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Journal articles on the topic 'Zernike moments'

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Published: 4 June 2021

Last updated: 11 September 2023

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1

Chong, Chee-Way, P. Raveendran, and R. Mukundan. "An Efficient Algorithm for Fast Computation of Pseudo-Zernike Moments." International Journal of Pattern Recognition and Artificial Intelligence 17, no. 06 (September 2003): 1011–23. http://dx.doi.org/10.1142/s0218001403002769.

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Pseudo-Zernike moments have better feature representation capability, and are more robust to image noise than those of the conventional Zernike moments. However, due to the computation complexity of pseudo-Zernike polynomials, pseudo-Zernike moments are yet to be extensively used as feature descriptors as compared to Zernike moments. In this paper, we propose two new algorithms, namely coefficient method and p-recursive method, to accelerate the computation of pseudo-Zernike moments. Coefficient method calculates polynomial coefficients recursively. It eliminates the need of using factorial functions. Individual order or index of pseudo-Zernike moments can be derived independently, which is useful if selected orders or indices of moments are needed as pattern features. p-recursive method uses a combination of lower order polynomials to derive higher order polynomials with the same index q. Fast computation is achieved because it eliminates the requirements of calculating polynomial coefficients, Bpqk, and power of radius, rk, in each polynomial. The performance of the proposed algorithms on moment computation and image reconstruction, as compared to those of the present methods, are experimentally verified using a set of binary and grayscale images.

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2

Al-Rawi, Mohammed. "Fast Zernike moments." Journal of Real-Time Image Processing 3, no. 1-2 (January 8, 2008): 89–96. http://dx.doi.org/10.1007/s11554-007-0069-2.

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3

Indian, Ajay, and Karamjit Bhatia. "An Approach to Recognize Handwritten Hindi Characters Using Substantial Zernike Moments With Genetic Algorithm." International Journal of Computer Vision and Image Processing 11, no. 2 (April 2021): 66–81. http://dx.doi.org/10.4018/ijcvip.2021040105.

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A technique to recognize off-line handwritten Hindi character is suggested by employing Zernike complex moments like a tool to describe the characteristics of a character. Further, an algorithm for selecting the features is employed to identify the substantial image moments from the extracted moments, as the extracted moments may have some insignificant ones. Insignificant moments can increase the computational time and can also degrade the classification accuracy. Thus, the objectives of the study are twofold: (1) to find the important Zernike moments by employing the Genetic algorithm (GA) and (2) the classification of each character is performed using neural network. This way, the performance of the proposed technique is evaluated on two parameters (i.e., speed and recognition accuracy). Further, the efficacy of GA for selecting the moment features is assessed, and the efficacy of selected Zernike complex moments using GA is analyzed for handwritten Hindi characters. Here, the authors used a resilient backpropagation learning algorithm (RPROP) as a classification model.

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4

Theodoridis, Thomas, Kostas Loumponias, Nicholas Vretos, and Petros Daras. "Zernike Pooling: Generalizing Average Pooling Using Zernike Moments." IEEE Access 9 (2021): 121128–36. http://dx.doi.org/10.1109/access.2021.3108630.

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5

Qin, Hua Feng, Lan Qin, and Jun Liu. "A Novel Recurrence Method for the Fast Computation of Zernike Moments." Applied Mechanics and Materials 121-126 (October 2011): 1868–72. http://dx.doi.org/10.4028/www.scientific.net/amm.121-126.1868.

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A new method is proposed for fast computation of Zernike moments. This method presents a recursive relation to compute the entire set of Zernike moments. The fast computation is achieved because it involves less addition and multiplication operations. The experimental results show that the proposed method for the fast computation of Zernike moments is much more efficient than existing fast methods in most cases

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6

Deng, An-Wen, and Chih-Ying Gwo. "Parallel Computing Zernike Moments via Combined Algorithms." SIJ Transactions on Computer Science Engineering & its Applications (CSEA) 04, no. 03 (June 28, 2016): 01–09. http://dx.doi.org/10.9756/sijcsea/v4i3/04020050101.

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7

Liu, Zhenghui, and Hongxia Wang. "A Speech Content Authentication Algorithm Based on Pseudo-Zernike Moments in DCT Domain." International Journal of Digital Crime and Forensics 5, no. 3 (July 2013): 15–34. http://dx.doi.org/10.4018/jdcf.2013070102.

