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11 Ant Colony Optimization ACO Fractal Image Compression 鄭志宏 義守大學 資工系 高雄縣大樹鄉 J. H. Jeng Department of Information Engineering I-Shou University, Kaohsiung County
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22 Outline Fractal Image Compression (FIC) Encoder and Decoder Transform Method Evolutionary Computation Methods Ant Colony Optimization () ACO for FIC
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33 Multimedia vs 心經 眼耳鼻舌身意 色聲香味觸法 眼: Text, Graphics, Image, Animation, Video 耳: Midi, Speech, Audio 鼻: 電子鼻, 機車廢氣檢測 舌: 成份分析儀, 血糖機, Terminator III 身: 壓力, 溫度感測器, 高分子壓電薄膜 意: Demolition Man 7-th “Sensor”
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44 Digital Image Compression Finite Set a, b, c, … ASCII 你, 我, … Big 5 Geometric Pattern Circle --- (x,y,r) Spline --- control points and polynomials Fractal Image Procedure, Iteration Natural Image JPEG, GIF
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55 Fractal Image –having details in every scale
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66 Fractal Image
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77 Affine Transformations
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88 Local Self-Similarity
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99 Fractal Image Compression Proposed by Barnsley in 1985, Realized by Jacquin in1992 Partitioned Iterated Function System (PIFS) Explore Self-similarity Property in Natural Image Lossy Compression Advantage: High compressed ratio High retrieved image quality Zoom invariant Drawback: Time consuming in encoding
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10 Domain Pool (D) Range Pool (R) ……. Original Image ……. Search for Best Match
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11 Expanded Codebook Search Every Vector in the Domain Pool For Each Search Entry: Eight orientations Contrast adjustment Brightness adjustment
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12 The Best Match : range block to be encoded : search entry in the Domain Pool : eight orientations,
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13 Eight Orientations (Dihedral Group) 12 43 34 21 41 32 14 23 21 34 32 41 43 1 2 23 14
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14 Rotate 0º Rotate 90º Rotate 270º Rotate 180º Flip of case 1 Flip of case 6 Flip of case 7 Flip of case 4 Matrix Representations
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15 Contrast and Brightness
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16 Affine Transform and Coding Format : contrast scale : intensity offset z : The gray level of a pixel : The position of a pixel : dihedral group : position
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17 De-Compression Make up all the Affine Transformations Choose any Initial Image Perform the Transformation to Obtain a New Image and Proceed Recursively Stop According to Some Criterions
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18 The Decoding Iterations Init Image Iteration=1 Iteration=2 Iteration=3 Iteration=4 Iteration=8
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19 Original 256 256 Lena image Encoding time = 22.4667 minutes PSNR=28.515 dB Full Search Coder
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20 Domain block=16 16 down to 8*8 #Domain blocks = #MSE= 58081 8 = 464648 Contrast and Brightness Adjustment Domain Pool (D) Range Pool (R) ……. Original Image ……. Image Size = 256 256 Range block = 8 8 #Range block = Complexity
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21 Deterministic Contrast and Brightness: Optimization The Dihedral Group: Transform Method
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22 Non-Deterministic Classification Method Correlation Method Soft Computing Method
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23 Soft Computing Machine Learning ANN, FNN, RBFN, CNN Statistical Learning, SVM Global Optimization Techniques Branch and Bound, Tabu Search MSC, SA GA, PSO, ACO To infinity and beyond
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24 Global Optimization Techniques Deterministic Branch and Bound (Decision Tree) Stochastic Monte-Carlo Simulation Simulated Annealing (Physics) Heuristics Tabu Search Evolutionary Computation (Survival of the Fittest)
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25 Evolutionary Computation Genotype and Phenotype Genetic Algorithms (GA) Memetic Algorithm (MA) Genetic Programming (GP) Evolutionary Programming (EP) Evolution Strategy (ES) Social Behavior Particle Swarm Optimization (PSO) Ant Colony Optimization (ACO)
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26 Genetic Algorithm Developed by John Holland in 1975 Mimicking the natural selection and natural genetics Advantage: Global search technique Suited to rough landscape Drawback: Final solution usually not optimal 26
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27 Spatial Correlation Genetic Algorithm (1) Two stage GA: 1. spatial correlation 27
