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
On the computational aspects of Zernike moments
Image and Vision Computing
Fast and accurate method for radial moment's computation
Pattern Recognition Letters
Two-Dimensional Polar Harmonic Transforms for Invariant Image Representation
IEEE Transactions on Pattern Analysis and Machine Intelligence
Radial and Angular Moment Invariants for Image Identification
IEEE Transactions on Pattern Analysis and Machine Intelligence
Accurate Computation of Zernike Moments in Polar Coordinates
IEEE Transactions on Image Processing
MPEG-7 visual shape descriptors
IEEE Transactions on Circuits and Systems for Video Technology
Error Analysis in the Computation of Orthogonal Rotation Invariant Moments
Journal of Mathematical Imaging and Vision
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The Orthogonal rotation invariant moments suffer from two major errors - the geometric error and the numerical integration error. As a consequence of this, their rotation and scale invariance properties are affected. In this paper, we study the behavior of these errors by analyzing their effect on rotational moments, also known as Fourier-Mellin moments and radial moments, as the former can be expressed as linear combinations of the later. We show that the existing approaches to minimize these errors are not very effective for practical applications. A computational framework based on numerical integration approach is developed which reduces the geometric error and the numerical integration error simultaneously. Two popular numerical integration methods, namely, the Simpson's method and Gaussian numerical integration method are used and their relative performance on the accuracy of the moments are analyzed. It is shown that the proposed approach provides more accurate moments which results in the significant improvement in rotation and scale invariance properties of the moments.