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A speech content authentication algorithm based on pseudo-Zernike moments in DCT domain is proposed in this paper, which is aimed at some shortcomings in some existing digital watermark schemes. The definition of coefficients self-correlation degree is given. Then the frequency domain watermark embedding method based on pseudo-Zernike moments in DCT domain is proposed. Watermark bits are generated by coefficients self-correlation degree and embedded by quantizing the pseudo-Zernike moments of DCT domain low-frequency coefficients. Comparing with the existing audio watermark algorithms based on pseudo-Zernike moments, the algorithm increases the watermarking embedding capacity and improves the efficiency greatly. Theoretical analysis and experimental evaluation results show that the proposed speech content authentication algorithm is effective.

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8

Singh, Chandan, Ekta Walia, and Neerja Mittal. "Discriminative Zernike and Pseudo Zernike Moments for Face Recognition." International Journal of Computer Vision and Image Processing 2, no. 2 (April 2012): 12–35. http://dx.doi.org/10.4018/ijcvip.2012040102.

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Usually magnitude coefficients of some selected orders of ZMs and PZMs have been used as invariant image features. The careful selection of the set of features, with higher discrimination competence, may increase the recognition performance. In this paper, the authors have used a statistical method to estimate the discrimination strength of all the extracted coefficients of ZMs and PZMs whereas for classification, only the coefficients with estimated higher discrimination strength are used in the feature vector. The performance of these selected Discriminative ZMs (DZMs) and Discriminative PZMs (DPZMs) features have been compared to that of their corresponding conventional approaches on YALE, ORL and FERET databases against illumination, expression, scale and pose variations. An extension to these DZMs and DPZMs have been proposed by combining them with PCA and FLD. It has been observed from the exhaustive experimentation that the recognition rate is improved by 2-6%, at reduced dimensions and with less computational complexity, than that of using the successive ZMs and PZMs features.

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9

Gao, Wenhan, Shanmin Zhou, Shuo Liu, Tao Wang, Bingbing Zhang, Tian Xia, Yong Cai, and Jianxing Leng. "Research on an Underwater Target-Tracking Method Based on Zernike Moment Feature Matching." Journal of Marine Science and Engineering 11, no. 8 (August 14, 2023): 1594. http://dx.doi.org/10.3390/jmse11081594.

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Sonar images have the characteristics of lower resolution and blurrier edges compared to optical images, which make the feature-matching method in underwater target tracking less robust. To solve this problem, we propose a particle filter (PF)-based underwater target-tracking method utilizing Zernike moment feature matching. Zernike moments are used to construct the feature-description vector for feature matching and contribute to the update of particle weights. In addition, the particle state transition method is optimized by using a first-order autoregressive model. In this paper, we compare Hu moments and Zernike moments, and we also compare whether to optimize the particle state transition on the tracking results or not based on the effects of each option. The experimental results based on the AUV (autonomous underwater vehicle) prove that the robustness and accuracy of this innovative method is better than the other combined methods mentioned in this paper.

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10

BADRA, FADY, ALA QUMSIEH, and GREGORY DUDEK. "ROBUST MOSAICING USING ZERNIKE MOMENTS." International Journal of Pattern Recognition and Artificial Intelligence 13, no. 05 (August 1999): 685–704. http://dx.doi.org/10.1142/s0218001499000409.

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This paper presents an approach to the registration of individual images to one another to produce a larger composite mosaic. The approach is based on the use of the moments of Zernike orthogonal polynomials to compute the relative scale, rotation and translation between the images. A preliminary stage involves the use of an attention-like operation to estimate potential approximate correspondence points between the images based on extrema of local edge element density. Experimental results illustrate that the technique is effective in a range of environments and over a broad range of image registration parameters. In particular, our method makes few assumptions regarding the image content and yet, unlike several alternative approaches, can perform registration for images with only a limited amount of overlap.

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11

Chong, Chee-Way, P. Raveendran, and R. Mukundan. "Translation invariants of Zernike moments." Pattern Recognition 36, no. 8 (August 2003): 1765–73. http://dx.doi.org/10.1016/s0031-3203(02)00353-9.

