Determining the rotation angle between two images is essential when comparing images that may include rotational variation. While there are three representative methods that utilize the phases of Zernike moments (ZMs) to estimate rotation angles, very little work has been done to compare the performances of these methods. In this paper, we compare the performances of these three methods and propose a new, angular radial transform (ART)-based method. Our method extends Revaud et al.'s method [1] and uses the phase of angular radial transform coefficients instead of ZMs. We show that our proposed method outperforms the ZM-based method using the MPEG-7 shape dataset when computation times are compared or in terms of the root mean square error vs. coverage.

In this paper we discuss a neural network model that can recognize patterns rotated at various angles. The model employs copy learning, a learning method entirely different from those used in conventional models. Copy-Learning is an effective learning method to attain the desired objective in a short period of time by making a copy of the result of basic learning through the application of certain rules. Our model using this method is capable of recognizing patterns rotated at various angles without requiring mathematical preprocessing. It involves two processes: first, it learns only the standard patterns by using part of the network. Then, it copies the result of the learning to the unused part of the network and thereby recognizes unknown input patterns by using all parts of the network. The model has merits over the conventional models in that it substantially reduces the time required for learning and recognition and can also recognize the rotation angle of the input pattern.