Scaling and rotation invariant analysis approach to object recognition based on Radon and Fourier–Mellin transforms

Various types of orthogonal moments have been widely used for object recognition and classification. However, these moments do not natively possess scaling invariance, essential image normalization and binarization prior to moments extraction will lead to error of resampling and requantifying. This paper describes a new scaling and rotation invariant analysis method for object recognition. In the proposed method, the Radon transform is utilized to project the image onto projection space to convert the rotation of the original image to a translation of the projection in the angle variable and the scaling of the original image to a scaling of the projection in the spatial variable together with an amplitude scaling of the projection, and then the Fourier–Mellin transform is applied to the result to convert the translation in the angle variable and the scaling in the spatial variable as well as the amplitude scaling of the projection to a phase shift and an amplitude scaling, respectively. In order to achieve a set of completely invariant descriptors, a rotation and scaling invariant function is constructed. A kk-nearest neighbors’ classifier is employed to implement classification. Theoretical and experimental results show the high classification accuracy of this approach as a result of using the rotation and scaling invariant function instead of image binarization and normalization, it is also shown that this method is relatively robust in the presence of white noise.