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12

Singh, Chandan, Ekta Walia, and Rahul Upneja. "Accurate calculation of Zernike moments." Information Sciences 233 (June 2013): 255–75. http://dx.doi.org/10.1016/j.ins.2013.01.012.

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13

Ono, Atsushi. "Face recognition with Zernike moments." Systems and Computers in Japan 34, no. 10 (July 10, 2003): 26–35. http://dx.doi.org/10.1002/scj.10414.

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14

Houdayer, Jérôme, and Patrice Koehl. "Stable Evaluation of 3D Zernike Moments for Surface Meshes." Algorithms 15, no. 11 (October 31, 2022): 406. http://dx.doi.org/10.3390/a15110406.

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The 3D Zernike polynomials form an orthonormal basis of the unit ball. The associated 3D Zernike moments have been successfully applied for 3D shape recognition; they are popular in structural biology for comparing protein structures and properties. Many algorithms have been proposed for computing those moments, starting from a voxel-based representation or from a surface based geometric mesh of the shape. As the order of the 3D Zernike moments increases, however, those algorithms suffer from decrease in computational efficiency and more importantly from numerical accuracy. In this paper, new algorithms are proposed to compute the 3D Zernike moments of a homogeneous shape defined by an unstructured triangulation of its surface that remove those numerical inaccuracies. These algorithms rely on the analytical integration of the moments on tetrahedra defined by the surface triangles and a central point and on a set of novel recurrent relationships between the corresponding integrals. The mathematical basis and implementation details of the algorithms are presented and their numerical stability is evaluated.

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15

Hosny, Khalid M., and Mohamed A. Hafez. "An Algorithm for Fast Computation of 3D Zernike Moments for Volumetric Images." Mathematical Problems in Engineering 2012 (2012): 1–17. http://dx.doi.org/10.1155/2012/353406.

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An algorithm was proposed for very fast and low-complexity computation of three-dimensional Zernike moments. The 3D Zernike moments were expressed in terms of exact 3D geometric moments where the later are computed exactly through the mathematical integration of the monomial terms over the digital image/object voxels. A new symmetry-based method was proposed to compute 3D Zernike moments with 87% reduction in the computational complexity. A fast 1D cascade algorithm was also employed to add more complexity reduction. The comparison with existing methods was performed, where the numerical experiments and the complexity analysis ensured the efficiency of the proposed method especially with image and objects of large sizes.

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16

Sucharitha, G., and Ranjan K. Senapati. "Shape Based Image Retrieval using Lower Order Zernike Moments." International Journal of Electrical and Computer Engineering (IJECE) 7, no. 3 (June 1, 2017): 1651. http://dx.doi.org/10.11591/ijece.v7i3.pp1651-1660.

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Shape is one of the significant features of Content Based Image Retrieval (CBIR). This paper proposes a strong and successful shape feature, which is based on a set of orthogonal complex moments of images known as Zernike moments. For shape classification Zernike moment (ZM) is the dominant solution. The radial polynomial of Zernike moment produces the number of concentric circles based on the order. As the order increases number of circles will increases, due to this the local information of an image will be ignored. In this paper, we introduced a novel method for radial polynomial where local information of an image given importance. We succeeded to extract the local features and shape features at very a low order of polynomial compared to the state of traditional ZM.The proposed method gives an advantage of a lower order, less complex, and lower dimension feature vector.For more similar images we find that simple Euclidian distance approximately zero. Proposed method tested on a MPEG-7 CE-1 shape database, Coil-100 databases. Experiments demonstrated that it is outperforming in identifying the shape of an object in the image and reduced the retrieving time and complexity of calculations.

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17

Fu, Bo, Xiu Xiang Fan, Qiong Cheng, Li Li, Bo Li, and Guo Jun Zhang. "Accurate Computation of Zernike Moments in Cartesian Coordinates." Applied Mechanics and Materials 195-196 (August 2012): 615–19. http://dx.doi.org/10.4028/www.scientific.net/amm.195-196.615.

