The transform function for geometric transform is approximated by polynomial. As the transform act on the image plane

the computation of the polynomial can be greatly simplified. A recursive algorithm is given in the paper. When realized by systolic architecture parallely

the algorithm needs only the time of one addition for each pixel. The hardware cost is only O（N）

where N is the order of polynomial. A theoretical error analysis is proposed for the whole structure The hardware system for 2 order polynomial transform has been successfully realized. The system can work at the TV rate.