This paper presents mathematical integration of Zernike Moments and United Moment Invariant for extracting printed insect images.  These features are further mining for granular information by investigating the variance  of Interclass and intra-class. The results reveal that the proposed integrated formulation yield better analysis compared to conventional Zernike moments and United Moment Invarian

Bakar, Norsharina Abu

Darus, Maslina

Shamsuddin, Siti Mariyam

English

Jurnal GENERIC

Vol.6 No.1 (Januari 2011) JURNAL GENERIC 1 ISSN: 1907-4093 (print) / 2087-9814 (online) © 2011 JURNAL GENERIC   Abstract— This paper presents mathematical integration of Zernike Moments and United Moment Invariant for extracting printed insect images.  These features are further mining for granular information by investigating the variance of Inter-class and intra-class. The results reveal that the proposed integrated formulation yield better analysis compared to conventional Zernike moments and United Moment Invariant.   Keywords— Feature Extraction, Granular Mining, Inter-class, Intra-class, Pattern Recognition, United Moment Invariant, and Zernike Moment Invariant,   I. INTRODUCTION he mathematical concept of moments has been around since 1960s. Some of them are used for mechanics and statistics to pattern recognition and image understanding. Past few years, there were many researchers on moment functions have been explored in pattern recognition such as United Moment Invariant, Aspect Moment Invariant and etc. The techniques have been investigated to improve conventional regular moment by proposing the scaling factor of geometrical function that has been proposed by Hu [1]. However, previous studies reveal that there are weaknesses in Hu’s scaling factor [2].  Table 1 shows previous studies on enhancement of Moment Invariants from year 1962 to year 2008. All the proposed techniques are based on the drawbacks of Geometric Moment Invariants. Some of the drawbacks are: 1) Not sensitivity to image noise, aspect of information redundancy and capability for image representation [6]. 2) Lose scale invariance in discrete condition [7]. 3) Not good in boundary condition [4]. 4) Error if the data are unequally scaling data [8]. On the other hand, [3] has proposed United Moment Invariant (UMI) that was based on the Geometric Moment Invariant (GMI) [3], and it was derived to improve the moment invariants of [4]. UMI was developed to handle with the images with boundary and shape representation. The remainder of this paper is organized as follows: Section II describes related work on Geometric Moment Invariants in pattern recognition. Section III describes an  1Norsharina Abu Bakar was in Universiti Teknologi Malaysia; e-mail: norsharina85@gmail.com).  2Siti Mariyam Shamsuddin is professor at Department of Computer Graphics & Multimedia, Faculty of Computer Science & Information Systems, Universiti Teknologi Malaysia (e-mail: mariyam@utm.my/ sitimariyams@gmail.com). 3Maslina Darus is professor at Pusat Pengajian Sains Matematik, Fakulti Sains dan Teknologi, Universiti Kebangsaan Malaysia. (e-mail: maslina@pkrisc.cc.ukm.my). integration of Zernike moments with United Moment Invariant, while Section IV presents the sample data of the study. Section V introduces the concept of inter-class and intra-class, and provides the experimental results and analysis of the proposed approach. Finally Section VI gives the conclusion of the study. TABLE I.  