On digital approximation of moment invariants
Computer Vision, Graphics, and Image Processing
A Computational Approach to Edge Detection
IEEE Transactions on Pattern Analysis and Machine Intelligence
IEEE Transactions on Pattern Analysis and Machine Intelligence
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
Nonlinear total variation based noise removal algorithms
Proceedings of the eleventh annual international conference of the Center for Nonlinear Studies on Experimental mathematics : computational issues in nonlinear science: computational issues in nonlinear science
IEEE Transactions on Pattern Analysis and Machine Intelligence
Regularization, Scale-Space, and Edge Detection Filters
Journal of Mathematical Imaging and Vision
On the Accuracy of Zernike Moments for Image Analysis
IEEE Transactions on Pattern Analysis and Machine Intelligence
Complete Sets of Complex Zernike Moment Invariants and the Role of the Pseudoinvariants
IEEE Transactions on Pattern Analysis and Machine Intelligence
Image Normalization by Complex Moments
IEEE Transactions on Pattern Analysis and Machine Intelligence
On the approximation power of convolution-based least squaresversus interpolation
IEEE Transactions on Signal Processing
Generalized sampling: stability and performance analysis
IEEE Transactions on Signal Processing
Accurate Computation of Zernike Moments in Polar Coordinates
IEEE Transactions on Image Processing
Enlargement or reduction of digital images with minimum loss of information
IEEE Transactions on Image Processing
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Zernike Moment (ZM) is an effective region-based shape representation technique. The extracted ZM features should be independent of scale, position and orientation, which can be achieved by ZM-based image normalization. Nevertheless, due to the discretization of digital image and the presence of noise, the normalization is imperfect. Thus, in practice Zernike Moment Invariants (ZMI) cannot perfectly preserve the invariant properties. In this paper, firstly the ZM-based image normalization criteria are derived, and then I theoretically and experimentally evaluate the accuracy of the ZM-based image normalization. Our theoretical and experimental results not only disclose some essential facts, but also have some new findings. The relations between the accuracy of ZM-based image normalization and its influencing factors are established. A creative pseudo-polar coordinate is proposed to cut down the geometrical errors to the greatest extent. Furthermore, I suggest several techniques to improve the accuracy of image normalization. By combining moment-based image normalization with the image regularization theory and the scale-space theory, and several new conclusions are drawn. Our experimental results show that the proposed techniques can preserve the invariance of image normalization and restrain the influence of noise quite effectively.