1. Fuzzy type Image Fusion using hybrid DCT-FFT based Laplacian Pyramid Transform
Authors: Rajesh Kumar Kakerda, Mahendra Kumar, Garima Mathur, R P Yadav, Jagdish Prasad Maheshwari
Presented By:
Mahendra Kumar
Faculty at UCE, RTU, Kota (Raj.) India
Director, MI Tech Society, Kota (Raj.) India

2. Contents Introduction Laplacian pyramid
Proposed DCT-FFT based Laplacian Pyramid transform
Image Fusion Process
Fusion Performance Evaluation
Results and Comparatively study
Conclusion
References

3. Introduction
This paper presents a fuzzy type image fusion technique using hybrid discrete Cosine transform (DCT) – Fast Fourier Transform (FFT) based laplacian pyramid.
It is concluded that fusion with higher level of pyramid provides better fusion quality.
This technique can be used for fusion of fuzzy images as well as multi model image fusion.
The proposed algorithm is very simple, easy to implement and could be used for real time applications.
This is paper also provided comparatively studied between proposed and previous existing technique and validation of the proposed algorithm as Peak Signal to Noise Ratio (PSNR), Root Mean Square Error (RMSE) and Correlation (CORR) .

4. Laplacian pyramid
The Laplacian pyramid was first introduced as a model for binocular fusion in human stereo vision [3], where the implementation used a Laplacian pyramid and a maximum selection rule at each point of the pyramid transform.
Essentially, the procedure involves a set of band-pass copies of an image is referred to as the Laplacian pyramid due to its similarity to a Laplacian operator.
Each level of the Laplacian pyramid is recursively constructed from its lower level by applying the following four basic steps: blurring (low-pass filtering);sub-sampling (reduce size); interpolation (expand); and differencing (to subtract two images pixel by pixel).
In the Laplacian pyramid, the lowest level of the pyramid is constructed from the original image [5].

5. Information flow diagram of pyramid a). Construction & b)
Information flow diagram of pyramid a). Construction & b). Reconstruction[5].

6. Proposed DCT-FFT based Laplacian Pyramid transform
The procedure for Laplacian pyramid construction and reconstruction is illustrated in Fig-1.
Reduced Function: The image at the 0th level g0 of size MxN is reduced to obtain next level g1 of size 0.5Mx0.5N where both spatial density and resolution are reduced. Similarly, g2 is the reduced version of g1 and so on. Image reduction is done by taking the DCT and applying the IDCT on first half of coefficients in both directions. The level to level image reduction is performed using the function reduce R.
Expand Function: The reverse of function reduces is expanded function E. Its effect is to expand the image of size MxN to image of size 2Mx2N by taking IFFT after padding the M zeros in horizontal and N zeros in vertical directions.

7. Image Fusion Process
Let, there are two images (I1 & I2) to be fused. Pyramid construction is done for each image and keeping the error records. Denote the constructed k levels of Laplacian image pyramid for 1st image is [5]
and similarly for of 2nd image is
Then the image fusion rule is as follows:

8. For k-1 to 0 levels
and the magnitude comparison is done on corresponding pixels. The pyramid If = g0f the fused image.

9. Fusion Performance Evaluation
Root Mean Square Error:
Peak Signal to Noise Ratio:
where, L in the number of gray levels in the image.

10. Results and Comparatively study
Reference fuzzy type Image
Fuzzy type Image 1
Fuzzy type Image 2

11. Proposed Hybrid Technique
Table 1
Proposed Hybrid Technique
Pyramid levels
Techniques 1 3 5 7
RMSE
DCTPT
9.3924
9.4921
FFTPT
7.9812
7.8937
7.9885
8.0075
PSNR
CORR
0.9988
0.9990
0.9981
0.9993

12. Comparatively study for RMSE between DCT based Pyramid Transform and Proposed Method

13. Comparatively study for PSNR between DCT based Pyramid Transform and Proposed Method

14. Comparatively study for Correlation between DCT based Pyramid Transform and Proposed Method

15. Conclusion
A novel image fusion technique using DCT-FFT based Laplacian pyramid has been presented and its performance evaluated.
It is concluded that fusion with higher level of pyramid provides better fusion quality. This technique can be used for fusion of fuzzy type images as well as multi model image fusion.
The proposed algorithm is very simple, easy to implement and could be used for real time applications.
This paper is also provided comparatively studied between proposed and DCT based Pyramid transform technique and validation of the proposed algorithm as Peak Signal to Noise Ratio (PSNR), Root Mean Square Error (RMSE) and Correlation (CORR) in table 1 and plots also.

16. REFERENCES
[1] A. Toet, “A morphological pyramid image decomposition”, Pattern Recogn. Lett. 9(4), 255–261 (1989).
[2] VPS Naidu and J.R. Raol, ”Pixel-Level Image Fusion using Wavelets and Principal Component Analysis – A Comparative Analysis” Defence Science Journal, Vol.58, No.3, pp , May 2008.
[3] VPS Naidu, “Discrete Cosine Transform-based Image Fusion”, Special Issue on Mobile Intelligent Autonomous System, Defence Science Journal, Vol. 60, No.1, pp.48-54, Jan
[4] Mahendra Kumar et.al., “Digital Image Watermarking using Fractional Fourier transform via image compression”, In IEEE International Conference on Computational Intelligence and Computing Research 2013 (IEEE ICCIC-2013), Dec., 2013.
[5] VPS Naidu, “A Novel Image Fusion Technique using DCT based Laplacian Pyramid”, International Journal of Inventive Engineering and Sciences (IJIES) ISSN: 2319–9598, Volume-1, Issue-2, January, 2013.
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[8] V.P.S. Naidu, J.R. Rao. “Pixel-level Image Fusion using Wavelets and Principal Component Analysis”, Defence Science Journal, pp , 2008.
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