The 4-parameter generalized lambda distribution (GLD) is a flexible distribution capable of mimicking the shapes of many distributions and data samples including those with heavy tails. The method of L-moments and the recently developed method of trimmed L-moments (TL-moments) are attractive techniques for parameter estimation for heavy-tailed distributions for which the Land TL-moments have be...

We study two types of crank moments and two types of rank moments for overpartitions. We show that the crank moments and their derivatives, along with certain linear combinations of the rank moments and their derivatives, can be written in terms of quasimodular forms. We then use this fact to prove exact relations involving the moments as well as congruence properties modulo 3, 5, and 7 for som...

Orthogonal moments are recognized as useful tools for object representation and image analysis. It has been shown that the recently developed discrete orthogonal moments have better performance than the conventional continuous orthogonal moments. In this paper, a new set of discrete orthogonal polynomials, namely Hahn polynomials, are introduced. The related Hahn moment functions defined on thi...

Moments of images provide efficient local descriptors and have been used extensively in image analysis applications. Their main advantage is their ability to provide invariant measures of shape. In this work, we present an overview of the most commonly used image moments, as well as a hardware architecture capable of fast calculation of geometric, Zernike and Tchebichef moments. Index Terms – I...

In this research, we have proposed the central-symmetrical property of image reconstructions from Zernike moments and pseudo-Zernike moments. We conducted the image reconstructions from the odd, even, and complete sets of Zernike moments and pseudo-Zernike moments, and verified the proposed central-symmetrical property. We have concluded that if the original image is centrally symmetrical, the ...

moment descriptors are commonly used in applications such as image classification, pattern recognition and identification. A radial-polar representation of image coordinate space is particularly useful in the above applications, since it facilitates the derivation of rotation invariants of any arbitrary order. Zernike moments and radial-Tchebichef moments fall into the category of moments that ...

Corresponding Author: Simon Liao The University of Winnipeg, Winnipeg, Manitoba, Canada, R3B 2E9, Canada Email: [email protected] Abstract: In this research, a numerical integration method is proposed to improve the computational accuracy of Legendre moments. To clarify the improved computation scheme, image reconstructions from higher order of Legendre moments, up to 240, are conducted. Wi...

The Wigner distribution of rotationally symmetric partially coherent light is considered, and the constraints for its moments are derived. Although all odd-order moments vanish, these constraints lead to a drastic reduction in the number of parameters that we need to describe all even-order moments: whereas in general we have (N + 1)(N + 2)(N + 3)/6 different moments of order N, this number red...