An efficient partitioning-based scheme for 2-D convolution and application to image registration

A new scheme for efficiently computing the 2-dimensional (2-D) convolution between a fixed filter and an input sequence is presented. The scheme is particularly suitable for a special type of convolution encountered in several 2-D applications. In this type of convolution the involved filter is assumed fixed for a number of outputs which is less than the number of filter taps. By properly partitioning both the filter and the input sequences the whole problem is divided into a number of smaller convolution problems which in turn are solved efficiently using FFT. The scheme exhibits considerably reduced computational complexity as compared to other well-known FFT-based techniques. Moreover it lends itself for efficient VLSI implementation since it employs FFTs of relatively small size, as well as for parallel implementation since most steps of the method can be performed in parallel.