Applications of discrete orthogonal polynomials (DOPs) in image processing have been recently emerging. In particular, Krawtchouk, Chebyshev, and Charlier DOPs have been applied as bases for image analysis in the frequency domain. However, fast realizations and fractional-type generalizations of DOP-based discrete transforms have been rarely addressed. In this paper, we introduce families of multiparameter discrete fractional transforms via orthogonal spectral decomposition based on Krawtchouk, Chebyshev, and Charlier DOPs. The eigenvalues are chosen arbitrarily in both unitary and non-unitary settings. All families of transforms, for varieties of eigenvalues, are applied in image watermarking. We also exploit recently introduced fast techniques to reduce complexity for the Krawtchouk case. Experimental results show the robustness of the proposed transforms against watermarking attacks.

最近出现了离散正交多项式 (DOP) 在图像处理中的应用。特别是，Krawtchouk、Chebyshev 和 Charlier DOP 已被用作频域中图像分析的基础。然而，很少涉及基于 DOP 的离散变换的快速实现和分数类型的泛化。在本文中，我们通过基于 Krawtchouk、Chebyshev 和 Charlier DOP 的正交谱分解介绍了多参数离散分数变换系列。在酉和非酉设置中任意选择特征值。对于各种特征值，所有变换族都应用于图像水印。我们还利用最近引入的快速技术来降低 Krawtchouk 案例的复杂性。