TRENDS OF MOMENT INVARIANT DERIVATION BASED ON GEOMETRIC FUNCTION Year Researcher Technique 1962 Hu Geometric Moment Invariant 1980 Teague Zernike Moment Invariant 1980 Teague Legendre Moment Invariant 1992 Flusser and Suk Affine Moment Invariant 1993 Chen Improve Moment Invariant 1994 Feng And Keane Aspect Moment Invariant 2000 S. M. Shamsuddin Higher Order Centralized  Scale – Invariant 2001 R.Mukundan Tchebichef Moment Invariant 2003 Yinan United Moment Invariant 2003 Yap  Krawtchouk Moment Invariant 2007 A.K. Muda, S.M Shamsuddin, M. Darus Higher Order United Scaled Invariants 2008 A.K Muda Aspect United Moment Invariant  II. RELATED WORK OF MOMENT INVARIANT Various studies have been conducted on improvement of the algorithms for United Moment Invariant and Zernike Moment Invariant. In 1934, F. Zernike introduced Zernike Moments, and later, in 1980, this technique was applied by M.Teague for digital images [5]. Consequently, there are many applications on using ZMI have been explored (Table II). Zernike moment has been proven better in terms of offering the ability of features and sensitivity to the noisy phase low despite its complex calculation. Its representation in terms of a concentrated moment is given as follows [5]:  ( )1 20 023 2 1ZM η ηpi  = + −   ( )2 22 20 02 1129 4ZM η η ηpi = − +   ( ) ( )2 23 03 21 30 12216 3ZM η η η ηpi = − + +   ( ) ( )2 24 03 21 30 122144 3ZM η η η ηpi = − + +    An Integrated Formulation of Zernike Invariant for Mining Insect Images Norsharina Abu Bakar1,  Siti Mariyam Shamsuddin2,  Maslina Darus3 T2  JURNAL GENERIC Norsharina Et Al. ( )( ) ( ) ( )( )( ) ( ) ( )2 203 21 03 21 03 21 30 125 4 2 230 12 30 12 30 12 03 213 3138243 3ZMη η η η η η η ηpi η η η η η η η η  − + + − +   =    − − + + − +    ( ) ( ) ( )( )( )2 202 20 30 12 03 216 311 03 21 30 128644ZMη η η η η ηpi η η η η η  − + − +   =   + + +    TABLE II.  APPLICATIONS OF ZERNIKE MOMENT INVARIANT No Authors Objective Year 1. Belkasim S.O Handwritten Numbers Recognition 1989 2. P.Pejnovic Tank, Helicopter Air-Craft and Ship recognition 1992 3. W. Y Kim et al Alphanumeric Machine-Printed Character recognition 1994 4. H.Lim et al Chinese character recognition 1996 5. J. Haddadnia et al. Face recognition 2001 6. Qing Chen,Xioli Yang,Jiying Zhao image watermarking 2005 7. Harikesh Singh, Dr. R. K. Sharma online handwritten character recognition 2007 8. R. Sanjeev Kuntee, RD Sudhaker Samuel Kanada character recognition 2007 9. Chong-Yaw Wee1, ∗Raveendran Paramesran1, Fumiaki Takeda2 Rice Sorting System 2007   On the other hand, United Moment Invariant which was derived by Yinan [7] in 2003, found that the rotation, translation and scaling can be discretely kept invariant to region, closed and unclosed boundary. The formulations of UMI is given [7]:  ( )( )1 2 12 6 1 43 5 44 5 3 45 1 5 2 36 1 2 3 67 1 5 3 68 3 4 5////////θ φ φθ φ φ φθ φ φθ φ φ φθ φ φ φ φθ φ φ φ φθ φ φ φ φθ φ φ φ====== +== +   However, in 2007, the integration techniques of High Order Moment Invariant and United Moment Invariant were purposed by A.K. Muda et. al [2]. This study has been extended to other unequal scaling invariant by integrating with Aspect Moment Invariants [9].                                   Figure 1.  Chronology of Zernike United Moment Invariant                 III. ZERNIKE UNITED MOMENT INVARIANT UMI was derived from Geometric Moment Invariant and Improve Moment Invariant (IMI) [3] (refer to Figure 1). GMI is usable for region representation in discrete condition; however it is high in computational times for boundary representation [4]. Thus, Chen proposed IMI that practical for boundary and increased the computation speed. However, Yinan proposed a new technique that was effectively the shape of image on both region and boundary in discrete and continuous condition [3]. The combination of Zernike and United Moment is implemented to get better formulations that will yield good representation for boundary, region, discrete and noise resilience, information redundancy and reconstruction capability. UMI formulation is based on geometrical representation that taken into consideration the Normalized Central Moment of GMI and Boundary Representation of IMI[4] .  