An efficient implementation of affine transformation using one-dimensional FFTs

In this paper, we propose a new decomposition scheme and an efficient interpolation algorithm for affine transformation of a digital image. We try to reconstruct the affine-transformed image by resampling it with the highest possible quality, lowest complexity and throughput rate. Based on the proposed decomposition, the transform is completed by a sequence of 3-pass translations and a scaling operation where each of them is one-dimensional in nature. This method preserves quality and guarantees simplicity. We place the emphasis on the feasibility of a parallel implementation that can benefit from pipeline technologies. Further, an efficient FFT-based implementation of this new algorithm is suggested. Experimental evidence of the effectiveness and robustness of the proposed method is reported. The problem is relevant to video transmission, image registration, and computer graphics manipulation.