由于正交矩对噪声鲁棒性强、重建效果好，因此被广泛应用于目标识别与分类中，但是正交矩本质上缺乏尺度变换不变性，而且必要的图像二值化与规一化过程会引入重采样与重量化误差。为此，在研究现有正交矩的基础上，提出了一种基于Radon变换和解析Fourier Mellin变换的尺度与旋转不变的目标识别算法。该算法首先直接对目标灰度图像进行Radon变换，然后对Radon变换结果进行进一步解析，通过Fourier Mellin变换将原图像的旋转变化转化为相位变化，将原图像的尺度变化转化为幅度变化；最后，通过定义一旋转与尺度不变函数，同时利用不变函数的4种特征，再应用k 近邻法实现分类。理论与实验结果表明，由于避免了正交矩方法存在的重采样与重量化误差，该算法的分类精度高于基于正交矩的分类方法，而且对白噪声的鲁棒性也显著高于基于正交矩的识别与分类方法。

Orthogonal moments have been widely used for image recognition and classification duo to their useful properties such as being less sensitive to noise and being very accurate in image reconstruction. However, their do not natively possess scaling invariance, essential image normalization and binarization process will lead to error of resampling and requantifying. A new scaling and rotation invariant analysis method for image recognition is proposed. In the proposed method, the Radon transform is utilized to project the image onto projection space, and then the analytic Fourier Mellin transform is applied to the projection space to convert the rotation of the original image to a phase shift and the scaling of the original image to a scaling of amplitude. In order to achieve a set of completely invariant descriptors, a rotation and scaling invariant function is constructed. Based on four features of the invariant function, a k-nearest neighbor classifier is employed to implement classification. Theoretical and experimental results show the high classification accuracy of this approach in comparison to the orthogonal moments based methods as a result of using the rotation and scaling invariant function instead of images binarization and normalization, it also shows that this method is more robust to white noise than the orthogonal moments based methods.