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Poster Session 4
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A New and Efficient Transform for Signal Processing Based on Gabor Discrete Disctete Cosine Transform
3. Results and Discussions
Image compression is needed for browse application on remotely sensed data at NRSA, India. for this purpose, it was found that Gabor DCT is a suitable technique and the necessary software was developed to implement the same. After a comprehensive study to improve computational speed another useful variant Gabor DCT which we call here New Transform has been developed. Software for implementation of the New Transform has also been developed as already described. The software is developed in 'C' on Unix platform (SUN workstation) and performances of both the transforms have been measured. The software computes number of transform expansions based on same Mean Square Error (MSE) for both the transforms and then each expansion is coded in B bits. Both the techniques ware applied to picture and remotely sensed data of different sizes viz 256x256, 512x512 and 1k x 1k pixels. Performance measurement is made on the basis of MSE, compression ratio and computational speed. The MSE is computed between original and reconstructed images. Fig. (1) shows the original image whereas Fig. (2) & (3) show the reconstructed images using Gabor DCT and New Transform techniques respectively.
Figure 1 Original Image
Figure 2 Reconstructed Image using Gabor Dct compression Rate : 0.25 Bits/Pixel
Figure 3 Reconstructed Image using New Transform Compression Rate " 0.20 Bits/Pixel
At NRSA, several images of different sizes were compressed using both the techniques viz Gabor DCT and New Transform and our observations are shown in Table (1) and Table (2). It is observed from both the tables that for the same MSE the New Transform gives better compression ratio and the same time takes lesser time for computation. Quality of the compressed image depends upon number of transform expansions stored for that image. If number of transform expansions increases, quality of compressed image also increases i.e. MSE is reduced but the execution increases.
Table (1) : Observations with Gabor DCT
| Sl. No. |
MSE |
Compression Ratio (bits/pixel) |
Execution Time (in sec.) |
Image Size |
| 1 |
5.28 |
0.5 |
7.9 |
256x256 |
| 2 |
9.08 |
0.5 |
75.6 |
512x512 |
| 3 |
9.53 |
0.5 |
681.4 |
kx1k |
| 4 |
10.11 |
0.125 |
3.3 |
256x256 |
| 5 |
17.65 |
0.25 |
29.0 |
512x512 |
| 6 |
19.02 |
0.25 |
276.7 |
1k x 1k |
Table (2) : Observations with New-Transform
| Sl. No. |
MSE |
Compression Ratio (bits/pixel) |
Execution Time (in sec.) |
Image Size |
| 1 |
5.28 |
0.4 |
7.7 |
25x256 |
| 2 |
9.08 |
0.4 |
72.8 |
512x512 |
| 3 |
9.53 |
0.4 |
632.4 |
kx1k |
| 4 |
10.11 |
0.25 |
3.2 |
256x256 |
| 5 |
17.65 |
0.25 |
28.1 |
512x512 |
| 6 |
19.02 |
0.25 |
240.6 |
1k x 1k |
4. Conclustions
Gobor DCT and New Transform have been applied on 2-D discrete signals, such as remotely sensed images, and performances of both have been examined. It has been found that the computational speed achieved here for implementing this New non-orthogonal transform is quite satisfactory and it is suitable for various applications, such as image analysis, segmentation and compression, in remote sensing. It is observed that performance of New Transform is much better than the Gabor DCT. Since, like the Gabor DCT, transform coefficients of New Transform have a more compact energy distribution, a better image compression result can be achieved. The 2-D New Transform is also useful for image analysis and segmentation because, it also extracts locally windowed 2-D spectral information concerning form and texture without sacrificing information about 2-D location or more global spatial relationships.
References
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Hang Wang, Hong Yan, "Efficient image coding method based on adaptive Gabor discrete cosine transforms", Journal of Electronic Imaging, January 1993, Vol.2, No.1, pp. 38-43.
- H. Wang and H. Yan, "Adaptive Gabor discrete cosine transform for image compression". Electronics Letters, Aug. 1992, Vol.28, No. 18, pp. 1155-1756.
- John G. Daugman , "Complete discrete 2-D Gabors transforms by neural networks for image anlysis and compression". IEEE Trans. on ASSP. Vol.36, No.7, July 1988, pp 1169-1179.
- J. Wexler and S. Raz, "Discrete Gabor expansion". Signal processing, Vol.21, No.3, Nov. 1990, pp. 207-220.
- Richard H. Orr, "Derivation of Gabor transform relations using Bessel's equality". Signal Processing, Vol.30, No.2, January 1993, pp. 257-262.
- Touradj Ebrahimi, Murat Kunt, "Image compression by Gabor expansion". Optical Engineering, July 1991, Vol.30, No.7, pp. 873-880.
- V. Srinivasan, P. Bhatial and S.H. Ong, "A fast implementation of the discrete 2-D Gabor transform". Signal Processing, vol.31. No.2, March 1993, pp. 229-233.
- Wang H. and Yan H., "Efficient implementation of Gabor transform for image compression". Electronics letters, 1992, Vol.21, No. 9, pp. 870-871.
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