Multiple-target recognition using the discrete rotational Fourier transform

Much research has been devoted to locating multiple targets on the conditio n that there is only one pattern in the reference image and more than one s uch pattern in the input image. We, however, propose a new correlator to lo cate and display multiple different targets when both the reference and the input images contain many different patterns. This correlator is based on the two-dimensional (2-D) discrete rotational Fourier transform (DRFT), whi ch extends the one-dimensional (1-D) DRFT. Since the DRFT domain of an imag e contains information both in the spatial domain and in the frequency doma in of the image, we use this property to locate and display the matched tar gets. The DRFT-based correlator first obtains X-alpha[u(1),u(2)]H*(alpha)[u (1),u(2)], where X-alpha[u(1),u(2)] and Ha[ u(1), u(2)] are the DRFTs of th e input image and the reference image, respectively; then the inverse discr ete Fourier transform (IDFT) of X-alpha[u(1), u(2)]H*(alpha)[u(1), u(2)] yi elds many cane-shaped correlation peaks. A correlation peak stands for a ma tched pattern between the input image and the reference image. To display t he shape of the matched pattern, Ha[ u(1), u(2)] is shifted according to th e position of the correlation peak yielding H ' (alpha)[ u(1), u(2)]. Final ly, /X-alpha[ u(1), u(2)]H ' (alpha)[ u(1), u(2)]/ displays the shape of th e matched pattern. Like the conventional correlator, the DRFT-based correla tor can recognize only the translated versions of the patterns in reference image. The purpose of this approach is to recognize multiple different tar gets simultaneously. The properties of the proposed 2-D DRFT are also prese nted. (C) 2001 society of Photo-Optical Instrumentation Engineers.