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28 Particle Swarm Optimization (PSO) Particle Swarm Optimization Introduced in 1995 by Kennedy and Eberhart Swarm Intelligence Simulation of a social model Population-based optimization Evolutionary computation Social Psychology Principles Bird flocking Fish schooling Elephant Herding
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29 Edge-Property Adapted PSO for FIC Hybrid Method vs Fused Methods Visual-Salience Tracking Edge-type Classifier, 5 Edge Types Predict the Best k (Dihedral Transformation) Intuitively Direct the Swarm Velocity Direction according to Edge Property
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30 Behavior of Ants Secrete and Lay Pheromone Detect and Follow with High Probability Reinforce the Trail
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31 Ant Colony Optimization (ACO) Proposed by Dorigo et al. (1996) Learn from real ants Pheromone Intensity Accumulation Communication
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32 Artificial Ants
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33 Ant system Proposed by Dorigo et al. (1996) Characteristics of AS to solve TSP Choose the town with a probability Town distance Amount of trail (pheromone) Force the ant to make legal tours Disallow visited towns until a tour is completed Lay trail on each edge visited when it completes a tour
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34 TSP Traveling Salesman Problem Problem of finding a minimal length closed tour that visits each town once. Parameters
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35 Probability of selecting town visibility ( ) control the relative importance of trail versus visibility Transition probability is a trade-off between visibility and trail intensity at time otherwise
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36 Pheromone Accumulation the evaporation of trail ( ) the intensity of trail on edge at time the sum of trail on edge by the ants between time and
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37 Global update constant the tour length of the kth ant if kth ants uses edge (i,j) in its tour (between time t and t+n) otherwise
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38 Local update Ant-density model Ant-quantity model Shorter edges are made more desirable if the kth ant goes from i and j between time t to t+1 otherwise if the kth ant goes from i and j between time t to t+1 otherwise
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39 TSP (Traveling Salesman Problem) 特性 規則簡單 計算複雜 拜訪 42 個城市需走過 演算法比較 螞蟻演算法 (Ant Colony Optimization) 彈性網路 (Elastic Net) 基因演算法 (Genetic Algorithm) 人腦
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40 TSP result 演算法比較 推銷員問題彈性網絡螞蟻王國基因演算法人腦(平均) Att48 5.81%2.86%( 875)3.0%(3256)!4.41%(7) Berlin52 6.90%1.52%(1388)7.4%(3816)!5.18%(6) Eil101 9.10%7.64%(1488)14.2%(5000)8.83%(6) Eil51 3.37%4.41%(1115)4.4%(5000)8.98%(3) St70 4.16%3.42%( 283)5.9%(4408)7.03%(3) Ulysses16 1.30%0%(3289)-0.1%( 901)!1.05%(2) Ulysses22 1.57%0%(4562)0.3%(1364)N/A
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41 TSP result 種子數為 10 , 20 , …100 產生 30 個城市 推銷員問題彈性網絡螞蟻王國 (1000) 螞蟻王國 (2000) 基因演算法 #1 4.4424.597( 62)4.442(2244) #2 4.0534.053(602)4.053(2887) #3 4.6344.480(367)4.480(2117) #4 4.7444.744(170)4.480(1207)4.799(2149) #5 4.8694.759(994)4.737(1759)4.737(1344) #6 4.3164.214(120)4.369(1734) #7 5.4985.061(467)5.049(1365)5.322(1083) #8 4.6214.601(416)4.846(1153) #9 4.3624.358(250)4.387(1776) #10 5.5355.211(139)5.454(2237) Average 4.7074.608(359)4.601(629)4.689(1972) Variance 0.2360.1280.1250.192
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42 ACO for FIC Ant: range block Secrete pheromone at cities instead of on the path between two cities City: domain block Visibility: reciprocal of the MSE Between the agent (range block) and the city (domain block)
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43 (a) Original image (b) Full search, 28.90 dB (c) ACO, 27.66 dB Lena FIC-ACO
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44 (a) Original image (b) Full search, 30.40 dB (c) ACO, 28.78 dB Pepper FIC-ACO
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45 Various pheromone evaporate rates Pheromone evaporate rate Quality (PSNR) Average (PSNR) 0.127.5927.4827.5327.6727.5527.56 0.227.6327.6027.5927.6027.5527.59 0.327.5627.5727.5227.5727.5327.55 0.427.5427.5527.5827.6327.5927.58 0.527.5527.6627.4627.6027.5627.57 0.627.5027.5727.55 27.5327.54 0.727.6327.5727.6227.5127.5427.57 0.827.5827.5027.6127.5927.6627.59 0.927.5327.5827.4927.5627.5327.54
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46 Various parameters Quality (PSNR) Average (PSNR) 1127.5827.5027.6127.5927.6627.59 2127.1727.2327.2727.2427.1027.20 1226.7126.5926.6727.0326.6126.72 2226.6226.3426.6326.5126.6526.55
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47 Result on various images LenaBaboonF16Pepper Full search method Quality (PSNR) 28.9020.1326.0930.41 Time3620371636843709 Proposed method Quality (PSNR) 27.5819.7525.7028.74 27.5019.7725.8128.78 27.6119.8025.7428.69 27.5919.7225.8028.80 27.6619.7824.4828.69 Average (PSNR) 27.5919.7625.5228.74 Time144145144146 Speedup25.125.625.825.2
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48 Thanks
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