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In this paper, a novel algorithm is proposed to accurately calculate Zernike moments in Cartesian Coordinates. We connect the corners of an image pixel with the origin to construct four triangles and then assign the intensity function value of the pixel to these triangles. The Fourier Mellin moment integration of the pixel is converted to a summation of four integrations within domains of these constructed triangles. By using the trigonometric resolution, we derive the analytic equations of the four integrations of these triangles. Then, the analytic expressions of the Fourier Mellin moments and Zernike moments are obtained. The algorithm eliminates the geometric and discretization errors theoretically. Finally, a set of efficient computational recursive relations is proposed. An experiment is designed to verify the performance of the proposed algorithm.

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18

Et al., Abu Bakar. "A Comparative Analysis of the Zernike Moments for Single Object Retrieval." Baghdad Science Journal 16, no. 2(SI) (June 20, 2019): 0504. http://dx.doi.org/10.21123/bsj.2019.16.2(si).0504.

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Zernike Moments has been popularly used in many shape-based image retrieval studies due to its powerful shape representation. However its strength and weaknesses have not been clearly highlighted in the previous studies. Thus, its powerful shape representation could not be fully utilized. In this paper, a method to fully capture the shape representation properties of Zernike Moments is implemented and tested on a single object for binary and grey level images. The proposed method works by determining the boundary of the shape object and then resizing the object shape to the boundary of the image. Three case studies were made. Case 1 is the Zernike Moments implementation on the original shape object image. In Case 2, the centroid of the shape object image in Case 1 is relocated to the center of the image. In Case 3, the proposed method first detect the outer boundary of the shape object and then resizing the object to the boundary of the image. Experimental investigations were made by using two benchmark shape image datasets showed that the proposed method in Case 3 had demonstrated to provide the most superior image retrieval performances as compared to both the Case 1 and Case 2. As a conlusion, to fully capture the powerful shape representation properties of the Zernike moment, a shape object should be resized to the boundary of the image.

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19

Otkupman, Dmitriy, Sergey Bezdidko, and Victoria Ostashenkova. "Application of Zernike moments in computer vision problems for infrared images." E3S Web of Conferences 310 (2021): 01002. http://dx.doi.org/10.1051/e3sconf/202131001002.

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The efficiency of using Zernike moments when working with digital images obtained in the infrared region of the spectrum is considered to improve the accuracy and speed of an autonomous thermal imaging system. The theoretical justification of the choice of Zernike moments for solving computer (machine) vision problems and the choice of a suitable threshold binarization method is given. In order to verify the adequacy and expediency of using the chosen method, practical studies were conducted on the use of Zernike methods for distorting various thermal images in shades of gray.

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20

Wu, Dong Mei, Jun Wei Li, and Li Hua Lin. "The Application of the Moment in the Human Recognition." Applied Mechanics and Materials 263-266 (December 2012): 2661–65. http://dx.doi.org/10.4028/www.scientific.net/amm.263-266.2661.

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The important method of the human recognition is to use the moment of the target. This paper is mainly dedicated to the method of human recognition use for Hu moment and Zernike moment, and separates some sports target using the minimum distance classifier. Comparing characteristic of these moments in specific application, have provided the certain basis for the choice of the invariant moments in the human recognition algorithm.

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21

Ye, Bin, Jia-Xiong Peng, Qiu-Shi Ren, and Wan-Rong Li. "Improvement and Invariance Analysis of Orthogonal Fourier–Mellin Moments." International Journal of Pattern Recognition and Artificial Intelligence 17, no. 06 (September 2003): 983–93. http://dx.doi.org/10.1142/s0218001403002757.

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Orthogonal Fourier–Mellin (OFM) moments have better feature representation capabilities, and are more robust to image noise than the conventional Zernike moments and pseudo-Zernike moments. However, OFM moments have not been extensively used as feature descriptors since they do not possess scale invariance. This paper discusses the drawbacks of the existing methods of extracting OFM moments, and proposes an improved OFM moments. A part of the theory, which proves the improved OFM moments possesses invariance of rotation and scale, is given. The performance of the improved OFM moments is experimentally examined using trademark images, and the invariance of the improved OFM moments is shown to have been greatly improved over the current methods.

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22

Karar, Subhajit, and Ranjan Parekh. "Palm Print Recognition using Zernike Moments." International Journal of Computer Applications 55, no. 16 (October 20, 2012): 15–19. http://dx.doi.org/10.5120/8839-3069.

