1. Presenter by : Mourad RAHALI
16th International Conference on Intelligent Systems Design and Applications (ISDA 2016)
The Improvement of an Image Compression Approach Using Weber-Fechner Law
Name of presentation
Company name
Presenter by : Mourad RAHALI
Realized by : Mourad Rahali
Dr. Habiba Loukil
Pr. Mohamed Salim Bouhlel

2. PLAN Problematic Image compression
The proposed image compression approach
Experimental and results
Conclusion and future work

3. Problematic Problem of storage and transmission Treatment results
digital images
Storage

4. Solutions Increase the capacity of storage media. Son rôle
Increase the rate and bandwidth of the transmission channels.
Problem of cost
Images compression
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Composition

5. PLAN Problematic Image compression
The proposed image compression approach
Experimental and results
Conclusion and future work

6. Image compression Son rôle
Reduce the size of data and facilitate the storage.
The basic idea of image compression is to reduce the average number of bits per pixel necessary for their representation
Save to better the visual quality of the image during their decompression.
It exists two types of compression approach :
Lossless compression (scalar quantization)
Lossy compression (vector quantization)
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Composition

7. Image compression approach
Scalar quantization:
Coding the pixel which are represented by a value.
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Composition
pixels
Image after transformation

8. Image compression approach
Vector quantization :
Coding the pixel which are represented by a many values.
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Composition
Blocs of pixels
Image after transformation

9. PLAN Problematic Image compression approach
The proposed image compression approach
Experimental and results
Conclusion and future work

10. The proposed image compression approach
Image compression steps :
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Composition
Weber-Fechner Law
Wavelet
Transform
Kohonen’s Network
Compressed
Image
Original Image
Apply the logarithmic quantization by using the principle of Weber-Fechner law on original image depending of the constant of Weber quantization.
Apply a wavelet transform of an original image depending on the decomposition level (1, 2, 3...) and the wavelet type (haar, db, sym,.. ).
Decompose the image into blocks according to a block size (for example 2x2, 4x4, 8x8 or 16x16).
Search the codebook for each block and the code word with a minimum distance from the block. The index of the selected word is added to the index vector that represents the compressed image.
Code the index vector by a Huffman coding.
Save the index vectors coded for use during decompression.

11. The proposed image compression approach
Logarithmic quantization using the Weber-Fechner law
Sensitivity to contrast is the ability of the human visual system to detect the changes in luminance (achromatic) and the chromatic changes.
Weber law regards the sensitivity of the human eye to luminance as a logarithmic function.
Weber developed a quantitative description of the relationship between the stimulus intensity and the discrimination which is now known as Weber law.
Where ∆S is the perceived intensity difference with respect to a stimulus S and K which is a constant. Fechner applied the law to the sensory experience. He found that the intensity of sensation is proportional to the logarithm of the stimulus intensity.

12. The proposed image compression approach
Logarithmic quantization using the Weber-Fechner law
If the absolute threshold is S0 = 1 and the associated sensation is P0 = 0, Fechner assumes that the amplitude of sensation is proportional to the logarithm of the stimulus. This relationship is called Weber-Fechner law.
According to Weber-Fechner law, the quality measurement must take into account the logarithmic sensitivity of the eye to light and the decreases in the image gray levels are considered imperceptible to the human eye. On the other side of the coin, the logarithmic quantization reduces the entropy of the image which will lead to a higher compression ratio without noticeable degradation of the original image.

13. The proposed image compression approach
Wavelet transform :
The two-dimension wavelet transform is adopted in our approach.
Wavelet transform decomposes an image into a set of different resolution sub-images, corresponding to the various frequency bands representing the information carried by the initial image at different levels (j) of resolution: the approximation image (LL), horizontal details of image (HL), vertical details (LH) and diagonal details (HH).
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14. Image compression approach
Wavelet transform :
The wavelet transform can apply two filters on the image, (lowpass and highpass).
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Composition
H(x)
L(x) 2
L(y)
H(y)
Image
originale LL LH HL HH
Lines
Columns
Decomposition of image

15. Image compression approach
Kohonen’s Network
Kohonen’s network algorithm follows these steps:
Each node's weights are initialized.
A vector is chosen at random from the set of training data.
Every node is examined to calculate which one's weights are most like the input vector.
Then the neighborhood is calculated. The amount of neighbors decreases over time.
The winning weight is rewarded with becoming more like the sample vector. The neighbors also become more like the sample vector.
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16. Image compression approach
Learning phase
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The first step of the learning is wavelet transform of an original image to obtain four sub-images: approximation image and three details images in different resolution depending on the decomposition level and wavelet choice. The second step is to decompose the four sub-images in blocks according to block size (2x2, 4x4, 8x8 or 16x16). The blocks are arranged in linear vectors to be presented in the Self-Organizing Map (SOM) one after the other. The third step is to adjust coupling the weights according to an index vectors. The weights obtained at the end of learning represent the codebook will be used for compression.
Codebook

17. PLAN Problematic Image compression approach
The proposed image compression approach
Experimental and results
Conclusion and future work

18. Experimental and results
In our work, we compare two compression methods: the classic method and the new method using Weber-Fechner law. We change the compression parameters: the wavelet decomposition level (j), the size of the input block (BS) and the size of Self Organization map (SOM).
To evaluate our new approach, we use three compression evaluation criteria: the compression ratio (CT), the means square error (MSE) and the Peak Signal to Noise Ratio (PSNR).
Where
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19. Experimental and results
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The reconstructed images are compared with the original images in terms of PSNR according to the number of bits per pixel (Nbpp). The figures indicate that the visual quality metric (PSNR) of the compressed images of the approach using Weber-Fechner law (green curve) in terms of the compression ratio (Nbpp) improves with respect to the classic approach (blue curve).
We notice that there is a significant improvement in the quality of the reconstructed image if the compression ratio is higher than 1 bits per pixel since the shape of the green curve (new approach) is going up for the four images.

20. PLAN Problematic Image compression approach
The proposed image compression approach
Experimental and results
Conclusion and future work

21. Conclusion and future Work
In this contribution, we have enhanced the compression quality of a still-image-compression approach based on the discrete wavelet transformation and neural networks by adding a new pre-treatment phase to quantify the signals of the original image through the use of the principle of Weber-Fechner law. We notice that the new approach is better than the classic approach in terms of quality according to the compression ratio feature if the number of bits per pixel is higher than 0.5. To boost our approach, we will quantify the original image in a semi-logarithmic manner by using the law of compression 'A' which is used in mobile telephone networks.

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