We discussed then how to compute two-dimensional digital convolution and two-dimensional DFT with the polynomial transforms, which are introduced in this paper.

In this paper, algorithms for computing 2-d circular convolution by using Fast Polynomial Transform (FPT) are reviewed and discussed, and then an improved algorithm is presented.

In chapter two, using piecewise quartic polynomial as kernel function, we give analytical convolution solutions for points, line segments, arcs, quadratic Bezier curves and triangle segments.