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3D object recognition using invariants of 2D projection curves

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Abstract

This paper presents a new method for recognizing 3D objects based on the comparison of invariants of their 2D projection curves. We show that Euclidean equivalent 3D surfaces imply affine equivalent 2D projection curves that are obtained from the projection of cross-section curves of the surfaces onto the coordinate planes. Planes used to extract cross-section curves are chosen to be orthogonal to the principal axes of the defining surfaces. Projection curves are represented using implicit polynomial equations. Affine algebraic and geometric invariants of projection curves are constructed and compared under a variety of distance measures. Results are verified by several experiments with objects from different classes and within the same class.

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References

  1. Costa MS, Shapiro LG (2000) 3D object recognition and pose with relational indexing. Comput Vis Image Underst 79(3):364–407

    Article  MATH  Google Scholar 

  2. Forsyth DA, Ponce J (2003) Computer vision: a modern approach. Prentice Hall

  3. Gonzalez E, Adan A, Feliu V, Sanchez L (2008) Active object recognition based on Fourier descriptors clustering. Pattern Recognit Lett 29(8):1060–1071

    Article  Google Scholar 

  4. Kim S, Kweon IS (2008) Scalable representation for 3D object recognition using feature sharing and view clustering. Pattern Recognit 41(2):754–773

    Article  MATH  Google Scholar 

  5. Rothganger F, Lazebnik S, Schmid C, Ponce J (2006) 3D object modeling and recognition using local affine-invariant image descriptors and multi-view spatial constraints. Int J Comput Vis 66(3):231–259

    Google Scholar 

  6. Lee TK, Drew MS (2007) 3D object recognition by eigen-scale-space of contours. In: First international conference on scale space methods and variational methods in computer vision (SSVM’07), pp 883–894

  7. Li W, Bebis G, Bourbakis N (2004) Integrating algebraic functions of views with indexing and learning for 3D object recognition. In: Computer vision and pattern recognition workshop, p 102, June 2004

  8. Nagabhushan P, Guru DS, Shekar BH (2006) Visual learning and recognition of 3D objects using two-dimensional principal component analysis: a robust and an efficient approach. Pattern Recognit 39(4):721–725

    Article  MATH  Google Scholar 

  9. Chen H, Bhanu B (2007) 3D free-form object recognition in range images using local surface patches. Pattern Recognit Lett 28(10):1252–1262

    Article  Google Scholar 

  10. Mian AS, Bennamoun M, Owens R (2006) Three-dimensional model-based object recognition and segmentation in cluttered scenes. IEEE Trans Pattern Anal Mach Intell 28(10):1584–1601

    Article  Google Scholar 

  11. Diplaros A, Gevers T, Patras I (2006) Combining color and shape Information for illumination-viewpoint invariant object recognition. IEEE Trans Image Process 15(1):1–11

    Google Scholar 

  12. Shotton J, Blake A, Cipolla R (2008) Multiscale categorical object recognition using contour fragments. IEEE Trans Pattern Anal Mach Intell 30(7):1270–1281

    Google Scholar 

  13. Adan A, Adan M (2004) A flexible similarity measure for 3D shapes recognition. IEEE Trans Pattern Anal Mach Intell 26(11):1507–1520

    Google Scholar 

  14. Shan Y, Sawhney HS, Matei B, Kumar R (2006) Shapeme histogram projection and matching for partial object recognition. IEEE Trans Pattern Anal Mach Intell 28(4):568–577

    Google Scholar 

  15. Pechuk M, Soldea O, Rivlin E (2008) Learning function based classification from 3D imagery. Comput Vis Image Underst 110(2):173–191

    Article  Google Scholar 

  16. Froimovich G, Rivlin E, Shimshoni I, Soldea O (2007) Efficient search and verification for function based classification from real range images. Comput Vis Image Underst 105(3):200–217

    Article  Google Scholar 

  17. Taubin G, Cooper DB (1992) 2D and 3D object recognition and positioning with algebraic invariants and covariants. In: Chapter 6 of Symbolic and numerical computation for artificial intelligence. Academic Press

  18. Huang ZH, Cohen FS (1996) Affine invariant B-spline moments for curve matching. Image Process 5(10):1473–1480

    Article  Google Scholar 

  19. Solina F, Bajcsy R (1990) Recovery of parametric models from range images: The case for superquadrics with global deformations. IEEE Trans Pattern Anal Mach Intell 12(2):131–147

    Article  Google Scholar 

  20. Ma S (1993) Conics-based stereo, motion estimation and pose determination. IJCV 10(1):7–25

    Google Scholar 

  21. Mundy JL, Zisserman A (1992) Geometric invariance in computer vision. The MIT Press

  22. Calabi E, Olver PJ, Shakiban C, Tannenbaum A, Haker S (1998) Differential and numerically invariant signature curves applied to object recognition. IJCV 26(2):107–135

