A bank of fast matched filters by decomposing the filter kernel

In this paper we introduce a bank of fast matched filters that are designed to extract gradients, edges, lines and various line crossings. Our work is based on previously introduced filtering approaches like conventional Matched Filtering (MF), Complex Matched Filtering (CMF) and Generalized Complex Matched Filtering (GCMF), and is aimed to speed up the image processing. Filter kernel decomposition method is demonstrated for the latter mentioned (GCMF) but can be similarly applied to any other filters (like MF, CMF, Gabor filters, spiculation filters, steerable MF, etc.) as well. By introducing the mask kernel approximation, we show how to substitute the GCMF with several more computationally efficient filters, which reduce the overall computation complexity by over hundred of times. Acquired Fast GCMF retains all of the functionality of GCMF (extracts the desired objects and obtains their angular orientation), losing in accuracy only about +26 dB in terms of PSNR.