Skip to main content
Log in

Robust classification of 3D objects using discrete orthogonal moments and deep neural networks

  • Published:
Multimedia Tools and Applications Aims and scope Submit manuscript

Abstract

In this paper, we propose a new model based on 3D discrete orthogonal moments and deep neural networks (DNN) to improve the classification accuracy of 3D objects under geometric transformations and noise. However, the utilization of moment invariants presents some drawbacks: They can’t describe the object efficiently, and their computation process is time consuming. Discrete orthogonal moments have the property to extract pertinent features from an image even in lower orders and are robust to noise. The main goal of this work is to investigate the robustness of the proposed model to geometric transformations like translation, scale and rotation and noisy conditions. The experiment simulations are conducted on datasets formed by applying some geometric transformations and noise on selected objects from McGill database. The obtained results indicate that the proposed model achieves high performance classification rates, robust to geometric transformations and noise degradation than other methods based on moment invariants.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5

Similar content being viewed by others

References

  1. Al-Ayyoub M, AlZu’bi S, Jararweh Y, Shehab M-A, Gupta B-B (2018) Accelerating 3D medical volume segmentation using GPUs. Multimed Tools Appl 77(4):4939–4958

    Google Scholar 

  2. AlZu’bi S, Shehab M, Al-Ayyoub M, Jararweh Y, Gupta B (2018) Parallel implementation for 3d medical volume fuzzy segmentation. Pattern Recogn Lett

  3. Batioua I, Benouini R, Zenkouar K, Zahi A, El Fadili H (2017) 3D image analysis by separable discrete orthogonal moments based on Krawtchouk and Tchebichef polynomials. Pattern Recogn 71:264–277

    Google Scholar 

  4. Belkasim SO, Shridhar M, Ahmadi M (1991) Pattern recognition with moment invariants: a comparative study and new results. Pattern Recogn 24:1117–1138

    Google Scholar 

  5. Benouini R, Batioua I, Zenkouar K, Najah S, Qjidaa H (2018) Efficient 3D object classification by using direct Krawtchouk moment invariants. Multimed Tools Appl:1–26

  6. Blum C (2005) Ant colony optimization: introduction and recent trends. Phys Life Rev 2(4):353–373

    Google Scholar 

  7. Canterakis N (1999) 3D Zernike moments and Zernike affine invariants for 3D image analysis and recognition. In proceedings of the 11th Scandinavian conference on image analysis SCIA’99, DSAGM, pp 85-93

  8. Chong C-W, Raveendran P, Mukundan R (2003) The scale invariants of pseudo-Zernike moments. Pattern Anal Applic 6:176–184

    MathSciNet  MATH  Google Scholar 

  9. Chong C-W, Raveendran P, Mukundan R (2004) Translation and scale invariants of Legendre moments. Pattern Recogn 37:119–129

    MATH  Google Scholar 

  10. Clevert DA, Unterthiner T, Hochreiter S (2016) Fast and accurate deep network learning by exponential linear units (ELUS). In: conference ICLR. arXiv:1511.07289

  11. Cyganski D, Orr JA (1988) Object recognition and orientation determination by tensor methods. JAI Press 3:101–144

    Google Scholar 

  12. Dai XB, Shu HZ, Luo LM, Han GN, Coatrieux JL (2010) Reconstruction of tomographic images from limited range projections using discrete radon transform and Tchebichef moments. Pattern Recogn 43:1152–1164

    MATH  Google Scholar 

  13. Fehr J, Burkhardt H (2008) 3D rotation invariant local binary patterns. In: 19th international conference on pattern recognition ICPR’08. IEEE Computer Society, Madison, pp 1–4

    Google Scholar 

  14. Flusser J, Suk T, Zitova B (2009) Moments and Moment Invariants in Pattern Recognition. Wiley, Hoboken

    MATH  Google Scholar 

  15. Flusser J, Suk T, Zitova B (2016) 2D and 3D image analysis by moments, Wiley, Hoboken

  16. Galvez JM, Canton M (1993) Normalization and shape recognition of three-dimensional objects by 3D moments. Pattern Recogn 26:667–681

    Google Scholar 

  17. Glorot X, Bengio Y (2010) Understanding the difficulty of training deep feed forward neural networks. In: proceedings of the 13th international conference on artificial intelligence and statistics. Pp 249-256

  18. Goh H-A, Chong C-W, Besar R, Abas FS, Sim K-S (2009) Translation and scale invariants of Hahn moments. Int J Image Graph 9:271–285

    Google Scholar 

  19. Guo X (1993) Three dimensional moment invariants under rigid transformation. In: proceedings of the fifth international Conf Comput anal images patterns (CAIP’93). Springer, pp 518–522

