On Image Analysis by the Methods of Moments
IEEE Transactions on Pattern Analysis and Machine Intelligence
Invariant Image Recognition by Zernike Moments
IEEE Transactions on Pattern Analysis and Machine Intelligence
Pattern recognition with moment invariants: a comparative study and new results
Pattern Recognition
IEEE Transactions on Pattern Analysis and Machine Intelligence
On the Accuracy of Zernike Moments for Image Analysis
IEEE Transactions on Pattern Analysis and Machine Intelligence
Content-based trademark retrieval system using visually salient features
CVPR '97 Proceedings of the 1997 Conference on Computer Vision and Pattern Recognition (CVPR '97)
Image analysis by moments
A Multibit Geometrically Robust Image Watermark Based on Zernike Moments
ICPR '04 Proceedings of the Pattern Recognition, 17th International Conference on (ICPR'04) Volume 4 - Volume 04
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
EURASIP Journal on Applied Signal Processing
On the reconstruction aspects of moment descriptors
IEEE Transactions on Information Theory
Fast computation of geometric moments using a symmetric kernel
Pattern Recognition
A unified methodology for the efficient computation of discrete orthogonal image moments
Information Sciences: an International Journal
A systematic method for efficient computation of full and subsets Zernike moments
Information Sciences: an International Journal
A study of Zernike invariants for content-based image retrieval
PSIVT'07 Proceedings of the 2nd Pacific Rim conference on Advances in image and video technology
A shape descriptors comparison for organs deformation sequence characterization in MRI sequences
ICIP'09 Proceedings of the 16th IEEE international conference on Image processing
Algorithms for fast computation of Zernike moments and their numerical stability
Image and Vision Computing
An approach for on-line signature authentication using Zernike moments
Pattern Recognition Letters
Face recognition using Zernike and complex Zernike moment features
Pattern Recognition and Image Analysis
Fast computation of exact Zernike moments using cascaded digital filters
Information Sciences: an International Journal
Mammogram retrieval through machine learning within BI-RADS standards
Journal of Biomedical Informatics
Discrete circular mapping for computation of Zernike moments
PReMI'11 Proceedings of the 4th international conference on Pattern recognition and machine intelligence
Pattern Recognition and Image Analysis
Automatic BI-RADS description of mammographic masses
IWDM'10 Proceedings of the 10th international conference on Digital Mammography
On invariance analysis of Zernike moments in the presence of rotation with crop and loose modes
Multimedia Tools and Applications
Mammogram retrieval on similar mass lesions
Computer Methods and Programs in Biomedicine
Error analysis and accurate calculation of rotational moments
Pattern Recognition Letters
Breast mass classification using orthogonal moments
IWDM'12 Proceedings of the 11th international conference on Breast Imaging
Analysis of algorithms for fast computation of pseudo Zernike moments and their numerical stability
Digital Signal Processing
Trademark image retrieval using an integrated shape descriptor
Expert Systems with Applications: An International Journal
Discriminative Zernike and Pseudo Zernike Moments for Face Recognition
International Journal of Computer Vision and Image Processing
Accurate calculation of Zernike moments
Information Sciences: an International Journal
Error Analysis in the Computation of Orthogonal Rotation Invariant Moments
Journal of Mathematical Imaging and Vision
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The set of Zernike moments belongs to the class of continuous orthogonal moments which is defined over a unit disk in polar coordinate system. The approximation error of Zernike moments limits its applications in real discrete-space images. The approximation error of Zernike moments is divided into geometrical and numerical errors. In this paper, the geometrical and numerical errors of Zernike moments are explored and methods are proposed to minimize them. The geometrical error is minimized by mapping all the pixels of discrete image inside the unit disk. The numerical error is eliminated using the proposed exact Zernike moments where the Zernike polynomials are integrated mathematically over the corresponding intervals of the image pixels. The proposed methods also overcome the numerical instability problem for high order Zernike moments. Experimental results prove the superiority and reliability of the proposed methods in providing better image representation and reconstruction capabilities. The proposed methods are also not lacking in preserving the scale and translation invariant properties of Zernike moments.