Abstract
Discrete orthogonal moments such as Meixner moments are powerful tools for characterizing image shape features for applications in pattern recognition and image classification. However, in the pattern recognition theory, classification of 2D/3D shapes regardless of their position, size, and orientation represents an important problem. In this paper, a new fast and accurate method is presented to obtain Meixner moments that are invariant to translation and uniform/non-uniform scaling directly from Meixner polynomials. These new invariants of Meixner moments are computed more quickly and require no numerical approximation, unlike the classical invariants of Meixner moments which are computed from geometric moments. This method is extended to compute the three-dimensional of Meixner invariant moments to translation and scaling. The results of experimental studies using scaled uniformly/non-uniformly and translated binary and gray-scale images are discussed to further verify the validity of the new invariants of Meixner moments for classification tasks.
Similar content being viewed by others
Abbreviations
- TIMMs :
-
Translation Invariants of Meixner Moments
- SIMMs :
-
Scale Invariants of Meixner Moments
- TSIMMs :
-
Translation and Scale Invariants of Meixner Moments
- ETIR :
-
Execution-Time Improvement Ratio
References
Abdulhussain SH, Ramli AR, Mahmmod BM, Al-Haddad SAR, Jassim WA (2017) Image edge detection operators based on orthogonal polynomials. Int J Image Data Fusion 8(3):293–308
Belkasim SO, Shridhar M, Ahmadi M (1991) Pattern recognition with moment invariants: a comparative study and new results. Pattern Recogn 24(12):1117–1138
Bin TJ, Lei A, Jiwen C, Wenjing K, Dandan L (2008) Subpixel edge location based on orthogonal Fourier–Mellin moments. Image Vis Comput 26(4):563–569
Caltech101. http://www.vision.caltech.edu/Image_Datasets/Caltech101/. Accessed 24 Aug 2020
CAVE | Software: COIL-20: Columbia Object Image Library. https://www.cs.columbia.edu/CAVE/software/softlib/coil-20.php. Accessed 24 Aug 2020
Chong C-W, Raveendran P, Mukundan R (2004) Translation and scale invariants of Legendre moments. Pattern Recogn 37(1):119–129. https://doi.org/10.1016/j.patcog.2003.06.003
Comtet L (2012) Advanced Combinatorics: the art of finite and infinite expansions. Springer Science & Business Media. https://doi.org/10.1007/978-94-010-2196-8
Daoui A, Yamni M, El ogri O, Karmouni H, Sayyouri M, Qjidaa H (2020) New algorithm for large-sized 2D and 3D image reconstruction using higher-order hahn moments. Circuits, Syst Signal Process 39(9):4552–4577
Doulamis A, Grammalidis N, Ioannidis M, Potsiou C, Doulamis ND, Stathopoulou EK, Ioannidis C, Chrysouli C, Dimitropoulos K (2015) 5D modelling: an efficient approach for creating spatiotemporal predictive 3D maps of large-scale cultural resources. ISPRS Annals of Photogrammetry, Remote Sensing & Spatial Information Sciences. https://doi.org/10.5194/isprsannals-II-5-W3-61-2015
El Fadili H, Zenkouar K, Qjidaa H (2003) Lapped block image analysis via the method of legendre moments. EURASIP J Adv Signal Process 2003:902–913. https://doi.org/10.1155/S1110865703305062
El ogri O, Daoui A, Yamni M, Karmouni H, Sayyouri M, Qjidaa H (2020) New set of fractional-order generalized Laguerre moment invariants for pattern recognition. Multimed Tools Appl 79(31-32):23261–23294
Flusser J, Suk T (1993) Pattern recognition by affine moment invariants. Pattern Recogn 26(1):167–174
Flusser J, Suk T, Zitova B (2016) 2D and 3D image analysis by moments. John Wiley & Sons
Hmimid A, Sayyouri M, Qjidaa H (2014) Image classification using a new set of separable two-dimensional discrete orthogonal invariant moments. J Electron Imaging 23(1):013026
