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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.

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Presentation on theme: "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."— Presentation transcript:

1 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

2 22 Outline Fractal Image Compression (FIC) Encoder and Decoder Transform Method Evolutionary Computation Methods Ant Colony Optimization () ACO for FIC

3 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”

4 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

5 55 Fractal Image –having details in every scale

6 66 Fractal Image

7 77 Affine Transformations

8 88 Local Self-Similarity

9 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

10 10 Domain Pool (D) Range Pool (R) ……. Original Image ……. Search for Best Match

11 11 Expanded Codebook Search Every Vector in the Domain Pool For Each Search Entry: Eight orientations Contrast adjustment Brightness adjustment

12 12 The Best Match : range block to be encoded : search entry in the Domain Pool : eight orientations,

13 13 Eight Orientations (Dihedral Group) 12 43 34 21 41 32 14 23 21 34 32 41 43 1 2 23 14

14 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

15 15 Contrast and Brightness

16 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

17 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

18 18 The Decoding Iterations Init Image Iteration=1 Iteration=2 Iteration=3 Iteration=4 Iteration=8

19 19 Original 256  256 Lena image Encoding time = 22.4667 minutes PSNR=28.515 dB Full Search Coder

20 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

21 21 Deterministic Contrast and Brightness: Optimization The Dihedral Group: Transform Method

22 22 Non-Deterministic Classification Method Correlation Method Soft Computing Method

23 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

24 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)

25 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)

26 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

27 27 Spatial Correlation Genetic Algorithm (1) Two stage GA: 1. spatial correlation 27

28 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

29 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

30 30 Behavior of Ants Secrete and Lay Pheromone Detect and Follow with High Probability Reinforce the Trail

31 31 Ant Colony Optimization (ACO) Proposed by Dorigo et al. (1996) Learn from real ants Pheromone Intensity Accumulation Communication

32 32 Artificial Ants

33 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

34 34 TSP Traveling Salesman Problem Problem of finding a minimal length closed tour that visits each town once. Parameters

35 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

36 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

37 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

38 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

39 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

40 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

41 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

42 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)

43 43 (a) Original image (b) Full search, 28.90 dB (c) ACO, 27.66 dB Lena FIC-ACO

44 44 (a) Original image (b) Full search, 30.40 dB (c) ACO, 28.78 dB Pepper FIC-ACO

45 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

46 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

47 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

48 48 Thanks


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