Orthogonal moments are used to represent digital images with minimum redundancy. Orthogonal moments with fractional-orders show better capabilities in digital image analysis than integer-order moments. In this work, the authors present new fractional-order shifted Gegenbauer polynomials. These new polynomials are used to define a novel set of orthogonal fractional-order shifted Gegenbauer moments (FrSGMs). The proposed method is applied in gray-scale image analysis and recognition. The invariances to rotation, scaling and translation (RST), are achieved using invariant fractional-order geometric moments. Experiments are conducted to evaluate the proposed FrSGMs and compare with the classical orthogonal integer-order Gegenbauer moments (GMs) and the existing orthogonal fractional-order moments. The new FrSGMs outperformed GMs and the existing orthogonal fractional-order moments in terms of image recognition and reconstruction, RST invariance, and robustness to noise.

正交矩用于表示具有最小冗余度的数字图像。具有分数阶的正交矩比整数阶矩在数字图像分析中显示出更好的功能。在这项工作中，作者提出了新的分数阶移位的Gegenbauer多项式。这些新的多项式用于定义一组新颖的正交分数阶移位的Gegenbauer矩（FrSGMs）。该方法应用于灰度图像的分析与识别。使用不变的分数阶几何矩实现旋转，缩放和平移（RST）的不变性。进行实验以评估所提出的FrSGM，并与经典正交整数阶Gegenbauer矩（GMs）和现有的正交分数阶矩进行比较。