (2014) Touchless palmprint recognition systems, vol 60. Springer

  26. Genovese A, Piuri V, Scotti F (2014) Palmprint biometrics. In: Touchless palmprint recognition systems, Springer, pp 49–109

  27. Ghorbel F, Daoudi M, Mokadem A, Avaro O, Sanson H (1996) Global planar rigid motion estimation applied to object-oriented coding. In: Proceedings of 13th international conference on pattern recognition, vol 2, IEEE, pp 641–645

  28. Gopalan R, Turaga P, Chellappa R (2010) Articulation-invariant representation of non-planar shapes. In: European conference on computer vision, Springer, pp 286–299

  29. Gope C, Kehtarnavaz N, Hillman G, Würsig B (2005) An affine invariant curve matching method for photo-identification of marine mammals. Pattern Recogn 38(1):125–132

    Google Scholar 

  30. Granger S, Pennec X (2002) Multi-scale em-icp: a fast and robust approach for surface registration. In: European conference on computer vision, Springer, pp 418–432

  31. Hemamalini G, Prakash J (2016) Medical image analysis of image segmentation and registration techniques. Int J Eng Technol (IJET) 8(5):2234–2241

    Google Scholar 

  32. Hu M-K (1962) Visual pattern recognition by moment invariants. IEEE Trans Inf Theory 8(2):179–187

    Google Scholar 

  33. Hu R, Jia W, Ling H, Huang D (2012) Multiscale distance matrix for fast plant leaf recognition. IEEE Trans Image Process 21(11):4667–4672

    MathSciNet  Google Scholar 

  34. Huang X, Wang B, Zhang L (2005) A new scheme for extraction of affine invariant descriptor and affine motion estimation based on independent component analysis. Pattern Recogn Lett 26(9):1244–1255

    Google Scholar 

  35. Huang X, Paragios N, Metaxas DN (2006) Shape registration in implicit spaces using information theory and free form deformations. IEEE Trans Pattern Anal Mach Intell 28(8):1303–1318

    Google Scholar 

  36. Jian B, Vemuri BC (2010) Robust point set registration using gaussian mixture models. IEEE Trans Pattern Anal Mach Intell 33(8):1633–1645

    Google Scholar 

  37. Kang E-Y, Cohen I, Medioni G (2000) A graph-based global registration for 2d mosaics. In: Proceedings 15th international conference on pattern recognition. ICPR-2000, vol 1, IEEE, pp 257–260

  38. Kaothanthong N, Chun J, Tokuyama T (2016) Distance interior ratio: a new shape signature for 2d shape retrieval. Pattern Recognit Lett 78:14–21

    Google Scholar 

  39. Ke Q, Li Y (2014) Is rotation a nuisance in shape recognition?. In: Proceedings of the IEEE conference on computer vision and pattern recognition, pp 4146–4153

  40. Kovalsky SZ, Cohen G, Hagege R, Francos JM (2010) Decoupled linear estimation of affine geometric deformations and nonlinear intensity transformations of images. IEEE Trans Pattern Anal Mach Intell 32(5):940–946

    Google Scholar 

  41. Krotosky SJ, Trivedi MM (2007) Mutual information based registration of multimodal stereo videos for person tracking. Comput Vis Image Underst 106(2–3):270–287

    Google Scholar 

  42. Latecki LJ, Lakamper R, Eckhardt T (2000) Shape descriptors for non-rigid shapes with a single closed contour. In: Proceedings IEEE conference on computer vision and pattern recognition. CVPR 2000 (Cat. No. PR00662), vol 1, IEEE, pp 424–429

  43. Leibe B, Schiele B (2003) Analyzing appearance and contour based methods for object categorization. In: 2003 IEEE Computer society conference on computer vision and pattern recognition, 2003. proceedings, vol 2, IEEE, p 409

  44. Lin W-S, Fang C-H (2007) Synthesized affine invariant function for 2d shape recognition. Pattern Recogn 40(7):1921–1928

    Google Scholar 

  45. Ling H, Jacobs DW (2007) Shape classification using the inner-distance. IEEE Trans Pattern Anal Mach Intell 29(2):286–299

    Google Scholar 

  46. Liu H (2014) Curves in affine and semi-euclidean spaces. RM 65 (1):235–249

    MathSciNet  Google Scholar 

  47. Liu C, Kong X, Zhao X (2020) Non-rigid point set registration based on new shape context and local structure constraint. In: Proceedings of the 2020 9th international conference on computing and pattern recognition, pp 439–446

  48. Ma J, Zhao J, Tian J, Tu Z, Yuille AL (2013) Robust estimation of nonrigid transformation for point set registration. In: Proceedings of the IEEE conference on computer vision and pattern recognition, pp 2147–2154

  49. MacQueen J et al (1967) Some methods for classification and analysis of multivariate observations. In: Proceedings of the fifth Berkeley symposium on mathematical statistics and probability, vol 1, Oakland, pp 281–297

