FAST FOURIER METHOD FOR THE ACCURATE ROTATION OF SAMPLED IMAGES

At present the best methods for rotation of discrete sampled images us e a combination of (fast) Fourier interpolation followed by cubic inte rpolation onto a rotated grid. A method is presented which uses only F ourier interpolation. The new method has a similar computational compl exity to the old, and is exactly reversible. The method uses the well- known decomposition of rotation into three pure shears. Each shear is performed using a 2D extension of the 1D Fourier shift theorem. This a llows the fast Fourier transform (FFT) to be used, With appropriate da ta padding (such as zero padding) in both the real and Fourier domains , the procedure gives near perfect results and minimal loss of informa tion in multiple rotation tests.