A complete translation and rotation invariant algorithm for pattern recognition

This paper introduces a new complete translation and rotation invariant algorithm. Applying this algorithm to a target image produces two transformed images which are invariant under translation and rotation to the original target image. This algorithm is complete; that is, the object in the original image can be completely recovered from the resultant images except for its position and orientation. The algorithm begins by taking a two dimensional Fourier transform of the target image, resulting in two 2-D images: the Fourier phase and magnitude. The Fourier magnitude is translation invariant. In order to make the magnitude also be rotation invariant, a circular Fourier transform is taken. Applying the TR-Taylor invariant operation to the resultant image produces the first translation and rotation invariant image. Under the Hessian-Taylor invariant, the phase image is transformed into a Hessian matrix which is translation invariant. A complete derivation of the algorithm leading to the final invariant images is given. Simulations applying the algorithm to test images are shown