Sayyouri Mhamed, Hmimid Abdeslam, Qjidaa Hassan
J Opt Soc Am A Opt Image Sci Vis. 2013 Nov 1;30(11):2381-94. doi: 10.1364/JOSAA.30.002381.
The discrete orthogonal moments are powerful descriptors for image analysis and pattern recognition. However, the computation of these moments is a time consuming procedure. To solve this problem, a new approach that permits the fast computation of Hahn's discrete orthogonal moments is presented in this paper. The proposed method is based, on the one hand, on the computation of Hahn's discrete orthogonal polynomials using the recurrence relation with respect to the variable x instead of the order n and the symmetry property of Hahn's polynomials and, on the other hand, on the application of an innovative image representation where the image is described by a number of homogenous rectangular blocks instead of individual pixels. The paper also proposes a new set of Hahn's invariant moments under the translation, the scaling, and the rotation of the image. This set of invariant moments is computed as a linear combination of invariant geometric moments from a finite number of image intensity slices. Several experiments are performed to validate the effectiveness of our descriptors in terms of the acceleration of time computation, the reconstruction of the image, the invariability, and the classification. The performance of Hahn's moment invariants used as pattern features for a pattern classification application is compared with Hu [IRE Trans. Inform. Theory 8, 179 (1962)] and Krawchouk [IEEE Trans. Image Process.12, 1367 (2003)] moment invariants.
离散正交矩是用于图像分析和模式识别的强大描述符。然而，这些矩的计算是一个耗时的过程。为了解决这个问题，本文提出了一种允许快速计算哈恩离散正交矩的新方法。所提出的方法一方面基于利用关于变量x而非阶数n的递推关系以及哈恩多项式的对称性来计算哈恩离散正交多项式，另一方面基于一种创新的图像表示方法，其中图像由多个均匀矩形块而非单个像素来描述。本文还提出了一组在图像平移、缩放和旋转下的哈恩不变矩。这组不变矩是通过对有限数量的图像强度切片的不变几何矩进行线性组合来计算的。进行了若干实验以验证我们的描述符在时间计算加速、图像重建、不变性和分类方面的有效性。将用作模式分类应用的模式特征的哈恩矩不变量的性能与胡[《IRE信息理论学报》8, 179 (1962)]和克拉夫丘克[《IEEE图像处理学报》12, 1367 (2003)]矩不变量进行了比较。