  20. Hinton G, Deng L, Yu D, Dahl G et al (2012) Deep neural networks for Accoustic Modelling in speech recognition. IEEE Signal Process Mag 29

  21. Hu M-K (1962) Visual pattern recognition by moment invariants. IRE Transaction on Information Theory 8:179–187

    MATH  Google Scholar 

  22. Iscan Z, Dokur Z, Olmez T (2010) Tumor detection by using Zernike moments on segmented magnetic resonance brain images. Expert Syst Appl 37:2540–2549

    Google Scholar 

  23. Jian M, Dong J, Lam K-M (2013) FSAM: a fast self-adaptive method for correcting non-uniform illumination for 3D reconstruction. Comput Ind 64(9):1229–1236

    Google Scholar 

  24. Jian M, Yin Y, Dong J, Zhang W (2018) Comprehensive assessment of non-uniform illumination for 3D heightmap reconstruction in outdoor environments. Comput Ind 99:110–118

    Google Scholar 

  25. Kazhdan M (2007) An approximate and efficient method for optimal rotation alignment of 3D models. IEEE Trans Pattern Anal Mach Intell 29(7):1221–1229

    MathSciNet  Google Scholar 

  26. Khotanzad A, Hong YH (1990) Invariant image recognition by Zernike moments. IEEE Trans Pattern Anal Mach Intell 12:489–497

    Google Scholar 

  27. Kingma, DP, Ba J (2014) Adam: A method for stochastic optimization. arXiv preprint arXiv:1412.6980.

  28. Krizhevsky A, Sutskever I, Hinton G (2012) ImageNet classification with deep convolutional neural networks. Adv Neural Inf Proces Syst:1079–1105

  29. Liao S, Chiang A, Lu Q, Pawlak M (2002) Chinese character recognition via gegenbauer moments. In: 2002 proceedings 16th international conference on pattern recognition. IEEE, pp 485–488

  30. Lo CH, Don HS (1989) 3-D moment forms: their construction and application to object identification and positioning. IEEE Trans Anal and Machine Intell 11:1053–1064

    Google Scholar 

  31. Loffe S, Szegedy C (2015) Batch normalization: Accelerating deep network training by reducing internal covariate shift. In: proceedings of the 32nd International Conference on Machine Learning. pp 448–456

  32. Luciano L, Hamza A-B (2018) Deep learning with geodesic moments for 3D shape classification. Pattern Recogn Lett 105:182–190

    Google Scholar 

  33. Mademlis A, Axenopoulos A, Daras P, Tzovaras D, Strintzis MG (2006) 3D content-based search based on 3D Krawtchouk moments. In: 2006 third international symposium on 3D data processing, visualization, and transmission (3DPVT’06). IEEE, pp 743–749

  34. McGill 3D Shape Benchmark. www.cim.mcgill.ca/~shape/benchMark/

  35. Mesbah A, Berrahou A, EL Mallahi M, Qjidaa H (2016) Fast and efficient computation of three-dimensional Hahn moments. Journal of Electronic Imaging 25:061621

    Google Scholar 

  36. Mesbah A, Berrahou A, Hammouchi H, Berbia H, Qjidaa H, Daoudi M (2018) Non-rigid 3D model classification using 3D Hahn moment convolutional neural networks

  37. Mesbah A, El Mallahi M, Lakhili Z, Qjidaa H, Berrahou A (2016) Fast and accurate algorithm for 3D local object reconstruction using Krawtchouk moments. In: 2016 IEEE 5th international conference on multimedia computing and systems (ICMCS). IEEE, pp 1–6

  38. Mukundan R, Ong SH, Lee PA (2001) Image analysis by Tchebichef moments. IEEE Trans Image Process 10:1357–1364

    MathSciNet  MATH  Google Scholar 

  39. Mukundan R, Ramakrishnan K (1998) Moment functions in image analysis—theory and applications.World scientific

  40. Mundy J-L, Zisserman A (1992) Geometric invariance in computer vision. MIT Press, Cambridge

    Google Scholar 

  41. Nair V, Hinton GE (2010) Rectified linear units improve restricted boltzmann machines. In: proceedings of the 27th international conference on machine learning (ICML-10). Pp 807–814

  42. Nasrabadi NM (2007) Pattern recognition and machine learning. Journal of Electronic Imaging 16:49901

    Google Scholar 

  43. Palaniappan R, Raveendran P, Omatu S (2000) New invariant moments for non-uniformly scaled images. Pattern Anal Applic 3:78–87

    Google Scholar 

  44. Pandey VK, Singh J, Parthasarathy H (2016) Translation and scale invariance of 2D and 3D Hahn moments. In: IEEE, pp 255–259

