Moment invariants are an especially important research topic in pattern recognition. There are many kinds of moment invariants published in the literature already. However, there is a need to further improve them, especially under the noisy environments. In this article, we develop a new set of moment invariants by means of ridgelet function. The ridgelet function is capable of capturing line features in an image, which is a particularly important property in pattern recognition. It is well-known that every curve can be approximated by short line segments, so ridgelet moment invariants should be good at robust pattern recognition. We can prove that this set of moments is invariant to the rotation of 2D images. Experiments show that our proposed ridgelet moment invariants are better than the Gaussian–Hermite moments, the Fourier–wavelet descriptor, and Zernike’s moment invariants for one Chinese character database and one 2D shape database. Furthermore, our proposed ridgelet moment invariants can do an excellent job for noise-robust pattern recognition.

矩不变量是模式识别中一个特别重要的研究课题。文献中已经发表了很多种矩不变量。但是，它们还需要进一步改进，尤其是在嘈杂的环境下。在本文中，我们通过脊波函数开发了一组新的矩不变量。脊波函数能够捕捉图像中的线特征，这是模式识别中一个特别重要的特性。众所周知，每条曲线都可以用短线段来近似，因此脊波矩不变量应该擅长鲁棒的模式识别。我们可以证明这组矩对于二维图像的旋转是不变的。实验表明，我们提出的脊波矩不变量优于高斯-厄米矩、傅立叶-小波描述符、一个汉字数据库和一个二维形状数据库的泽尼克矩不变量。此外，我们提出的脊波矩不变量可以在噪声鲁棒模式识别方面做得很好。