Hosny KM (2007) Exact and fast computation of geometric moments for gray level images. Appl Math Comput 189(2):1214–1222
Hosny KM (2012) Fast computation of accurate Gaussian–Hermite moments for image processing applications. Digit Signal Process 22(3):476–485
Hu M-K (1962) Visual pattern recognition by moment invariants. IRE Trans Inf Theory 8(2):179–187. https://doi.org/10.1109/TIT.1962.1057692
Ioannidou A, Chatzilari E, Nikolopoulos S, Kompatsiaris I (2017) Deep learning advances in computer vision with 3d data: a survey. ACM Comput Surv (CSUR) 50(2):1–38
Jahid T, Hmimid A, Karmouni H, Sayyouri M, Qjidaa H, Rezzouk A (2018) Image analysis by Meixner moments and a digital filter. Multimed Tools Appl 77(15):19811–19831
Jahid T, Karmouni H, Sayyouri M, Hmimid A, Qjidaa H (2019) Fast algorithm of 3D discrete image orthogonal moments computation based on 3D cuboid. J Math Imaging Vis 61(4):534–554
Karmouni H, Jahid T, Lakhili Z, Hmimid A, Sayyouri M, Qjidaa H, Rezzouk A (2017) Image reconstruction by Krawtchouk moments via digital filter. In: 2017 Intelligent Systems and Computer Vision (ISCV), pp. 1–7. https://doi.org/10.1109/ISACV.2017.8054958
Karmouni H, Yamni M, El Ogri O, Daoui A, Sayyouri M, Qjidaa H (2020) Fast computation of 3D Meixner’s invariant moments using 3D image cuboid representation for 3D image classification. Multimed Tools Appl. https://doi.org/10.1007/s11042-020-09351-1
Kazhdan M, Funkhouser T, Rusinkiewicz S (2003) Rotation invariant spherical harmonic representation of 3D shape descriptors. Symp Geom Process 6:156–164
Khotanzad A, Hong YH (1990) Invariant image recognition by Zernike moments. IEEE Trans Pattern Anal Mach Intell 12(5):489–497. https://doi.org/10.1109/34.55109
Kyriakaki G, Doulamis A, Doulamis N, Ioannides M, Makantasis K, Protopapadakis E, Hadjiprocopis A, Wenzel K, Fritsch D, Klein M, Weinlinger G (2014) 4D reconstruction of tangible cultural heritage objects from web-retrieved images. Int J Herit Digit Era 3(2):431–451
Lo C-H, Don H-S (1989) 3-D moment forms: their construction and application to object identification and positioning. IEEE Trans Pattern Anal Mach Intell 11(10):1053–1064
Luo L-M, Xie X-H, Bao X-D (1994) A modified moment-based edge operator for rectangular pixel image. IEEE Trans Circ Syst Video Technol 4(6):552–554
Mademlis A, Daras P, Tzovaras D, Strintzis MG (2009) 3D object retrieval using the 3D shape impact descriptor. Pattern Recogn 42(11):2447–2459
McGill 3D Shape Benchmark. http://www.cim.mcgill.ca/~shape/benchMark/. Accessed 08 Mar 2020
Mukundan R, Ong SH, Lee PA (2001) Image analysis by Tchebichef moments. IEEE Trans Image Process 10(9):1357–1364
Nikiforov AF, Uvarov VB, Suslov SK (1991) Classical orthogonal polynomials of a discrete variable. Classical orthogonal polynomials of a discrete variable, Springer, pp. 18–54
Papakostas GA, Karakasis EG, Koulouriotis DE (2010) Accurate and speedy computation of image Legendre moments for computer vision applications. Image Vis Comput 28(3):414–423
Sayyouri M, Hmimid A, Qjidaa H (2015) A fast computation of novel set of Meixner invariant moments for image analysis. Circ Syst Signal Process 34(3):875–900
Sayyouri M, Hmimid A, Karmouni H, Qjidaa H, Rezzouk A (2015) Image classification using separable invariant moments of Krawtchouk-Tchebichef. In: 2015 IEEE/ACS 12th International Conference of Computer Systems and Applications (AICCSA), pp. 1–6. https://doi.org/10.1109/AICCSA.2015.7507142
Sayyouri M, Hmimid A, Qjidaa H (2016) Image analysis using separable discrete moments of Charlier-Hahn. Multimed Tools Appl 75(1):547–571
Shape Matching/Retrieval. http://www.dabi.temple.edu/~shape/MPEG7/dataset.html. Accessed 14 Jul 2019.
