Abstract
In this work, we propose new sets of 2D and 3D rotation invariants based on orthogonal radial dual Hahn moments, which are orthogonal on a non-uniform lattice. We also present theoretical mathematics to derive them. Thus, this paper presents in the first case new 2D radial dual Hahn moments based on polar representation of an image by one-dimensional orthogonal discrete dual Hahn polynomials and a circular function. The dual Hahn polynomials are general case of Tchebichef and Krawtchouk polynomials. In the second case, we introduce new 3D radial dual Hahn moments employing a spherical representation of volumetric image by one-dimensional orthogonal discrete dual Hahn polynomials and a spherical function, which are orthogonal on a non-uniform lattice. The 2D and 3D rotational invariants are extracts from the proposed 2D and 3D radial dual Hahn moments respectively. In order to test the proposed approach, three problems namely image reconstruction, rotational invariance and pattern recognition are attempted using the proposed moments. The result of experiments shows that the radial dual Hahn moments have performed better than the radial Tchebichef and Krawtchouk moments, with and without noise. Simultaneously, the mentioned reconstruction converges quickly to the original image using 2D and 3D radial dual Hahn moments, and the test images are clearly recognized from a set of images that are available in COIL-20 database for 2D image and PSB database for 3D image.
Similar content being viewed by others
References
Sadjadi FA, Hall EL (1980) Three-dimensional moment invariants. IEEE Trans Pattern Anal Mach Intell 2(2):127–136
Cyganski D, Orr JA (1988) Object recognition and orientation determination by tensor methods. JAI Press 7(6):662–673
Lo CH, Don HS (1989) 3-D moment forms: their construction and application to object identification and positioning. IEEE Trans Pattern Anal Machine Intell 11(10):1053–1064
Guo X (1993) Three-dimensional moment invariants under rigid transformation. In: CAIP’93: Proceedings of the 5th international conference on computer analysis of images and patterns, London. Springer, Berlin, pp 518–522
Galvez JM, Canton M (1993) Normalization and shape recognition of three-dimensional objects by 3D moments. Pattern Recognit 26(5):667–681
Reiss TH (1992) Features invariant to linear transformations in 2D and 3D. In: Proceedings of the 11th IAPR international conference on pattern recognition. Conference C: image, speech and signal analysis, vol III, pp 493–496
Canterakis N (1996) Complete moment invariants and pose determination for orthogonal transformations of 3D objects. In: Mustererkennung, 18. DAGM Symposium, Informatik aktuell. Springer, pp 339–350
Canterakis N (1999) 3D Zernike moments and Zernike affine invariants for 3D image analysis and recognition. In: Proceedings of the 11 th Scandinavian conference on image analysis scia’99, DSAGM, pp 85–93
Flusser J (2000) On the independence of rotation moment invariants. Pattern Recognit 33:1405–1410
Flusser J, Boldyš J, Zitová B (2003) Moment forms invariant to rotation and blur in arbitrary number of dimensions. IEEE Trans Pattern Anal Mach Intell 25(2):234–246
Venkataramana A (2007) Image watermarking using Krawtchouk moments. In: International conference on computing: theory and applications, Kolkata, India, pp 676–680
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
Yap P-T, Paramesran R, Ong S-H (2007) Image analysis using Hahn moments. IEEE Trans Pattern Anal Mach Intell 29(11):2057–2062
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
Xu D, Li H (2008) Geometric moment invariants. Pattern Recognit 41:240–249
Langbein M, Hagen H (2009) A generalization of moment invariants on 2D vector fields to tensor fields of arbitrary order and dimension. In: Proceedings of the 5th international symposium, ISVC 2009, Las Vegas, NV, November 30–December 2. Springer, Berlin, pp 1151–1160
Kakarala R, Mao D (2010) A theory of phase-sensitive rotation invariance with spherical harmonic and moment-based representations. In: IEEE conference on computer vision and pattern recognition CVPR’10, pp 105–112
Fehr J (2010) Local rotation invariant patch descriptors for 3D vector fields. In: Proceedings of the 20th international conference on pattern recognition ICPR’10. IEEE Computer Society, pp 1381–1384
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), vol 2, pp 212–219
Skibbe H, Reisert M, Burkhardt H (2011) SHOG-spherical HOG descriptors for rotation invariant 3D object detection. In: Mester R, Felsberg M (eds) Deutsche Arbeitsgemeinschaft für Mustererkennung DAGM’11, Lecture notes in computer science, vol 6835. Springer, pp 142–151
Xiao B, Ma J-F, Cui J-T (2012) Radial Tchebichef moment invariants for image recognition. J Vis Commun Image Represent 23(2):381–386
Xiao B, G-y Wang (2013) Generic radial orthogonal moment invariants for invariant image recognition. J Vis Commun Image Represent 24(7):1002–1008
Xiao B, G-y Wang, W-s Li (2014) Radial shifted Legendre moments for image analysis and invariant image recognition. Image Vis Comput 32(12):994–1006
Zhu H, Shu H, Zhou J, Luo L, Coatrieux JL (2007) Image analysis by discrete orthogonal dual Hahn moments. Pattern Recognit Lett 28:1688–1704
http://www.cs.columbia.edu/CAVE/software/softlib/coil-20.php
Princeton, Princeton Shape Benchmark, PSB database. http://www.cim.mcgill.ca/~shape/benchMark/
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
El Mallahi, M., Zouhri, A., Mesbah, A. et al. 3D radial invariant of dual Hahn moments. Neural Comput & Applic 30, 2283–2294 (2018). https://doi.org/10.1007/s00521-016-2782-x
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00521-016-2782-x