    Article  Google Scholar 

  23. Wu MF, Sheu HT (1998) Representation of 3D surfaces by two-variable Fourier descriptors. IEEE Trans Pattern Anal Mach Intell 20(8):583–588

    Article  Google Scholar 

  24. Taubin G, Cukierman F, Sullivan S, Ponce J, Kriegman DJ (1994) Parameterized families of polynomials for bounded algebraic curve and surface fitting. IEEE PAMI 16:287–303

    Google Scholar 

  25. Keren D, Cooper DB, Subrahmonia J (1994) Describing complicated objects by implicit polynomials. IEEE Trans Pattern Anal Mach Intell 16:38–53

    Article  Google Scholar 

  26. Sahin T, Unel M (2005) Fitting globally stabilized algebraic surfaces to range data. In: 10th IEEE international conference on computer vision (ICCV’05), October 2005

  27. Sahin T, Unel M (2008) Stable algebraic surfaces for 3D object representation. J Math Imaging Vis 32(2):127–137

    Google Scholar 

  28. Sahin T, Unel M (2004) Globally stabilized 3L curve fitting. In: Lecture notes in computer science (LNCS-3211), pp 495–502. Springer

  29. Wolovich W, Unel M (1998) The determination of implicit polynomial canonical curves. IEEE Trans Pattern Analysis Mach Intell 20(10):1080–1089

    Article  Google Scholar 

  30. Unel M, Wolovich WA (1999) A new representation for quartic curves and complete sets of geometric invariants. Int J Pattern Recognit Artif Intell 13(8):1137–1149

    Google Scholar 

  31. Unel M, Wolovich WA (2000) On the construction of complete sets of geometric invariants for algebraic curves. Adv Appl Math 24(1):65–87

    Article  MATH  MathSciNet  Google Scholar 

  32. Subrahmonia J, Cooper DB, Keren D (1996) Practical reliable bayesian recognition of 2D and 3D objects using implicit polynomials and algebraic invariants. IEEE Trans Pattern Anal Mach Intell 18(5):505–519

    Article  Google Scholar 

  33. Vijayakumar B, Kriegman DJ, Ponce J (1995) Invariant-based recognition of complex curved 3D objects from image contours. In: International conference on computer vision, Boston, MA

  34. Wolovich W, Albakri H, Yalcin H (2002) The precise modeling and measurement of free-form surfaces. J Manuf Sci Eng 2002

  35. Keren D (1994) Using symbolic computation to find algebraic invariants. IEEE Trans Pattern Anal Mach Intell 16(11): 1143–1149

    Article  Google Scholar 

  36. Strang G (1998) Introduction to linear algebra. Wellesley-Cambridge Press

  37. Duda RO, Hart PE, Stork DG (2001) Pattern classification. Wiley

  38. Sheynin SA, Tuzikov AV (2003) Moment computation for objects with spline curve boundary. IEEE Trans Pattern Anal Mach Intell 25(10): 1317–1322

    Article  Google Scholar 

  39. Faber P, Fischer RB (2001) Pros and cons of Euclidean fitting. In: Proceedings of annual German symposium for pattern recognition (DAGM01, Munich). Springer LNCS 2191, Berlin, pp 414–420, Sep 2001

  40. Blane M, Lei Z et al (2000) The 3L algorithm for fitting implicit polynomial curves and surfaces to data. IEEE Trans Pattern Anal Mach Intell 22(3):298–313

    Google Scholar 

  41. Shilane P, Min P, Kazhdan M, Funkhouser T (2004) The Princeton Shape Benchmark, Shape Modeling International, Genova, Italy, June 2004

  42. Zhang J, Siddiqi K, Macrini D, Shokoufandeh A, Dickinson S (2005) Retrieving articulated 3-D models using medial surfaces and their graph spectra. In: International workshop On energy minimization methods in computer vision and pattern recognition

  43. Stroustrup B (2000) The C++ programming language, special edn. Addison Wesley, Reading, Mass

  44. Numerical Recipes (2007) The art of scientific computing, 3rd edn. Cambridge University Press, ISBN-10: 0521880688

  45. Kitware Inc (2009) The visualization toolkit. http://www.vtk.org/

  46. Viewer M (2009) http://mview.sourceforge.net/

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Authors and Affiliations

  1. Faculty of Engineering and Natural Sciences, Sabanci University, Istanbul, Turkey

    Mustafa Unel, Octavian Soldea, Erol Ozgur & Alp Bassa

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  1. Mustafa Unel
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  2. Octavian Soldea
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  3. Erol Ozgur
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  4. Alp Bassa
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Correspondence to Mustafa Unel.

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Unel, M., Soldea, O., Ozgur, E. et al. 3D object recognition using invariants of 2D projection curves. Pattern Anal Applic 13, 451–468 (2010). https://doi.org/10.1007/s10044-010-0179-5

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  • DOI: https://doi.org/10.1007/s10044-010-0179-5

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