On Image Analysis by the Methods of Moments
IEEE Transactions on Pattern Analysis and Machine Intelligence
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 Line Fitting in a Noisy Image by the Method of Moments
IEEE Transactions on Pattern Analysis and Machine Intelligence
Advanced Engineering Mathematics: Maple Computer Guide
Advanced Engineering Mathematics: Maple Computer Guide
Image analysis by moments
Orthogonal Legendre Moments and Their Calculation
ICPR '96 Proceedings of the 13th International Conference on Pattern Recognition - Volume 2
Image indexing using moments and wavelets
IEEE Transactions on Consumer Electronics
Exact Legendre moment computation for gray level images
Pattern Recognition
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
Accurate and speedy computation of image Legendre moments for computer vision applications
Image and Vision Computing
An efficient method for the exact computation of Legendre moments of binary images
DSP'09 Proceedings of the 16th international conference on Digital Signal Processing
Refined translation and scale Legendre moment invariants
Pattern Recognition Letters
Fast computation of tchebichef moments for binary and grayscale images
IEEE Transactions on Image Processing
Image representation using accurate orthogonal Gegenbauer moments
Pattern Recognition Letters
Fast and low-complexity method for exact computation of 3D Legendre moments
Pattern Recognition Letters
Rotation and translation invariants of Gaussian-Hermite moments
Pattern Recognition Letters
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Legendre moments are continuous moments, hence, when applied to discrete-space images, numerical approximation is involved and error occurs. This paper proposes a method to compute the exact values of the moments by mathematically integrating the Legendre polynomials over the corresponding intervals of the image pixels. Experimental results show that the values obtained match those calculated theoretically, and the image reconstructed from these moments have lower error than that of the conventional methods for the same order. Although the same set of exact Legendre moments can be obtained indirectly from the set of geometric moments, the computation time taken is much longer than the proposed method.