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) 1 Background (1) Image Compression and Applications Watermarking Digital Movie Theater Image Database Image Compression 2 Background (2) - Fuzzy World Tokyo Institute of Technology Hirota Laboratory ICF Wavelet Morphology DCT Fractal 3 Vector Quantization ICF Image Compression and Reconstruction Method based on Fuzzy Relational Equation [Hirota, Pedrycz (1999)] y RGB Planes x 255 1.0 0 0.0 Original Image (RGB Planes) Fuzzy Relation 4 (RGB Planes) Image Compression Process (1) [Hirota, Pedrycz (1999)] Fuzzy Relational Equation Composition Fuzzy Relation Fuzzy Relation Fuzzy Relation Compression 255 0 Original Image Coder (X axis) Coder (Y axis) Image Compression Compressed Image 5 Image Compression Process (2) [Hirota, Pedrycz (1999)] Coding Systems J N M Compressed Image (I x J) Original Image (M x N) I Composition (= Compression) 6 Coder I 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 1.0 1.0 1.0 1.0 1.0 1.01.0 1.0 M Fuzzy Relation Fuzzy Set I 7 Image Reconstruction Process [Hirota, Pedrycz (1999)] Solving Fuzzy Relational Equation Fuzzy Relation Fuzzy Relation Fuzzy Relation Given Reconstruction ? Coder Compressed Image Reconstructed Image Image Reconstruction 8 Image Compression/Reconstruction based on Various Types of Fuzzy Relational Equations [Nobuhara et al, JIEE 2001] Duality Max-t System Min-s System Adjointness Max-t Adjoint System Adjointness Duality Min-s Adjoint System 9 Reconstructed Images and Solutions Compression Rate = 0.0625 [Hirota, Pedrycz (1999)] ? The Greatest Original Minimal Solution Space 10 The Greatest Solution and Minimal Solutions Compression Rate = 0.0625 The Greatest Solution One of Minimal Solutions 11 Example (Reconstructed Image) Compression 0.0625 Rate - 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) Root Mean Square Error 44.26 12 (440MHz, Sun Ultra 10) Experiments H-P Method VS Proposed Method Reconstruction Time Work Space 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 13 Test Images (Standard Image DataBAse) 14 Experimental Results (Reconstruction Time) Compression Rate 0.0156 H-P Method 168.98 (s) Proposed Method 1 / 132 Work Space : 100.00 % 0.0625 546.67 (s) Work Space : 100.00 % 1.28 (s) Work Space : 12.50% 1 / 382 1.62 (s) Work Space : 25.00% 15 Example (Reconstructed Image) Compression 0.0625 Rate - 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) Root Mean Square Error 44.26 16 (440MHz, Sun Ultra 10) How to Improve Reconstructed Image Quality ? ? The Greatest Approximate Solution Original17 [Nobuhara, Takama and Hirota, JIEE 2001] Comparison of Proposed Method with Original Method [Nobuhara, Takama, and Hirota JIEE 2001] Original Method Proposed Method RMSE : 44.26 22.09 25.41 14.43 Compression Rate 0.0625 Compression Rate 0.2500 18 Comparison of ICF with DCT DCT Type II ICF VS Computation Time Image Quality 19 Computation Time Comparison Compression Rate ICF DCT 0.93 (s) 0.38 (s) 1.28 (s) 0.69 (s) 1.49 (s) 0.62 (s) 1.62 (s) 0.98 (s) 0.0156 0.0625 20 Image Quality Comparison (1) VS Proposed DCT Type II Compression Rate = 0.0625 21 Image Quality Comparison (2) : PSNR (Average of 20 Images of Standard Image DataBAse) 22
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