The integration formulation of ZMI and UMI is given as below. We define standard scaling equation as below:  Improved Moment Invariant  Usable in boundary-continuous  condition  Improve computation speed Zernike Moment Invariant  Outperforming in terms of noise resilience, information redundancy and reconstruction capability.   United Moment Invariant  Usable in region-discrete condition  Usable in boundary (close -unclose) Zernike United Moment Invariant  Usable in region-discrete condition  Usable in boundary (close -unclose) -continuous condition  Outperforming in terms of noise resilience, information redundancy and reconstruction capability.  Geometric Moment Invariant  Usable in region (discrete) and boundary(continuous) condition  Problem In boundary-computational time  Lose in scale invariance indiscrete condition  Vol.6 No.1 (Januari 2011) JURNAL GENERIC 3 ISSN: 1907-4093 (print) / 2087-9814 (online) © 2011 JURNAL GENERIC ( ) 200 2pqpq p qµηµ+ +=                                 ( ) 200'2p qp qpq pq pqp qρη ρ η µµ+++ += =                      ( ) 100''pqpq p qµηµ + +=                  From the above equations, we find that, each term has pqµ . Yinan [3] said that if we can contemporary avoid the influence of 00µ and, the united formula can be materialized. Hence, the eight formulas for United Moment Invariants (UMI) is presented as:  ( )( )1 2 12 6 1 43 5 44 5 3 45 1 5 2 36 1 2 3 67 1 5 3 68 3 4 5////////θ φ φθ φ φ φθ φ φθ φ φ φθ φ φ φ φθ φ φ φ φθ φ φ φ φθ φ φ φ====== +== +  However, in this integration, the φ values are substituted by Zernike’s moments as shown below.  ( )( )( ) ( )( ) ( )( ) ( ) ( ) ( )( )( ) ( ) ( )1 20 022 22 20 02 1122 23 03 21 30 1222 24 03 21 30 1222 203 21 03 21 03 21 30 125 4 2 230 12 30 12 30 12 03 213 2 19 416 3144 33 3138243 3ZMZMZMZMZMη ηpiη η ηpiη η η ηpiη η η ηpiη η η η η η η ηpi η η η η η η η η = + −  = − +   = − + +   = − + +   − + + − +  = − − + + − +( ) ( ) ( )( )( )2 202 20 30 12 03 216 311 03 21 30 128644ZMη η η η η ηpi η η η η η       − + − +   =   + + +    For example,   ( )( ) ( )22 22 20 02 112 220 02 112 4003 49 1 4ϕ η η ηpiµ µ µpi µ   = × − +       = × × − +      and  ( )( ) ( )1 20 02 0020 022003 23 12 1ϕ η η ηpiµ µpi µ = × + −     = × × + −      so,    ( ) ( )( ) ( )( )( )( )( )2112 220 02 112 40020 02200220 02 2112 20020 02009 1 43 12 19 43 2 1ϕθϕµ µ µpi µµ µpi µµ µ µpi µµ µpi µ=  × × − +  =    × × + −     − × +  =  +  × × −       Using the same approach as above, we get:   ( )( )( )( )( )( )( )( )( )( )( )( )22 220 02 11120 20 002420 02 2112 4 200 00220 022 200 00220 02 2112 20020 02003' ' 4 '' 3 2 ' ' '9 43 2 19 43 2 1η η ηpiθη η ηpiµ µρ µpi µ µµ µρpi µ µµ µ µpi µµ µpi µ   × − +     = × + −  − × × +  =  +  × × −     − × +  =  +  × × −        4  JURNAL GENERIC Norsharina Et Al. ( )( )( )( )( )( )( )( )( )( )2420 02 2112 4 200 00220 022 200 00220 02 2112 20020 02009 43 2 19 43 2 1µ µρ µpi µ µµ µρpi µ µµ µ µpi µµ µpi µ − × × +  =  +  × × −     − × +  =  +  × × −       and   ( )( )( ) ( )( ) ( )( )( )( )( )22 220 02 11120 20 002 220 02 112 60020 02300220 02 2112 20020 02003'' '' 4 '''' 3 2 '' '' ''9 1 43 12 19 43 2 1η η ηpiθη η ηpiµ µ µpi µµ µpi µµ µ µpi µµ µpi µ   × − +     = × + −   × × − +  =    × × + −     − × +  =  +  × × −       From the above derivation, we found that 1 1 1'' 'θ θ θ= = . Hence, this has proven that 1θ can be applied for both region and boundary in discrete and continues condition.   