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23

Hyung Shin Kim and Heung-Kyu Lee. "Invariant image watermark using zernike moments." IEEE Transactions on Circuits and Systems for Video Technology 13, no. 8 (August 2003): 766–75. http://dx.doi.org/10.1109/tcsvt.2003.815955.

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24

Kotoulas, L., and I. Andreadis. "Real-time computation of Zernike moments." IEEE Transactions on Circuits and Systems for Video Technology 15, no. 6 (June 2005): 801–9. http://dx.doi.org/10.1109/tcsvt.2005.848302.

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25

Aggarwal, Ashutosh, and Chandan Singh. "Zernike Moments-Based Gurumukhi Character Recognition." Applied Artificial Intelligence 30, no. 5 (May 27, 2016): 429–44. http://dx.doi.org/10.1080/08839514.2016.1185859.

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26

Biswas, Rajarshi, and Sambhunath Biswas. "Polar Zernike moments and rotational invariance." Optical Engineering 51, no. 8 (September 5, 2012): 087204–1. http://dx.doi.org/10.1117/1.oe.51.8.087204.

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27

Khotanzad, A., and Y. H. Hong. "Invariant image recognition by Zernike moments." IEEE Transactions on Pattern Analysis and Machine Intelligence 12, no. 5 (May 1990): 489–97. http://dx.doi.org/10.1109/34.55109.

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28

Belkasim, S., E. Hassan, and T. Obeidi. "Explicit invariance of Cartesian Zernike moments." Pattern Recognition Letters 28, no. 15 (November 2007): 1969–80. http://dx.doi.org/10.1016/j.patrec.2007.05.010.

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29

Bin, Ye, and Peng Jia-Xiong. "Invariance analysis of improved Zernike moments." Journal of Optics A: Pure and Applied Optics 4, no. 6 (September 20, 2002): 606–14. http://dx.doi.org/10.1088/1464-4258/4/6/304.

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30

Lu, Xiaoqi, and Jianwei Yang. "Image analysis with logarithmic Zernike moments." Digital Signal Processing 133 (March 2023): 103829. http://dx.doi.org/10.1016/j.dsp.2022.103829.

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31

Liyun, Wang, Ling Hefei, Zou Fuhao, Lu Zhengding, and Wang Zhendi. "Spermatogonium image recognition using Zernike moments." Computer Methods and Programs in Biomedicine 95, no. 1 (July 2009): 10–22. http://dx.doi.org/10.1016/j.cmpb.2009.01.008.

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32

Mohammed, Al-Rawi, and Jie Yang. "Practical fast computation of Zernike moments." Journal of Computer Science and Technology 17, no. 2 (March 2002): 181–88. http://dx.doi.org/10.1007/bf02962210.

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33

Hosny, Khalid M. "Fast computation of accurate Zernike moments." Journal of Real-Time Image Processing 3, no. 1-2 (November 24, 2007): 97–107. http://dx.doi.org/10.1007/s11554-007-0058-5.

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34

Al-Rawi, Mohammed Sadiq. "Fast computation of pseudo Zernike moments." Journal of Real-Time Image Processing 5, no. 1 (March 21, 2009): 3–10. http://dx.doi.org/10.1007/s11554-009-0118-0.

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35

Wang, Guang-Long, Jie Tian, Wen-Jie Zhu, and Dan Fang. "HOGHS and Zernike Moments Features-Based Motion-Blurred Object Tracking." International Journal of Humanoid Robotics 16, no. 01 (February 2019): 1950004. http://dx.doi.org/10.1142/s021984361950004x.

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Motion-blurred object tracking method integrating Histogram of Oriented Gradients and Hue Saturation (HOGHS) with Zernike moments features and based on ECO_HC tracker was proposed in this study to deal with object blur caused by the motion of the camera or the object itself. HOGHS was constructed by integrating fHOG with color features, and the properties of Zernike moments were introduced. The object was represented by combining HOGHS and Zernike moments. Furthermore, a novel quality evaluation method of response map considering both positioning accuracy and robustness was proposed and based on the method an adaptive fusion strategy utilizing the complementary properties of HOGHS and Zernike moments was implemented. Experiments were performed on the motion blur sequences from OTB-100 datasheet. Our method was compared with four other state-of-the-art methods. The precision as well as success rate were 0.849 and 0.827, respectively. Speed was 38.4 FPS. It is superior to VOT-2016’s excellent tracker ECO_HC, with relative gains of 2.3% for Pre-20 and 2.4% for AUC. The results show that the proposed method can effectively achieve the objective of motion-blurred object tracking.

