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

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

Problematic Problem of storage and transmission Treatment results digital images Storage

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

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

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) Son rôle Composition

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

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

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

The proposed image compression approach Image compression steps : Son rôle 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.

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.

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.

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). Son rôle Composition

Image compression approach Wavelet transform : The wavelet transform can apply two filters on the image, (lowpass and highpass). Son rôle Composition H(x) L(x) 2 L(y) H(y) Image originale LL LH HL HH Lines Columns Decomposition of image

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. Son rôle Composition

Image compression approach Learning phase Son rôle 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

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

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 Son rôle Composition

Experimental and results Son rôle Composition 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.

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

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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