SIPI Image Database. http://sipi.usc.edu/database/. Accessed 13 May 2020
Tangelder JW, Veltkamp RC (2008) A survey of content based 3D shape retrieval methods. Multimed Tools Appl 39(3):441–471
Teague MR (1980) Image analysis via the general theory of moments. J Opt Soc Am JOSA 70(8):920–930. https://doi.org/10.1364/JOSA.70.000920
Tsougenis ED, Papakostas GA, Koulouriotis DE (2015) Image watermarking via separable moments. Multimed Tools Appl 74(11):3985–4012. https://doi.org/10.1007/s11042-013-1808-y
Wang X, Shi G, Guo F (2018) A comment on ‘translation and scale invariants of Tchebichef moments’ by Hongqing Zhu [pattern recognition 40 (2007) 2530–2542]. Pattern Recogn 77:458–463
Yamni M, Daoui A, El Ogri O, Karmouni H, Sayyouri M, Qjidaa H (2019) Influence of Krawtchouk and Charlier moment’s parameters on image reconstruction and classification. Procedia Comput Sci 148:418–427
Yamni M, Daoui A, El Ogri O, Karmouni H, Sayyouri M, Qjidaa H, Flusser J (2020) Fractional Charlier moments for image reconstruction and image watermarking. Signal Process 171:107509. https://doi.org/10.1016/j.sigpro.2020.107509
Yamni M, Karmouni H, Sayyouri M, Qjidaa H, Flusser J (2021) Novel Octonion Moments for color stereo image analysis. Digit Signal Process 108:102878
Yang B, Li G, Zhang H, Dai M (2011) Rotation and translation invariants of Gaussian–Hermite moments. Pattern Recogn Lett 32(9):1283–1298
Yap P-T, Paramesran R, Ong S-H (2003) Image analysis by Krawtchouk moments. IEEE Trans Image Process 12(11):1367–1377
Yap P-T, Paramesran R, Ong S-H (2007) Image analysis using Hahn moments. IEEE Trans Pattern Anal Mach Intell 29(11):2057–2062. https://doi.org/10.1109/TPAMI.2007.70709
Zarpalas D, Daras P, Axenopoulos A, Tzovaras D, Strintzis MG (2006) 3D model search and retrieval using the spherical trace transform. EURASIP J Adv Signal Process 2007:1–14
Zhi R, Cao L, Cao G (2018) Translation and scale invariants of Krawtchouk moments. Inf Process Lett 130:30–35
Zhu H, Shu H, Xia T, Luo L, Coatrieux JL (2007) Translation and scale invariants of Tchebichef moments. Pattern Recogn 40(9):2530–2542
Zhu H, Liu M, Shu H, Zhang H, Luo L (2010) General form for obtaining discrete orthogonal moments. IET Image Process 4(5):335–352
Acknowledgments
The authors would like to thank the anonymous referees for their helpful comments and suggestions.
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
The authors declare no conflict of interest.
Additional information
Publisher’s note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Yamni, M., Daoui, A., El ogri, O. et al. Accurate 2D and 3D images classification using translation and scale invariants of Meixner moments. Multimed Tools Appl 80, 26683–26712 (2021). https://doi.org/10.1007/s11042-020-10311-y
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11042-020-10311-y