Journal of the Optical Society of America A
Vol. 30,
Issue 11,
pp. 2381-2394
(2013)
•https://doi.org/10.1364/JOSAA.30.002381

Improving the performance of image classification by Hahn moment invariants

Mhamed Sayyouri, Abdeslam Hmimid, and Hassan Qjidaa

Not Accessible

Your library or personal account may give you access

Get PDF
Email
Share
Get Citation
Copy Citation Text
Mhamed Sayyouri, Abdeslam Hmimid, and Hassan Qjidaa, "Improving the performance of image classification by Hahn moment invariants," J. Opt. Soc. Am. A 30, 2381-2394 (2013)

Export Citation
- BibTex
- Endnote (RIS)
- HTML
- Plain Text
Citation alert
Save article

Abstract

The discrete orthogonal moments are powerful descriptors for image analysis and pattern recognition. However, the computation of these moments is a time consuming procedure. To solve this problem, a new approach that permits the fast computation of Hahn’s discrete orthogonal moments is presented in this paper. The proposed method is based, on the one hand, on the computation of Hahn’s discrete orthogonal polynomials using the recurrence relation with respect to the variable $x$ instead of the order $n$ and the symmetry property of Hahn’s polynomials and, on the other hand, on the application of an innovative image representation where the image is described by a number of homogenous rectangular blocks instead of individual pixels. The paper also proposes a new set of Hahn’s invariant moments under the translation, the scaling, and the rotation of the image. This set of invariant moments is computed as a linear combination of invariant geometric moments from a finite number of image intensity slices. Several experiments are performed to validate the effectiveness of our descriptors in terms of the acceleration of time computation, the reconstruction of the image, the invariability, and the classification. The performance of Hahn’s moment invariants used as pattern features for a pattern classification application is compared with Hu [IRE Trans. Inform. Theory 8, 179 (1962)] and Krawchouk [IEEE Trans. Image Process. 12, 1367 (2003)] moment invariants.

Full Article | PDF Article

More Like This

Texture classification using discrete Tchebichef moments

J. Víctor Marcos and Gabriel Cristóbal
J. Opt. Soc. Am. A 30(8) 1580-1591 (2013)

Orthogonal Fourier–Mellin moments for invariant pattern recognition

Yunlong Sheng and Lixin Shen
J. Opt. Soc. Am. A 11(6) 1748-1757 (1994)

High-precision and fast computation of Jacobi–Fourier moments for image description

C. Camacho-Bello, C. Toxqui-Quitl, A. Padilla-Vivanco, and J. J. Báez-Rojas
J. Opt. Soc. Am. A 31(1) 124-134 (2014)

Previous Article Next Article

Cited By

You do not have subscription access to this journal. Cited by links are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access Optica Member Subscription

Figures (12)

You do not have subscription access to this journal. Figure files are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access Optica Member Subscription

Tables (9)

You do not have subscription access to this journal. Article tables are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access Optica Member Subscription

Equations (50)

You do not have subscription access to this journal. Equations are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access Optica Member Subscription

	Hahn Moment Invariants
Translation Vector (TV)	${HMI}_{00}$	${HMI}_{01}$	${HMI}_{10}$	${HMI}_{11}$	${HMI}_{20}$	${HMI}_{02}$	${HMI}_{21}$	${HMI}_{12}$	${HMI}_{22}$
0 0	$6,55360000 E + 04$	$- 3,71916800 E + 08$	$- 8,15189197 E + 09$	$2,11514721 E + 12$	$1,89037805 E + 14$	$5,76047704 E + 11$	$- 2,06973287 E + 17$	$- 1,38867671 E + 16$	$2,69573599 E + 19$
$- 5$ $- 5$	$6,55360000 E + 04$	$- 3,71916800 E + 08$	$- 8,15189197 E + 09$	$2,11514760 E + 12$	$1,89037605 E + 14$	$5,76057863 E + 11$	$- 2,06973187 E + 17$	$- 1,38867571 E + 16$	$2,69573699 E + 19$
$- 5$ $+ 5$	$6,55360000 E + 04$	$- 3,71916800 E + 08$	$- 8,15189197 E + 09$	$2,11514649 E + 12$	$1,89037805 E + 14$	$5,76047704 E + 11$	$- 2,06973187 E + 17$	$- 1,38867771 E + 16$	$2,69573599 E + 19$
$+ 5$ $- 5$	$6,55360000 E + 04$	$- 3,71916800 E + 08$	$- 8,15189197 E + 09$	$2,11514793 E + 12$	$1,89037705 E + 14$	$5,76047704 E + 11$	$- 2,06973387 E + 17$	$- 1,38867571 E + 16$	$2,69573699 E + 19$
$+ 5$ $+ 5$	$6,55360000 E + 04$	$- 3,71916800 E + 08$	$- 8,15189197 E + 09$	$2,11514689 E + 12$	$1,89037875 E + 14$	$5,76057863 E + 11$	$- 2,06973287 E + 17$	$- 1,38867671 E + 16$	$2,69573599 E + 19$
Performance $σ / \| μ \| (%)$	$0,00000000 E + 00$	$1,22052957 E - 13$	$5,23186668 E - 14$	$2,68777296 E - 05$	$5,56905643 E - 05$	$9,65904698 E - 04$	$4,04517583 E - 05$	$6,02349291 E - 05$	$2,03424824 E - 05$