  50. Mai F, Chang C, Hung Y (2010) Affine-invariant shape matching and recognition under partial occlusion. In: 2010 IEEE International conference on image processing, IEEE, pp 4605–4608

  51. Matuk J, Bharath K, Chkrebtii O, Kurtek S (2021) Bayesian framework for simultaneous registration and estimation of noisy, sparse, and fragmented functional data. J Am Stat Assoc 1–17

  52. Mokhtarian F, Abbasi S (2001) Affine curvature scale space with affine length parametrisation. Pattern Anal Appl 4(1):1–8

    MathSciNet  Google Scholar 

  53. Moons T, Pauwels EJ, Van Gool L, Oosterlinck A (1995) Foundations of semi-differential invariants. Int J Comput Vis 14(1):25–47

    Google Scholar 

  54. Morel J-M, Yu G (2009) Asift: a new framework for fully affine invariant image comparison. SIAM J Imaging Sci 2(2):438–469

    MathSciNet  Google Scholar 

  55. Mori G, Belongie S, Malik J (2005) Efficient shape matching using shape contexts. IEEE Trans Pattern Anal Mach Intell 27(11):1832–1837

    Google Scholar 

  56. Myronenko A, Song X (2010) Point set registration: coherent point drift. IEEE Trans Pattern Anal Mach Intell 32(12):2262–2275

    Google Scholar 

  57. Opelt A, Pinz A, Zisserman A (2006) A boundary-fragment-model for object detection. In: European conference on computer vision, Springer, pp 575–588

  58. Pauwels EJ, Moons T, Van Gool L, Kempenaers P, Oosterlinck A (1995) Recognition of planar shapes under affine distortion. Int J Comput Vis 14 (1):49–65

    Google Scholar 

  59. Petrakis EGM, Diplaros A, Milios E (2002) Matching and retrieval of distorted and occluded shapes using dynamic programming. IEEE Trans Pattern Anal Mach Intell 24(11):1501–1516

    Google Scholar 

  60. Pham N, Helbert D, Bourdon P, Carré P (2018) Spectral graph wavelet based nonrigid image registration. In: 2018 25th IEEE international conference on image processing (ICIP), IEEE, pp 3348–3352

  61. Pulli K (1999) Multiview registration for large data sets. In: Second international conference on 3-d digital imaging and modeling (cat. no. pr00062), IEEE, pp 160–168

  62. Raviv D, Kimmel R (2015) Affine invariant geometry for non-rigid shapes. Int J Comput Vis 111(1):1–11

    MathSciNet  Google Scholar 

  63. Rusinkiewicz S, Levoy M (2001) Efficient variants of the icp algorithm. In: Proceedings third international conference on 3-D digital imaging and modeling, IEEE, pp 145–152

  64. Sakrani K, Elghoul S, Falleh S, Ghorbel F (2021) Sa (2, r) multi-scale contour registration based on em algorithm. In: 2021 International conference on visual communications and image processing (VCIP), IEEE, pp 1–5

  65. Sebastian TB, Klein PN, Kimia BB (2004) Recognition of shapes by editing their shock graphs. IEEE Trans Pattern Anal Mach Intell 26(5):550–571

    Google Scholar 

  66. Sellami M, Ghorbel F (2012) An invariant similarity registration algorithm based on the analytical fourier-mellin transform. In: 2012 Proceedings of the 20th European signal processing conference (EUSIPCO), IEEE, 390–394

  67. Shekar B, Pilar B, Kittler J (2015) An unification of inner distance shape context and local binary pattern for shape representation and classification. In: Proceedings of the 2nd international conference on perception and machine intelligence, pp 46–55

  68. Shu X, Wu X-J (2011) A novel contour descriptor for 2d shape matching and its application to image retrieval. Image Vis Comput 29(4):286–294

    Google Scholar 

  69. Shu X, Pan L, Wu X-J (2015) Multi-scale contour flexibility shape signature for fourier descriptor. J Vis Commun Image Represent 26:161–167

    Google Scholar 

  70. Söderkvist O (2001) Computer vision classification of leaves from Swedish trees

  71. Sokic E, Konjicija S (2014) Novel fourier descriptor based on complex coordinates shape signature. In: 2014 12th International workshop on content-based multimedia indexing (CBMI), IEEE, pp 1–4

  72. Spivak M (1970) A comprehensive introduction to differential geometry part, vol 2. Publish or Perish, Boston

    Google Scholar 

  73. Temlyakov A, Munsell BC, Waggoner JW, Wang S (2010) Two perceptually motivated strategies for shape classification. In: 2010 IEEE Computer society conference on computer vision and pattern recognition, IEEE, pp 2289–2296

  74. Thorndike RL (1953) Who belongs in the family. In: Psychometrika. Citeseer

  75. Tu Z, Yuille AL (2004) Shape matching and recognition–using generative models and informative features. In: European conference on computer vision, Springer, pp 195–209

