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A New Image Data Compression/Reconstruction Method based on Fuzzy Relational Equation

A New Image Data Compression/Reconstruction Method based on Fuzzy Relational Equation. *Kaoru Hirota **Hajime Nobuhara, and **Witold Pedrycz. *Tokyo Institute of Technology (Japan) ** University of Alberta (Canada). Background (1). Digital Movie Theater. Image Database. Watermarking.

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A New Image Data Compression/Reconstruction Method based on Fuzzy Relational Equation

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  1. A New Image Data Compression/Reconstruction Method based on Fuzzy Relational Equation *Kaoru Hirota **Hajime Nobuhara, and **Witold Pedrycz *Tokyo Institute of Technology (Japan) ** University of Alberta (Canada)

  2. Background (1) Digital Movie Theater Image Database Watermarking Image Compression Image Compression and Applications

  3. Background (2) - Fuzzy World - Tokyo Institute of Technology Hirota Laboratory Wavelet Morphology DCT Fractal Vector Quantization ICF

  4. Image Compression and Reconstruction Method based on Fuzzy Relational Equation ICF y RGB Planes x 255 1.0 0 0.0 Fuzzy Relation Original Image (RGB Planes) (RGB Planes) [Hirota, Pedrycz (1999)]

  5. Fuzzy Relational Equation Composition Fuzzy Relation Fuzzy Relation Fuzzy Relation Compression Coder (X axis) Coder (Y axis) 255 Compressed Image 0 Original Image Image Compression Image Compression Process (1) [Hirota, Pedrycz (1999)]

  6. Image Compression Process (2) J N M I [Hirota, Pedrycz (1999)] Coding Systems Compressed Image (I x J) Original Image (M x N) Composition (= Compression)

  7. I 0.0 1.0 0.0 1.0 0.0 1.0 0.0 0.0 1.0 1.0 0.0 1.0 0.0 0.0 1.0 1.0 M Fuzzy Relation Fuzzy Set I Coder

  8. Image Reconstruction Process Fuzzy Relation Fuzzy Relation Fuzzy Relation Given ? Compressed Image Coder Reconstructed Image [Hirota, Pedrycz (1999)] Fuzzy Relational Equation Solving Fuzzy Relation Fuzzy Relation Fuzzy Relation Reconstruction ? Compressed Image Coder Reconstructed Image Image Reconstruction

  9. Duality Min-s System Max-t System Adjointness Adjointness Duality Min-s Adjoint System Max-t Adjoint System Image Compression/Reconstruction based on Various Types of Fuzzy Relational Equations [Nobuhara et al, JIEE 2001]

  10. Reconstructed Images and Solutions Compression Rate = 0.0625 ? The Greatest Original Minimal Solution Space [Hirota, Pedrycz (1999)]

  11. The Greatest Solution and Minimal Solutions Compression Rate = 0.0625 The Greatest Solution One of Minimal Solutions

  12. Compression Rate 0.0625 - Compression Rate - Compressed Image Size Reconstructed Image (The Greatest Solution) Original Image Original Image Size (Corel Gallery, CD-8, Arizona Directory, File No “611003”.) Compression Time 1.43 (s) Reconstruction Time 546.67 (s) 44.26 Root Mean Square Error Example (Reconstructed Image) (440MHz, Sun Ultra 10)

  13. Experiments H-P Method Proposed Method 20 Test Images (Standard Image DataBAse) : 256 x 256 pixels Compression Rate = 0.0156, and 0.0625 (I x J = 32x32, and 64x64) 440 MHz, Sun Ultra 10 VS Reconstruction Time Work Space

  14. Test Images (Standard Image DataBAse)

  15. 1 / 132 168.98 (s) 1.28 (s) Compression Rate 0.0156 H-P Method Proposed Method Work Space : 100.00 % Work Space : 12.50% 1 / 382 546.67 (s) 1.62 (s) 0.0625 Work Space : 100.00 % Work Space : 25.00% Experimental Results (Reconstruction Time)

  16. Compression Rate 0.0625 - Compression Rate - Compressed Image Size Reconstructed Image (The Greatest Solution) Original Image Original Image Size (Corel Gallery, CD-8, Arizona Directory, File No “611003”.) Compression Time 1.43 (s) Reconstruction Time 1.62 (s) 44.26 Root Mean Square Error (440MHz, Sun Ultra 10) Example (Reconstructed Image)

  17. The Greatest ? Approximate Solution Original How to Improve Reconstructed Image Quality ? [Nobuhara, Takama and Hirota, JIEE 2001]

  18. Comparison of Proposed Method with Original Method [Nobuhara, Takama, and Hirota JIEE 2001] Original Method Proposed Method Compression Rate 0.0625 RMSE : 44.26 22.09 Compression Rate 0.2500 25.41 14.43

  19. Comparison of ICF with DCT DCT Type II ICF VS Computation Time Image Quality

  20. ICF DCT Compression Rate Computation Time Comparison 0.38 (s) 0.93 (s) 0.0156 0.69 (s) 1.28 (s) 1.49 (s) 0.62 (s) 0.0625 1.62 (s) 0.98 (s)

  21. Proposed DCT Type II Image Quality Comparison (1) VS Compression Rate = 0.0625

  22. Image Quality Comparison (2) : PSNR (Average of 20 Images of Standard Image DataBAse)

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