  45. Reiss T-H (1993) Recognizing planar objects using invariant image features. Springer, Berlin

    MATH  Google Scholar 

  46. Reverdy P, Leonard NE (2016) Parameter estimation in Softmax decision-making models with linear objective functions. IEEE Trans Autom Sci Eng 13:54–67

    Google Scholar 

  47. Ruder S (2016) An overview of gradient descent optimization algorithms. arXiv preprint arXiv:1609.04747

  48. Rumelhart D-E, Hinton G-E, Williams R-J (1985) Learning internal representations by error propagation. Nature 323(99):533–536

    MATH  Google Scholar 

  49. Sadjadi FA, Hall EL (1980) Three-dimensional moment invariants. IEEE Trans Pattern Anal Mach Intell:127–136

  50. Sheng Y, Shen L (1994) Orthogonal Fourier-Mellin moments for invariant pattern recognition. JOSA A 11:1748–1757

    Google Scholar 

  51. Sietsma J, Dow R-J (1991) Creating artificial neural networks that generalize. Neural Netw 4(1):67–79

    Google Scholar 

  52. Singh C (2012) Local and global features based image retrieval system using orthogonal radial moments. Opt Lasers Eng 50:655–667

    Google Scholar 

  53. Singh C, Walia E, Upneja R (2012) Analysis of algorithms for fast computation of pseudo Zernike moments and their numerical stability. Digit Signal Process 22:1031–1043

    MathSciNet  Google Scholar 

  54. Srivastava N, Hinton G, Krizhevsky A, Sutskever I, Salakhutdinov R (2014) Dropout: a simple way to prevent neural networks from overfitting. J Mach Learn Res 15:1929–1958

    MathSciNet  MATH  Google Scholar 

  55. Suk T, Flusser J (2003) Combined blur and affine moment invariants and their use in pattern recognition. Pattern Recogn 36:2895–2907

    MATH  Google Scholar 

  56. Suk T, Flusser J (2011) Tensor method for constructing 3D moment invariants. In: proceedings of the 14th international conference on computer analysis of images and patterns (CAIP’11), pp 212-219

  57. Teague MR (1980) Image analysis via the general theory of moments. JOSA 70:920–930

    MathSciNet  Google Scholar 

  58. Wu H, Coatrieux JL, Shu H (2013) New algorithm for constructing and computing scale invariants of 3D Tchebichef moments. Math Probl Eng

  59. Xiao B, Zhang Y, Li L, Li W, Wang G (2016) Explicit Krawtchouk moment invariants for invariant image recognition. Journal of Electronic Imaging 25:023002

    Google Scholar 

  60. Xu B, Wang N, Chen T, Li M (2015) Empirical evaluation of rectified activations in convolutional network. arXiv:1505.00853

  61. Yang B, Dai M (2011) Image analysis by Gaussian-Hermite moments. Signal Process 91:2290–2303

    MATH  Google Scholar 

  62. Yang B, Flusser J, Suk T (2015) 3D rotation invariants of Gaussian–Hermite moments. Pattern Recogn Lett 54:18–26

    Google Scholar 

  63. Yap P-T, Paramesran R, Ong S-H (2003) Image analysis by Krawtchouk moments. IEEE Trans Image Process 12:1367–1377

    MathSciNet  Google Scholar 

  64. Zhang Y, Wen C, Zhang Y, Soh YC (2002) Determination of blur and affine combined invariants by normalization. Pattern Recogn 35:211–221

    MATH  Google Scholar 

  65. Zhou J, Shu H, Zhu H, Toumoulin C, Luo L (2005) Image analysis by discrete orthogonal Hahn moments. In: Image Analysis Recognition. Springer, pp 524–531

  66. Zhu H, Shu H, Liang J, Luo L, Coatrieux J-L (2007) Image analysis by discrete orthogonal Racah moments. Signal Process 87:687–708

    MATH  Google Scholar 

  67. Zhu H, Shu H, Xia T, Luo L, Coatrieux JL (2007) Translation and scale invariants of Tchebichef moments. Pattern Recogn 40:2530–2542

    MATH  Google Scholar 

  68. Zhu H, Shu H, Zhou J, Luo L, Coatrieux J-L (2007) Image analysis by discrete orthogonal dual Hahn moments. Pattern Recogn Lett 28:1688–1704

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Zouhir Lakhili.

Additional information

Publisher’s note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Lakhili, Z., El Alami, A., Mesbah, A. et al. Robust classification of 3D objects using discrete orthogonal moments and deep neural networks. Multimed Tools Appl 79, 18883–18907 (2020). https://doi.org/10.1007/s11042-020-08654-7

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11042-020-08654-7

Keywords

Navigation