Generalized complex 2D matched filtering for local regular line-like feature detection

In pattern recognition systems it is usually necessary to detect different image details, like edges, lines, corners, blobs, etc. For this purpose a bank of special filters, matching each individual detail can be used. As the details usually are oriented in different directions and have different scales, the image processing leads to many convolution operations. The complex 2D matched filter (CMF) is an angle invariant line detection filter, which also provides additional information about orientation of detected lines. In this paper we follow the idea of complex matched filtering, and develop generalized complex matched filtering (GCMF) approach, which is a whole bank of different angle invariant filters, where each filter is denoted by the order. These filters can be used to detect a broader range of image details: edges, lines, line intersections and corners; and, like its predecessor, the GCMF provides additional information about the detected features - the orientation angle. Each kernel from the GCMF bank is analyzed in polar coordinates and the specifics of detail detection are explained. A method of generating GCMF normalized kernels of arbitrary order is proposed. GCMF algorithm is presented and its performance is demonstrated on test images.