	Hahn Moment Invariants
Scaling Factor (SF)	${HMI}_{00}$	${HMI}_{01}$	${HMI}_{10}$	${HMI}_{11}$	${HMI}_{20}$	${HMI}_{02}$	${HMI}_{21}$	${HMI}_{12}$	${HMI}_{22}$
1	$6,55360000 E + 04$	$- 3,71916800 E + 08$	$- 8,15189197 E + 09$	$2,11514721 E + 12$	$1,89037805 E + 14$	$5,76047704 E + 11$	$- 2,06973287 E + 17$	$- 1,38867671 E + 16$	$2,69573599 E + 19$
0,8	$6,55360000 E + 04$	$- 3,71916800 E + 08$	$- 8,15189197 E + 09$	$2,11514229 E + 12$	$1,89037192 E + 14$	$5,76047897 E + 11$	$- 2,06977669 E + 17$	$- 1,38869671 E + 16$	$2,69573699 E + 19$
0,9	$6,55360000 E + 04$	$- 3,71916800 E + 08$	$- 8,15189197 E + 09$	$2,11514229 E + 12$	$1,89037147 E + 14$	$5,76047692 E + 11$	$- 2,06977669 E + 17$	$- 1,38867681 E + 16$	$2,69573799 E + 19$
1,1	$6,55360000 E + 04$	$- 3,71916800 E + 08$	$- 8,15189197 E + 09$	$2,11514589 E + 12$	$1,89037985 E + 14$	$5,76047321 E + 11$	$- 2,06977669 E + 17$	$- 1,38867651 E + 16$	$2,69573499 E + 19$
1,2	$6,55360000 E + 04$	$- 3,71916800 E + 08$	$- 8,15189197 E + 09$	$2,11514833 E + 12$	$1,89037297 E + 14$	$5,76047263 E + 11$	$- 2,06977669 E + 17$	$- 1,38866671 E + 16$	$2,69573699 E + 19$
Performance $σ / \| μ \| (%)$	$0,00000000 E + 00$	$0,00000000 E + 00$	$0,00000000 E + 00$	$1,32319057 E - 04$	$2,02801987 E - 04$	$4,72301524 E - 05$	$9,46756755 E - 04$	$7,89206995 E - 04$	$4,23135005 E - 05$

Rotation Angle (RA)	Hahn Moment Invariants
Rotation Angle (RA)	${HMI}_{00}$	${HMI}_{01}$	${HMI}_{10}$	${HMI}_{11}$	${HMI}_{20}$	${HMI}_{02}$	${HMI}_{21}$	${HMI}_{12}$	${HMI}_{22}$
0	$6,55360000 E + 04$	$- 3,71916800 E + 08$	$- 8,15189197 E + 09$	$2,11514721 E + 12$	$1,89037805 E + 14$	$5,76047704 E + 11$	$- 2,06973287 E + 17$	$- 1,38867671 E + 16$	$2,69573599 E + 19$
45	$6,55360000 E + 04$	$- 3,71916800 E + 08$	$- 8,15189197 E + 09$	$2,11547246 E + 12$	$1,89037826 E + 14$	$5,76056587 E + 11$	$- 2,06973539 E + 17$	$- 1,38867770 E + 16$	$2,69576400 E + 19$
90	$6,55360000 E + 04$	$- 3,71916800 E + 08$	$- 8,15189197 E + 09$	$2,11514723 E + 12$	$1,89037815 E + 14$	$5,76057863 E + 11$	$- 2,06973594 E + 17$	$- 1,38881689 E + 16$	$2,69572778 E + 19$
135	$6,55360000 E + 04$	$- 3,71916800 E + 08$	$- 8,15189197 E + 09$	$2,11514722 E + 12$	$1,89037854 E + 14$	$5,76056587 E + 11$	$- 2,06973518 E + 17$	$- 1,38864150 E + 16$	$2,69576741 E + 19$
180	$6,55360000 E + 04$	$- 3,71916800 E + 08$	$- 8,15189197 E + 09$	$2,11514722 E + 12$	$1,89037844 E + 14$	$5,76057863 E + 11$	$- 2,06973187 E + 17$	$- 1,38860748 E + 16$	$2,69578765 E + 19$
Performance $σ / \| μ \| (%)$	$0,000000 E + 00$	$1,492688 E - 13$	$8,272308 E - 14$	$6,876410 E - 03$	$1,064082 E - 05$	$7,473760 E - 04$	$8,564783 E - 05$	$5,739797 E - 03$	$9,069392 E - 04$

