Distortion-invariant pattern recognition using synthetic discriminant function based multiple phase-shifted-reference fringe-adjusted joint transform correlation Mohammed Nazrul Islam a, ⁎, K. Vijayan Asari b , Mohammad A. Karim c , Mohammad S. Alam d a Security Systems, Farmingdale State University of New York, Farmingdale, NY 11735, United States b Electrical and Computer Engineering, University of Dayton, College Park, Dayton 45469, United States c Electrical and Computer Engineering, Old Dominion University, Norfolk, VA 23529, United States d Electrical and Computer Engineering, University of South Alabama, Mobile, AL 36688, United States abstract article info Article history: Received 3 March 2010 Accepted 14 November 2010 Keywords: Fringe-adjusted filter Joint power spectrum Joint transform correlation Pattern recognition Synthetic discriminant function Target detection This paper proposes a novel pattern recognition system for invariance to noise and distortions. The technique first generates a synthetic discriminant function of the target image from its different distorted versions. It then takes four different phase-shifted versions of the reference image, which are individually joint transform correlated with the given input scene. Thus the proposed algorithm produces a single cross-correlation signal corresponding to each potential target. Also a fringe-adjusted filter is designed to generate a delta-like correlation peak with high discrimination between the signal and the noise. The pattern recognition system is also designed for the identification of multiple targets belonging to multiple reference objects simultaneously in a given input scene. The proposed technique is investigated using computer simulation including real-life images in different complex environments. © 2010 Elsevier B.V. All rights reserved. 1. Introduction Optical joint transform correlation (JTC) technique has been successful in recognizing an object of interest in an arbitrary input scene. It offers a number of advantages over other correlation techniques, such as Vanderlugt filter, in that it allows real-time updating of the reference image, permits parallel Fourier transforma- tion of the reference image and input scene, operates at video frame rates and eliminates the precise positioning requirement of a complex matched filter in the Fourier plane [1,2]. However, the classical JTC technique suffers from poor correlation discrimination, wide side- lobes, conjugate correlation peak, strong zero-order correlation, and failure to perform in noisy environment. Several modifications of the classical JTC technique have been proposed in the literature to alleviate these problems, which include binary JTC [3], phase-only JTC [4,5], fringe-adjusted JTC (FJTC) [6], shifted phase-encoded JTC [7], and complementary-reference and complementary-scene JTC [8]. However, these algorithms are not as efficient in producing highly discriminant correlation signals for potential targets and rejecting all non-target objects in the input scene with a simple system architecture and high speed operation for real-time pattern recognition applications. An additional challenge for these techni- ques is to make the pattern recognition performance invariant to distortions due to scale and rotation variations of the targets in the input scene. The objective of this paper is to develop a novel pattern recognition algorithm employing synthetic discriminant function (SDF) and multiple phase-shifted-reference JTC (MRJTC) technique. The recently proposed MRJTC technique processes four phase-shifted reference images with the same input scene and hence removes all the unwanted correlation terms and produces a single and highly discriminant correlation peak for each potential target [9]. The MRJTC technique is modified by incorporating the SDF function to make the performance invariant to distortions. An SDF reference image is generated from a set of training images of the target including possible scale and rotational variations. Computer simulation results show that the proposed technique is successful in recognizing the potential targets present in a real-life input scene with complex background conditions. 2. Analysis Fig. 1 shows the block diagrams of the proposed MRJTC based pattern recognition technique including SDF reference image. As shown in Fig. 1(a), the SDF reference image is formed from a set Optics Communications 284 (2011) 1532–1539 ⁎ Corresponding author. Tel.: + 1 631 420 2485. E-mail address: islamn@farmingdale.edu (M.N. Islam). 0030-4018/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.optcom.2010.11.042 Contents lists available at ScienceDirect Optics Communications journal homepage: www.elsevier.com/locate/optcom