IV. SAMPLE DATA The insect images will be used in this research.  Initially, the insect images are scanned with 300 dpi (dot per inch) and 150 dpi resolutions. Figure 2 depicts sample of insect’s images and Figure 3 illustrates various orientations of insect images in the same class.    Figure 2.  Insect Images    Figure 3.  Insect Images (Orientation)  V. RESULT AND ANALYSIS In this study, the invarianceness of the proposed integrated formulations are validated using intra-class and inter-class by calculating the MAE (Min Absolute Error) as shown below:  ( )∑=−=niii rxnMAE11,  where n  is number of image, ix  is the current image and ir  is the reference image. The first image is the reference image. Intra-class is the process that defines the similar images with the small value of MAE. However, inter-class is the process of defining the difference images with high MAE value.   A. Intraclass Analysis For intra-class analysis, we used eight sample insect images to get the invariance’s of the techniques. All the images have different orientation with same class. The random samples of images are bactrocera maculigera (BM), bean bruchid (BB), chocolate moth (CM), dried current moth (DC), grain weevil (GW), indian meal moth (IM), rusty grain beetle (RG), and saw-toothed grain beetle (ST). Figure 4 shows example of intra-class analysis/ Bactrocera maculigera(BM) insect images are used in this study with different orientations.    Vol.6 No.1 (Januari 2011) JURNAL GENERIC 5 ISSN: 1907-4093 (print) / 2087-9814 (online) © 2011 JURNAL GENERIC   Figure 4.  Sample insect image for intra-class analysis  From Table III, intra-class distance of ZUMI has smaller value for seven insect images and one insect image in UMI (saw-toothed grain beetle).  TABLE III.  RESULT  OF INTRA-CLASS ANALYSIS ZUMI UMI ZMI BB 0.915747 1.615862986 15.22766 BM 0.392484 1.705341657 3.969996 CM 1.108088 2.120735 1.634658 DC 0.919749 1.315753805 27.96692 GW 1.046265 1.881051745 27.3219 IM 0.969856 1.996245217 9.254302 RG 1.251929 2.426967495 31.0565 ST 1.913044 1.846069911 65.39193   Figure 5 illustrates that Zernike Moment Invariant (ZMI) gives higher value of MAE compared to other techniques.      Figure 5.  Intraclass Analysis of Insects’ Images. From Figure 5, it shows that ZUMI gives smaller value of MAE for all images. However, Figure 6 shows that UMI gives smaller MAE compared to ZUMI for saw-toothed grain beetle (ST) images. The difference MAE value is about 0.0066974089.    Figure 6.  Comparison result between ZUMI and UMI.  B. Interclass analysis The samples of images for interclass analysis are shown in Figure 7. There are 4 experiments for defining interclass analysis, and these include: 1) Interclass distance between saw-toothed grain beetle (ST) and rusty grain beetle (RG). 2) Interclass distance between chocolate moth(CM) and cocoa pod pentatomid(CP). 3) Interclass distance between bactrocera maculigera(BM) and natal fruit fry(NF). 4) Interclass distance between 6 and 9 (for testing only).        Figure 7.  Sample insect images of inter-class analysis  Table IV depicts the comparison between three Moment Invariants (ZUMI, UMI, and ZMI). We label the experiments as below:  1) B1: the comparison between saw-toothed grain beetle        (ST) and rusty grain beetle (RG). 2) B2: the comparison between chocolate moth(CM) and cocoa pod pentatomid(CP). 