Multiple-target recognition using the discrete rotational Fourier transform

Abstract

Neng-Chung Hu Kuo-Kan Yu Hong-I Chang National Taiwan University of Science and Technology Department of Electronic Engineering 43 Keelung Road, Sec. 4 Taipei, Taiwan E-mail: nchu@et.ntust.edu.tw Abstract. Much research has been devoted to locating multiple targets on the condition that there is only one pattern in the reference image and more than one such pattern in the input image. We, however, propose a new correlator to locate 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), which extends the one-dimensional (1-D) DRFT. Since the DRFT domain of an image contains information both in the spatial domain and in the frequency domain of the image, we use this property to locate and display the matched targets. The DRFT-based correlator first obtains Xa@u1 ,u2#Ha*@u1 ,u2#, where Xa@u1 ,u2# and Ha@u1 ,u2# are the DRFTs of the input image and the reference image, respectively; then the inverse discrete Fourier transform (IDFT) of Xa@u1 ,u2#Ha*@u1 ,u2# yields many cone-shaped correlation peaks. A correlation peak stands for a matched pattern between the input image and the reference image. To display the shape of the matched pattern, Ha@u1 ,u2# is shifted according to the position of the correlation peak yielding Ha8 @u1 ,u2#. Finally, uXa@u1 ,u2#Ha8 @u1 ,u2#u displays the shape of the matched pattern. Like the conventional correlator, the DRFT-based correlator can recognize only the translated versions of the patterns in reference image. The purpose of this approach is to recognize multiple different targets simultaneously. The properties of the proposed 2-D DRFT are also presented. © 2001 Society of Photo-Optical Instrumentation Engineers. [DOI: 10.1117/1.1386371]