	Hahn Moment Invariants
Mixed Transformation	${HMI}_{00}$	${HMI}_{01}$	${HMI}_{10}$	${HMI}_{11}$	${HMI}_{20}$	${HMI}_{02}$	${HMI}_{21}$	${HMI}_{12}$	${HMI}_{22}$
TV: (0 0); SF:1; RA:0°	$6,55360000 E + 04$	$- 3,71916800 E + 08$	$- 8,15189197 E + 09$	$2,11514721 E + 12$	$1,89037805 E + 14$	$5,76047704 E + 11$	$- 2,06973287 E + 17$	$- 1,38867671 E + 16$	$2,69573599 E + 19$
TV: ( $- 5$ $- 5$ ); SF:0,8; RA:45°	$6,55360000 E + 04$	$- 3,71916800 E + 08$	$- 8,15189197 E + 09$	$2,11514723 E + 12$	$1,89037117 E + 14$	$5,76049475 E + 11$	$- 2,06972786 E + 17$	$- 1,38867675 E + 16$	$2,69573598 E + 19$
TV: ( $- 5$ $+ 5$ ); SF:0,9; RA:90°	$6,55360000 E + 04$	$- 3,71916800 E + 08$	$- 8,15189197 E + 09$	$2,11514724 E + 12$	$1,89037058 E + 14$	$5,76041767 E + 11$	$- 2,06972782 E + 17$	$- 1,38867673 E + 16$	$2,69573596 E + 19$
TV: ( $+ 5$ $- 5$ ); SF:1,1; RA:135°	$6,55360000 E + 04$	$- 3,71916800 E + 08$	$- 8,15189197 E + 09$	$2,11514721 E + 12$	$1,89037487 E + 14$	$5,76045940 E + 11$	$- 2,06972785 E + 17$	$- 1,38867671 E + 16$	$2,69573593 E + 19$
TV: ( $+ 5$ $+ 5$ ); SF:1,2; RA:180°	$6,55360000 E + 04$	$- 3,71916800 E + 08$	$- 8,15189197 E + 09$	$2,11514767 E + 12$	$1,89037490 E + 14$	$5,76041031 E + 11$	$- 2,06972780 E + 17$	$- 1,38867472 E + 16$	$2,69573590 E + 19$
Performance $σ / \| μ \| (%)$	$0,00000000 E + 00$	$1,36929095 E - 13$	$5,88827168 E - 14$	$5,78925663 E - 07$	$1,84309313 E - 04$	$5,73220713 E - 04$	$1,21591815 E - 04$	$6,46627083 E - 05$	$1,66512503 E - 06$

Invariant Moments	Noise Free	Salt and Pepper Noise
Invariant Moments	Noise Free	1%	2%	3%	4%
Hu	100%	95.5%	86.23%	76.26%	72.25%
Krawchouk	100%	97.12%	94.32%	91.25%	89.56%
Hahn	100%	97.5%	94.26%	92.45%	92.23%

		Salt and Pepper Noise
Invariant Moments	Noise Free	1%	2%	3%	4%
Hu	100%	94.28%	84.12%	75.03%	71.24%
Krawchouk	100%	96.85%	92.64%	90.26%	89.95%
Hahn	100%	97.56%	93.94%	92.15%	92.14%

		Salt and Pepper Noise
Invariant Moments	Noise Free	1%	2%	3%	4%
Hu	94.58%	92.26%	85.27%	74.86%	70.01%
Krawchouk	96.48%	95.17%	90.87%	85.98%	77.25%
Hahn	97.35%	96.71%	91.45%	86.58%	78.56%

		Salt and Pepper Noise
Invariant Moments	Noise Free	1%	2%	3%	4%
Hu	93.56%	91.25%	85.21%	73.42%	68.87%
Krawchouk	95.79%	94.18%	90.64%	84.76%	76.54%
Hahn	96.27%	96.11%	91.15%	88.44%	77.86%

	Average Time Computation of HMI by
Set of	Direct Method	Fast Method	ETIR%
Binary images	0.1418	0.0485	65.80%
Gray-scale images	0.2562	0.1025	59.59%

Improving the performance of image classification by Hahn moment invariants

Author Affiliations

Abstract

Cited By

Figures (12)

Tables (9)

Equations (50)

Journal of the Optical Society of America A