On Image Analysis by the Methods of Moments
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
Robust Rotation Angle Estimator
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)
New computational methods for full and subset Zernike moments
Information Sciences—Informatics and Computer Science: An International Journal - Mining stream data
Fast Zernike wavelet moments for Farsi character recognition
Image and Vision Computing
On the computational aspects of Zernike moments
Image and Vision Computing
A new class of Zernike moments for computer vision applications
Information Sciences: an International Journal
Sketch-Based 3D-Shape Creation for Industrial Styling Design
IEEE Computer Graphics and Applications
Circularly orthogonal moments for geometrically robust image watermarking
Pattern Recognition
Calligraphic Interfaces: Classifier combination for sketch-based 3D part retrieval
Computers and Graphics
Improving Zernike Moments Comparison for Optimal Similarity and Rotation Angle Retrieval
IEEE Transactions on Pattern Analysis and Machine Intelligence
Complex Zernike moments features for shape-based image retrieval
IEEE Transactions on Systems, Man, and Cybernetics, Part A: Systems and Humans - Special section: Best papers from the 2007 biometrics: Theory, applications, and systems (BTAS 07) conference
Testing for image symmetries: with application to confocal microscopy
IEEE Transactions on Information Theory
A systematic method for efficient computation of full and subsets Zernike moments
Information Sciences: an International Journal
A zernike moment phase-based descriptor for local image representation and matching
IEEE Transactions on Image Processing
Algorithms for fast computation of Zernike moments and their numerical stability
Image and Vision Computing
Fast computation of exact Zernike moments using cascaded digital filters
Information Sciences: an International Journal
Image reconstruction with polar zernike moments
ICAPR'05 Proceedings of the Third international conference on Pattern Recognition and Image Analysis - Volume Part II
A Bayesian 3-D Search Engine Using Adaptive Views Clustering
IEEE Transactions on Multimedia
On the reconstruction aspects of moment descriptors
IEEE Transactions on Information Theory
Geometric Invariance in image watermarking
IEEE Transactions on Image Processing
Accurate Computation of Zernike Moments in Polar Coordinates
IEEE Transactions on Image Processing
Orthogonal Rotation-Invariant Moments for Digital Image Processing
IEEE Transactions on Image Processing
Invariant image watermark using Zernike moments
IEEE Transactions on Circuits and Systems for Video Technology
Zernike-Moment-Based Image Super Resolution
IEEE Transactions on Image Processing
Shape classification by manifold learning in multiple observation spaces
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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Zernike moments (ZMs) are very effective global image descriptors which are used in many digital image processing applications. The digitization process compromises the accuracy of the moments and therefore, several of its properties are affected. There are two major discretization errors, namely, the geometric error and numerical integration error. In this paper we propose two new algorithms which eliminate these errors. The first algorithm performs the exact computation of geometric moments (GMs) over a unit disk and then uses GMs-to-ZMs relationship to compute the latter. This algorithm is computationally more expensive and it becomes numerically instable for higher order moments, therefore, we develop a second algorithm based on Gaussian quadrature numerical integration. The second algorithm reduces both the errors simultaneously and its accuracy increases as the degree of Gaussian quadrature numerical integration increases. The proposed algorithms are observed to provide very accurate ZMs which result in improved image reconstruction, reduction in reconstruction error and improvement in rotation and scale invariance. Exhaustive experiments are provided to support improved accuracy of ZMs and time complexity analysis is performed for the existing and the proposed methods.