Discrete orthogonal moments such as Meixner moments are powerful tools for characterizing image shape features for applications in pattern recognition and image classification. However, in the pattern recognition theory, classification of 2D/3D shapes regardless of their position, size, and orientation represents an important problem. In this paper, a new fast and accurate method is presented to obtain Meixner moments that are invariant to translation and uniform/non-uniform scaling directly from Meixner polynomials. These new invariants of Meixner moments are computed more quickly and require no numerical approximation, unlike the classical invariants of Meixner moments which are computed from geometric moments. This method is extended to compute the three-dimensional of Meixner invariant moments to translation and scaling. The results of experimental studies using scaled uniformly/non-uniformly and translated binary and gray-scale images are discussed to further verify the validity of the new invariants of Meixner moments for classification tasks.

离散正交矩（例如Meixner矩）是用于表征图像形状特征的强大工具，可用于模式识别和图像分类。但是，在模式识别理论中，无论2D / 3D形状的位置，大小和方向如何，分类都是一个重要的问题。本文提出了一种新的快速准确的方法，可以直接从Meixner多项式获得平移不变和均匀/不均匀缩放的Meixner矩。Meixner矩的这些新不变量的计算速度更快，并且不需要数值逼近，这与Meixner矩的经典不变量是根据几何矩计算得出的。扩展了该方法，以计算Meixner不变矩的三维，以进行平移和缩放。