1. Application of Generalized Representations for Image Compression Application of Generalized Representations for Image Compression using Vector Quantization Technion - Israel Institute of Technology Department of Electrical Engineering The Image and Computer Vision Laboratory Sheingart Michael & Tseitlin Yuri Supervisor: Wajcer Daniel

2. Project Goals Checking an efficiency of the multifrequency representation used for image compressing and coding. Implementing and simulation of the Wavelet Image Coder. Comparation with another families of Image Coders.

3. The general structure The Wavelet Transform. The Vector Quantization. The Entropy Coder is implemented by Adaptive Arithmetic Coding.

4. The Wavelet Coder Scheme

5. The reasons for using Wavelet Transform Majority of information is stored in low pass filter and high pass filters are very sparse. The lack of redundancy between the transform coefficients. The transform is mathematically stable.

6. The Vector Quantization Computing the binary tree by Splitting Algorithm and training the codebooks by Max-Lloyd Algorithm. Pruning the tree by ROPA Algorithm. The Bit Allocation Algorithm to obtain the desired Rate.

7. The Adaptive Arithmetic Coder The coder is free from the statistical issues associated with the design of Huffman Code. The coder adapts to varied statistic features of a source. There is free error coding.

8. Comparative performance of the Vector Quantizer The comparation between Entropy - Constrained Scalar Quantizer ( right ) and our Vector Quantizer ( left ).

9. Comparative performance of the Wavelet Image Coder The comparation between Embedded Zerotree Wavelet Coder ( right ) and our Wavelet Image Coder ( left ).

10. Performance of Wavelet Image Coder 1. Original picture 2. Quantized picture with __Rate = 1 bpp 3. Coded picture with __training codebook 2 1 3

11. Conclusion The wavelet representation is powerful tool for image coding and compression. The vector quantization using Splitting Algorithm yields a minimum distortion quantizer for fixed code word length vectors. Any intermediate rate can be obtained. The quantizer is sub-optimal but easy for training and using since it is tree- structured quantizer.