Fast computation of accurate Gaussian–Hermite moments for image processing applications

Gaussian–Hermite moments are orthogonal moments widely used in image processing and computer vision applications. Similar to the other families of orthogonal moments, highly computational demands represent the main challenging. In this work, an efficient method is proposed for fast computation of highly accurate Gaussian–Hermite moments for gray-level images. The proposed method achieves the accuracy through the integration of Gaussian–Hermite polynomials over the image pixels. To achieve the efficiency, the symmetry property of Gaussian–Hermite polynomials is employed where the computational complexity is reduced by 75%. Fast computational methodology is employed to significantly accelerate the computational process where the 2D Gaussian–Hermite moments are treated in a separated form. Numerical experiments are performed where the results are compared with the conventional method. The comparison of the obtained results clearly ensures the efficiency of the proposed method.

► A new method is proposed for fast computation of accurate Gaussian–Hermite moments.
► Symmetry property is applied where 75% of the computational complexity is reduced.
► The proposed method is suitable for large databases of binary and gray-level images.
► It is suitable for online image processing and computer vision applications.