On Image Analysis by the Methods of Moments
IEEE Transactions on Pattern Analysis and Machine Intelligence
Recovery of Parametric Models from Range Images: The Case for Superquadrics with Global Deformations
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
An Efficient Method for the Computation of Legendre Moments
IEEE Transactions on Pattern Analysis and Machine Intelligence
Scale Invariants of Three-Dimensional Legendre Moments
ICPR '06 Proceedings of the 18th International Conference on Pattern Recognition - Volume 03
Exact Legendre moment computation for gray level images
Pattern Recognition
Orthogonal moments based texture analysis of CT liver images
Pattern Recognition Letters
Refined translation and scale Legendre moment invariants
Pattern Recognition Letters
Fast Template Matching With Polynomials
IEEE Transactions on Image Processing
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A new method is proposed for fast and low-complexity computation of exact 3D Legendre moments. The proposed method consists of three main steps. In the first step, the symmetry property is employed where the computational complexity is reduced by 87%. In the second step, exact values of 3D Legendre moments are obtained by mathematically integrating the Legendre polynomials over digital image voxels. An algorithm is employed to significantly accelerate the computational process. In this algorithm, the equations of 3D Legendre moments are treated in a separated form. The proposed method is applied to determine translation-scale invariance of 3D Legendre moments in a very simple way. Numerical experiments are performed where the results are compared with those of the existing methods. Complexity analysis and results of the numerical experiments clearly ensure the efficiency of the proposed method.