3) B3: the comparison between bactrocera maculigera(BM) and natal fruit fry(NF). 4) B4: the comparison between 6 and 9 (for testing only).  TABLE IV.  RESULT OF INTER-CLASS ANALYSIS B1 B2 B3 B4 U 0.289149 0.591789 2.705702 0.07581 Z 0.747368 55.49137 11.68222 4.54826 ZU 0.760303 0.311496 0.589317 2.371722  From Table IV, experiment B1 for inter-class shows that ZUMI gives the higher MAE values than others. However, for other experiments (B2, B3, B4), it shows that ZMI gives the highest MAE values compared to others. Experiment B3 shows that UMI gives smaller MAE values than others. However, in the last experiment for interclass analysis, the ZUMI gives higher value of MAE compared to UMI. Besides that, ZMI gives higher MAE values for all experiments compared to others as shown in Figure 8.    6  JURNAL GENERIC Norsharina Et Al.  Figure 8.  The graph of inter-class anylisis result.  VI. CONCLUSION From this study, we found that the proposed integrated formulations yield promising results compared to the conventional Zernike Moment Invariant and United Moment Invariant. The summary of the results are presented in Table V. As a whole, our proposed method is better in giving invarianceness of insect images in terms of inter-class and intra-class.  TABLE V.  SUMMARIZATION OF THE RESULT Technique Invarianceness Decision The proposed Integrated Formulation (Zernike United Moment Invariant) Intra-class Good Inter-class Better Zernike Moment Invariant Intra-class Bad Inter-class Good United Moment Invariant Intra-class Better Inter-class Bad   ACKNOWLEDGMENT Authors would like to thank Research Management Centre (RMC) Universiti Teknologi Malaysia, for the research activities, Soft Computing Research Group (SCRG) for the support in making this study a success.   REFERENCES [1] Hu, M.-K. (1962). "Visual pattern recognition by moment invariants."  Information Theory, IRE Transactions 8(2):179-187. [2] Muda, A. K., S. M. Shamsuddin, et al. (2007). "Invariancenes       of higher order united scaled invariants." Advances in Computer Science and Engineering 1(2): 105-118 [3] Sun, Y., W. Liu, et al. (2003). United moment invariants for shape discrimination. Robotics, Intelligent Systems and Signal Processing, 2003. Proceedings. 2003 IEEE International Conference  [4] Chaur-Chin Chen, “Improved Moment Invariant for Shape       Discrimination” Pattern Recognition 26, pp.683-686, 1993. [5] Teague, M. R. (1980). "Image analysis via the general theory  of moments." J. Opt. Soc. Am. 70(8): 920. [6] Teh, C.-H. and R. T. Chin (1988). "On Image Analysis by the       Methods of Moments." IEEE Trans. Pattern Anal. Mach. Intell.      10(4): 496-513. [7] Mingyue Ding, Jinling Chang and Jiaxiong Peng,”Research on Moment Invariant Algorithm,” Journal of Data Acquisition & Processing vol.7      No.1,pp1-9,Mar,1992. [8] S. M. Shamsuddin, M. N. Sulaiman, and M. Darus, "Invarianceness of       Higher Order Centralised Scaled-invariants Undergo Basic       Transformations," International Journal of Computer Mathematics,       vol. 79, pp. 39 - 48, Taylor & Francis, 2002. [9] Azah Kamila Muda,Siti Mariyam Shamsuddin & Maslina Darus.     2008. Discretization of Integrated Moment Invariants for Writer Identification. Proceeding of The 4th IASTED International Conference on Advances in Computer Science and Technology (ACST 2008-ACTA Press), 2-4 April, Langkawi,pp:372-377. 

An Integrated Formulation of Zernike Invariant for Mining Insect Images

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An Integrated Formulation of Zernike Invariant for Mining Insect Images

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