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Vaidehi K. and Manivannan R. "Automated Math Symbol Classification Using SVM." International Journal of e-Collaboration 18, no. 2 (March 1, 2022): 1–14. http://dx.doi.org/10.4018/ijec.304037.

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Handwritten character/symbol recognition is an important area of research in the present digital world. The solving of problems such as recognizing handwritten characters/symbols written in different styles can make the human job easier. Mathematical expression recognition using machines has become a subject of serious research. The main motivation for this work is both recognizing of the handwritten mathematical symbol, digits and characters which will be used for mathematical expression recognition. The system first identifies the contour in handwritten document segmentation and features extracted are given into SVM classifier for classification. GLCM and Zernike Moments are the two different feature extraction techniques used in this work. SVM with RBF kernel is used for classification. Zernike Moment features overperforms than GLCM. Zernike Moment achieves 97.89% accuracy and GLCM achieves 87.61% accuracy.

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Huynh-Kha, Tu, Thuong Le-Tien, Synh Ha, and Khoa Huynh-Van. "Improving the Computational Cost for Copied Region Detection in Forensic Images." Journal of Science and Technology: Issue on Information and Communications Technology 2, no. 1 (August 31, 2016): 55. http://dx.doi.org/10.31130/jst.2016.28.

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This research work develops a new method to detect the forgery in image by combining the Wavelet transform and modified Zernike Moments (MZMs) in which the features are defined from more pixels than in traditional Zernike Moments. The tested image is firstly converted to grayscale and applied one level Discrete Wavelet Transform (DWT) to reduce the size of image by a half in both sides. The approximation sub-band (LL), which is used for processing, is then divided into overlapping blocks and modified Zernike moments are calculated in each block as feature vectors. More pixels are considered, more sufficient features are extracted. Lexicographical sorting and correlation coefficients computation on feature vectors are next steps to find the similar blocks. The purpose of applying DWT to reduce the dimension of the image before using Zernike moments with updated coefficients is to improve the computational time and increase exactness in detection. Copied or duplicated parts will be detected as traces of copy-move forgery manipulation based on a threshold of correlation coefficients and confirmed exactly from the constraint of Euclidean distance. Comparisons results between proposed method and related ones prove the feasibility and efficiency of the proposed algorithm.

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38

Ma, Ziping, Baosheng Kang, Ke Lv, and Mingzhu Zhao. "Nonlinear Radon Transform Using Zernike Moment for Shape Analysis." Computational and Mathematical Methods in Medicine 2013 (2013): 1–9. http://dx.doi.org/10.1155/2013/208402.

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We extend the linear Radon transform to a nonlinear space and propose a method by applying the nonlinear Radon transform to Zernike moments to extract shape descriptors. These descriptors are obtained by computing Zernike moment on the radial and angular coordinates of the pattern image's nonlinear Radon matrix. Theoretical and experimental results validate the effectiveness and the robustness of the method. The experimental results show the performance of the proposed method in the case of nonlinear space equals or outperforms that in the case of linear Radon.

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Mustaffa Kamal, Nur Diyanah, Nor’aini Jalil, and Hadzli Hashim. "The Analysis of Shape-based, DWT and Zernike Moments Feature Extraction Techniques for Fasterner Recognition Using 10-Fold Cross Validation Multilayer Perceptrons." International Journal of Electrical & Electronic Systems Research (IEESR) 9, no. 1 (June 24, 2019): 41. http://dx.doi.org/10.24191/ieesr.v9i1.1425.

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This paper presents an analysis of three feature extraction techniques which are the shape-based, Zernike moments and Discrete Wavelet Transform for fastener recognition. RGB colour features are also added to these major feature extractors to enhance the classification result. The classifier used in this experiment is back propagation neural network and the result in general is strengthen using ten-fold cross validation. The result is measured using percentage accuracy and Kappa statistics. The overall results showed that the best feature extraction techniques are Zernike moment group 3 and DWT both with added colour features.

