Camacho-Bello César, Padilla-Vivanco Alfonso, Toxqui-Quitl Carina, Báez-Rojas José Javier
Universidad Politécnica de Tulancingo , Ingenierías No. 100, Hidalgo 43629, México.
Instituto Nacional de Astrofísica , Óptica y Electrónica. Luis Enrique Erro No. 1, Puebla 72840, México.
J Med Imaging (Bellingham). 2016 Jan;3(1):014004. doi: 10.1117/1.JMI.3.1.014004. Epub 2016 Mar 11.
A detailed analysis of the quaternion generic Jacobi-Fourier moments (QGJFMs) for color image description is presented. In order to reach numerical stability, a recursive approach is used during the computation of the generic Jacobi radial polynomials. Moreover, a search criterion is performed to establish the best values for the parameters [Formula: see text] and [Formula: see text] of the radial Jacobi polynomial families. Additionally, a polar pixel approach is taken into account to increase the numerical accuracy in the calculation of the QGJFMs. To prove the mathematical theory, some color images from optical microscopy and human retina are used. Experiments and results about color image reconstruction are presented.
本文对用于彩色图像描述的四元数通用雅可比 - 傅里叶矩（QGJFMs）进行了详细分析。为了实现数值稳定性，在计算通用雅可比径向多项式时采用了递归方法。此外，执行了一个搜索准则来确定径向雅可比多项式族参数[公式：见正文]和[公式：见正文]的最佳值。另外，考虑采用极坐标像素方法以提高QGJFMs计算中的数值精度。为了证明该数学理论，使用了一些来自光学显微镜和人类视网膜的彩色图像。文中给出了关于彩色图像重建的实验和结果。