  76. Tu Z, Zheng S, Yuille A (2008) Shape matching and registration by data-driven em. Comput Vis Image Underst 109(3):290–304

    Google Scholar 

  77. Wang G, Chen Y (2017) Fuzzy correspondences guided gaussian mixture model for point set registration. Knowl-Based Syst 136:200–209

    Google Scholar 

  78. Wang B, Gao Y (2014) Hierarchical string cuts: a translation, rotation, scale, and mirror invariant descriptor for fast shape retrieval. IEEE Trans Image Process 23(9):4101–4111

    MathSciNet  Google Scholar 

  79. Wang J, Bai X, You X, Liu W, Latecki LJ (2012) Shape matching and classification using height functions. Pattern Recogn Lett 33(2):134–143

    Google Scholar 

  80. Weiss I (1993) Geometric invariants and object recognition. Int J Comput 11263on 10(3):207–231

    Google Scholar 

  81. Wiskott L, Krüger N, Kuiger N, Von Der Malsburg C (1997) Face recognition by elastic bunch graph matching. IEEE Trans Pattern Anal Mach Intell 19(7):775–779

    Google Scholar 

  82. Wolter D, Latecki LJ (2004) Shape matching for robot mapping. In: Pacific rim international conference on artificial intelligence, Springer, pp 693–702

  83. Xu H, Yang J, Tang Y, Li Y (2015) A hybrid shape descriptor for object recognition. In: 2015 IEEE International conference on robotics and biomimetics (ROBIO), IEEE, pp 96–101

  84. Xu H, Yang J, Yuan J (2016) Invariant multi-scale shape descriptor for object matching and recognition. In: 2016 IEEE International conference on image processing (ICIP), IEEE, pp 644–648

  85. Yang B, Chen C (2015) Automatic registration of uav-borne sequent images and lidar data. ISPRS J Photogramm Remote Sens 101:262–274

    Google Scholar 

  86. Yang C, Yu Q (2019) Multiscale fourier descriptor based on triangular features for shape retrieval. Signal Process Image Commun 71:110–119

    Google Scholar 

  87. Yang C, Yu Q (2021) Invariant multiscale triangle feature for shape recognition. Appl Math Comput 403:126096

    Google Scholar 

  88. Yang X, Koknar-Tezel S, Latecki LJ (2009) Locally constrained diffusion process on locally densified distance spaces with applications to shape retrieval. In: 2009 IEEE conference on computer vision and pattern recognition, IEEE, pp 357–364

  89. Yang J, Wang H, Yuan J, Li Y, Liu J (2016) Invariant multi-scale descriptor for shape representation, matching and retrieval. Comput Vis Image Underst 145:43–58

    Google Scholar 

  90. Yang C, Wei H, Yu Q (2016) Multiscale triangular centroid distance for shape-based plant leaf recognition. In: ECAI, pp 269–276

  91. Yang C, Wei H, Yu Q (2018) A novel method for 2d nonrigid partial shape matching. Neurocomputing 275:1160–1176

    Google Scholar 

  92. Yang K, Chen Y, Zhang H, Liu X, Zhao W, et al. (2019) Robust point set registration method based on global structure and local constraints. Digit Med 5(2):76

    Google Scholar 

  93. Zhang D, Lu G (2005) Study and evaluation of different fourier methods for image retrieval. Image Vis Comput 23(1):33–49

    Google Scholar 

  94. Zhang D, Lu G et al (2002) A comparative study of fourier descriptors for shape representation and retrieval. In: Proceedings of the 5th Asian conference on computer vision, Citeseer, p 35

  95. Zhang T, Li J, Jia W, Sun J, Yang H (2018) Fast and robust occluded face detection in atm surveillance. Pattern Recogn Lett 107:33–40

    Google Scholar 

  96. Zheng Y, Guo B, Li C, Yan Y (2019) A weighted fourier and wavelet-like shape descriptor based on idsc for object recognition. Symmetry 11(5):693

    Google Scholar 

  97. Zheng Y, Meng F, Liu J, Guo B, Song Y, Zhang X, Wang L (2020) Fourier transform to group feature on generated coarser contours for fast 2d shape matching. IEEE Access 8:90141–90152

    Google Scholar 

  98. Zuliani M, Bhagavathy S, Manjunath B, Kenney C S (2004) Affine-invariant curve matching. In: 2004 International conference on image processing, 2004. ICIP’04, vol 5, IEEE, pp 3041–3044

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    1. CRISTAL Laboratory, GRIFT Research Group National School of Computer Science (ENSI), Manouba University, Manouba, 2010, Tunisia

      Khaoula Sakrani, Sinda Elghoul & Faouzi Ghorbel

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    Sakrani, K., Elghoul, S. & Ghorbel, F. Optimized multi-scale affine shape registration based on an unsupervised Bayesian classification. Multimed Tools Appl 83, 7057–7083 (2024). https://doi.org/10.1007/s11042-023-14890-4

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