Robust and discriminative image representation is a long-lasting battle in the computer vision and pattern recognition. Moment-based image representation model is effective in satisfying the core conditions of semantic description, due to its geometric invariance and independence. However, moment-based descriptors suffer from a contradiction between the robustness and discriminability, which limits the further improvement of description quality. In this paper, a set of generic moments along with a novel representation framework are proposed to mitigate this troublesome contradiction. We first define a new set of orthogonal moments, named Fractional-order Jacobi-Fourier Moments (FJFM), which is characterized by the generic nature and time-frequency analysis capability. We then develop a new framework to improve both the robustness and discriminability of image representation, called Mixed Low-order Moment Feature (MLMF), by fully exploiting the time-frequency property of FJFM. Extensive experimental results and a real-world application are provided to demonstrate the superior performance of our FJFM-based MLMF, with respect to robustness and discriminability.

强大而有区别的图像表示是计算机视觉和模式识别领域的长期战役。基于矩的图像表示模型由于其几何不变性和独立性，在满足语义描述的核心条件方面是有效的。但是，基于矩的描述符在健壮性和可辨别性之间存在矛盾，这限制了描述质量的进一步提高。在本文中，提出了一组通用时刻以及一个新颖的表示框架，以缓解这种麻烦的矛盾。我们首先定义一组新的正交矩，称为分数阶Jacobi-Fourier矩（FJFM），其特征在于通用性质和时频分析功能。然后，我们通过充分利用FJFM的时频特性，开发了一种新的框架来改善图像表示的鲁棒性和可分辨性，称为混合低阶矩特征（MLMF）。提供了广泛的实验结果和实际应用，以证明我们的基于FJFM的MLMF在鲁棒性和可辨别性方面的优越性能。