Complexity and Nonlinear Dynamics in STEM
IIT Hyderabad, 05-07 June 2023
Wavelet-modified logarithmic fringe-adjusted joint transform correlator
Jyoti Bikash Mohapatra, Akash Pal, Jyothish Jojy*, and Naveen K. Nishchal**
Fourier transform-based information processing is one
of the prominent operations in optical pattern recognition.
The joint transform correlator (JTC) is an attractive technique for real time optical processing, which has been
modified by applying various operations in order to improve the correlation outputs. Fringe-adjusted JTC is another modified approach in which the joint power spectrum is modulated by a real-valued filter, called the fringe
adjusted filter. Obtaining one more Fourier transform operation yields better correlation output [1,2].
In this paper, we study the influence of wavelet transform on logarithmic fringe-adjusted JTC. In this technique, we combine the benefits of the classical JTC with
the logarithmic fringe adjustment which enhances the object detection ability.
Wavelet transform is used to improve the recognition
accuracy and robustness to noise and occlusions [2]. A
Mexican hat wavelet function has been applied to logarithm modified joint power spectrum. The twodimensional Mexican hat wavelet, which is a second derivative of the Gaussian function, is represented as,

2
h x, y   1   x 
 

y
2

 exp  




x y
2
2
2





a
b
c
(1)
Here, we find that correlation peak height is enhanced due
to wavelet modification to joint power spectrum. If compared, wavelet-modified approach performs better in comparison to without wavelet use. The method is more effective in real world scenarios where the target objects may be
partially occluded or have low contrast against background
or when target is embedded in noise corrupted input
scenes.
Computer simulation results confirm the effectiveness
of the proposed algorithm. The results have been shown in
Figure 1.
Figure 1(a) Joint input image, (b) correlation output employing logarithmic fringe-adjusted JTC, and (c) waveletmodified logarithmic fringe-adjusted JTC.
Acknowledgement
Financial support from IISU Thiruvananthapuram is
acknowledged.
References
[1] M. Alam and M. Karim, “Fringe-adjusted joint transform
correlation,” Appl. Opt. 32(23):4344-4350, 1993.
[2] A. Bhagatji, N. K. Nishchal, A. K. Gupta, and B. P. Tyagi,
“Wavelet-modified fringe adjusted joint transform correlator,” Opt. Laser Technol.40:99-112, 2008.
*ISRO Inertial Systems Unit (IISU), Thiruvananthapuram
695022, Kerala.
**Department of Physics, Indian Institute Technology
Patna, Bihta, Patna-801106, Bihar. E-mail: nkn@iitp.ac.in