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Ant Colony Optimization ACO Fractal Image Compression

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. 1. Outline. Fractal Image Compression (FIC) Encoder and Decoder Transform Method Evolutionary Computation Methods

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Ant Colony Optimization ACO Fractal Image Compression

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  1. 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 1

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

  3. 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” 3

  4. 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 4

  5. Fractal Image –having details in every scale 5

  6. Fractal Image 6

  7. Affine Transformations 7

  8. Local Self-Similarity 8

  9. 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 9

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

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

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

  13. 2 4 1 3 2 3 4 1 3 2 4 3 2 4 1 1 2 3 3 2 1 2 4 1 4 1 3 4 3 1 4 2 Eight Orientations (Dihedral Group) 13

  14. Matrix Representations Rotate 0º Flip of case 1 Flip of case 6 Rotate 90º Flip of case 7 Rotate 270º Rotate 180º Flip of case 4 14

  15. Contrast and Brightness 15

  16. Affine Transform and Coding Format : The position of a pixel z : The gray level of a pixel : position : dihedral group : contrast scale : intensity offset 16

  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 17

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

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

  20. Complexity Original Image ……. ……. ……. Domain Pool (D) Range Pool (R) Image Size = 256256 Domain block=1616 down to 8*8 #Domain blocks = #MSE= 580818 = 464648 Contrast and Brightness Adjustment Range block = 88 #Range block = 20

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

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

  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 23

  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. 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) 25

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

  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 28

  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 29

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

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

  32. Artificial Ants

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

  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. 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. Global update if kth ants uses edge (i,j) in its tour (between time t and t+n) • constant • the tour length of the kth ant otherwise

  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. 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. TSP result • 演算法比較

  41. TSP result • 種子數為 10，20，…100產生30個城市

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

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

  45. Various pheromone evaporate rates

  46. Various parameters

  47. Result on various images

  48. Thanks 48

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