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40

Meng, Xiang Lin, Wan Tao He, and Can Zhao. "A Stable Least Squares Ellipses Fitting Algorithm Based on Zernike Moments." Advanced Materials Research 142 (October 2010): 199–203. http://dx.doi.org/10.4028/www.scientific.net/amr.142.199.

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This paper presents a stable least squares ellipses fitting algorithm based on Zernike orthogonal moments. The algorithm uses Zernike orthogonal moments for sub-pixel edge detection, and a mask of seven multiply seven was derived in the meantime. The optimal ellipse parameters were computed according to the data points extracted previously. This stable, robust and non-iterative algorithm can be easily implemented. The experiment results show that the proposed algorithm is effective in various situations.

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41

Papakostas, G. A., Y. S. Boutalis, D. A. Karras, and B. G. Mertzios. "Efficient computation of Zernike and Pseudo-Zernike moments for pattern classification applications." Pattern Recognition and Image Analysis 20, no. 1 (March 2010): 56–64. http://dx.doi.org/10.1134/s1054661810010050.

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42

Naji, Driss, M. Fakir, B. Bouikhalene, and M. Boutaounte. "Recognition of Color Objects Using Hybrids Descriptors." International Journal of Computer Vision and Image Processing 3, no. 4 (October 2013): 60–68. http://dx.doi.org/10.4018/ijcvip.2013100105.

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In this paper, the authors came up with a different approach based on the combination of the different descriptors. For object recognition, regardless of orientation, size and position, feature vectors are computed with the help of Zernike moments and Centrist descriptors. For a large data base the fact of using the classic descriptors has never been a satisfying method for perfect recognition rates. The authors deduced that the combination of descriptors can have good recognition rates, accordingthe result of a comparative study of the different descriptors and the different combinations (Zernike + Centrist, Zernike + ACP, Centrist + ACP). The Zernike moment with Centrist descriptors ended up being the best hybrid description. For the recognition process, the authors opted for support vector machine (SVM) and Neural Networks (NN). The authors illustrate the proposed method on 3D objects using representations of two-dimensional images that are taken from different angles of view are the main features leading the authors to their objective.

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Tripathy, Jyotsnarani. "Reconstruction of Oriya Alphabets Using Zernike Moments." International Journal of Computer Applications 8, no. 8 (October 10, 2010): 26–32. http://dx.doi.org/10.5120/1227-1785.

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Pang, Ying-Han, Andrew Teoh B. J., and David Ngo C. L. "Enhanced pseudo Zernike moments in face recognition." IEICE Electronics Express 2, no. 3 (2005): 70–75. http://dx.doi.org/10.1587/elex.2.70.

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WANG, Zhong, and Yu SUN. "Zero watermarking algorithm based on Zernike moments." Journal of Computer Applications 28, no. 9 (June 5, 2009): 2233–35. http://dx.doi.org/10.3724/sp.j.1087.2008.02233.

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Ismail. "Invariant Image Watermarking Using Accurate Zernike Moments." Journal of Computer Science 6, no. 1 (January 1, 2010): 52–59. http://dx.doi.org/10.3844/jcssp.2010.52.59.

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Babkina, L. A., Yu P. Garmai, D. V. Lebedev, R. A. Pantina, M. V. Filatov, and V. V. Isaev-Ivanov. "Using Zernike moments for analysis of images." Numerical Analysis and Applications 6, no. 2 (April 2013): 131–44. http://dx.doi.org/10.1134/s1995423913020055.

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Xia, Ting, Hongqing Zhu, Huazhong Shu, Pascal Haigron, and Limin Luo. "Image description with generalized pseudo-Zernike moments." Journal of the Optical Society of America A 24, no. 1 (January 1, 2007): 50. http://dx.doi.org/10.1364/josaa.24.000050.

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Singhal, Nitin, Young-Yoon Lee, Chang-Su Kim, and Sang-Uk Lee. "Robust image watermarking using local Zernike moments." Journal of Visual Communication and Image Representation 20, no. 6 (August 2009): 408–19. http://dx.doi.org/10.1016/j.jvcir.2009.04.002.

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Mukundan, R., and K. R. Ramakrishnan. "Fast computation of Legendre and Zernike moments." Pattern Recognition 28, no. 9 (September 1995): 1433–42. http://dx.doi.org/10.1016/0031-3203(95)00011-n.

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