Racah多项式高阶矩的加速和改进镇定
Accelerated and Improved Stabilization for High Order Moments of Racah Polynomials
摘要：
离散Racah多项式（DRP）及其矩是最有效的正交矩之一，被用于许多科学领域，包括图像处理和计算机视觉。矩是信号在多项式基函数上的投影。Racah多项式是由Wilson提出并由Zhu修正的用于图像处理的多项式，它们在离散集上是正交的。然而，当矩阶较高时，它们会遇到数值不稳定性的问题。在本文中，我们提出了一种新的算法称为改进的稳定（ImSt）的DRP系数的计算。在所提出的算法中，{DRP平面被划分为四个部分，这是不对称的，因为它们依赖于多项式大小和DRP参数的值。}利用对数Γ函数来计算初始值，这使得能够针对大范围的DRP参数值以及大尺寸的多项式来计算初始值。此外，一个新的公式被用来计算基于初始值的初始集合的值。此外，我们优化使用的稳定条件在特定部分的算法。ImSt适用于更宽的参数范围，直到比当前算法更高的程度。我们在一些实验中与其他方法进行了比较。
英文摘要：
One of the most effective orthogonal moments, discrete Racah polynomials (DRPs) and their moments are used in many disciplines of sciences, including image processing, and computer vision. Moments are the projections of a signal on the polynomial basis functions. Racah polynomials were introduced by Wilson and modified by Zhu for image processing and they are orthogonal on a discrete set of samples. However, when the moment order is high, they experience the issue of numerical instability. In this paper, we propose a new algorithm for the computation of DRPs coefficients called Improved Stabilization (ImSt). In the proposed algorithm, {the DRP plane is partitioned into four parts, which are asymmetric because they rely on the values of the polynomial size and the DRP parameters.} The logarithmic gamma function is utilized to compute the initial values, which empower the computation of the initial value for a wide range of DRP parameter values as well as large size of the polynomials. In addition, a new formula is used to compute the values of the initial sets based on the initial value. Moreover, we optimized the use of the stabilizing condition in specific parts of the algorithm. ImSt works for wider range of parameters until higher degree than the current algorithms. We compare it with the other methods in a number of experiments.
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