1. Image-Guided Maze Construction 논문 세미나 고려대학교 그래픽스 연구실 윤종철 2007.10.18 1

2. 목차 Abstract Introduction Maze basics Related work Maze textures ◦ Directional mazes ◦ Spiral and vortex mazes ◦ Random mazes ◦ User-defined lines User-specified solution paths Additional effects ◦ Tone reproduction ◦ Foreshortening Implementation and results Conclusions and Future Work 2

3. Abstract a set of graphical and combinatorial algorithms for designing mazes based on images 3

4. Introduction 4

5. Introduction Mazes and labyrinths have enjoyed a long, venerable tradition in the history of art and design. They have been used as pure visual art, as architectural decoration, and as cultural and religious artifacts An interactive application that lets a designer author a maze at a high level. 5

6. Related work Vortex maze construction [Jie Xu 2006] ◦ Technique for drawing abstract geometric mazes based on arrangements of vortices Organic Labyrinths and Mazes [Pedersen 2006] ◦ Single paths with no branch 6

7. Maze basics Kruskal’s algorithm ◦ 1. graph 의 모든 edge 를 가중치로 오름차순 정렬 ◦ 2. 가중치가 가장 작은 곳에 edge 를 삽입, 이때 cycle 을 형성하는 edge 는 삽입할 수 없으므로 다 음 가중치가 작은 edge 삽입 ◦ 3. n-1 개의 edge 를 삽입할 때까지 2 반복 ◦ 4. edge 가 n-1 개가 되면 spanning tree 완성 7

8. Maze basics Kruskal’s algorithm ◦ Cycle 판별  a 와 b 라는 노드가 선택되었을 때,  1) a 와 b 가 서로 다른 집합이면 a 와 b 는 연결해도 cycle 이 생기지 않는다.  2) a 와 b 가 서로 같은 집합에 속해 있다면 a 와 b 를 연결하면 cycle 이 생긴다.  1 번의 경우 edge 를 연결하고 a 가 속한 집합과 b 가 속한 집합 을 합쳐주고, 2 번의 경우에는 edge 를 선택하지 않는다. 8

9. Maze basics 9

10. ex) To bias maze construction ◦ 0<a<b<1 ◦ Assign horizontal walls weights chosen from the interval [0,b], and vertical walls weights from [a,1] Horizontal walls are therefore more likely to be deleted first 10

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13. 13 Perfect maze : When each of these paths is unique then the maze contains no cycles and is called perfect

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15. Segmentation 15 not automate the segmentation, Intelligent Scissors [Mortensen 1995]

16. Maze textures ◦ Directional mazes ◦ Spiral and vortex mazes ◦ Random mazes ◦ User-defined lines 16

17. Maze textures (a) directional region (b) spiral region, (c) random region (d) user-defined lines 17

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19. Vortex texture 19

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22. Random texture 22

23. Random texture 23

24. User-specified solution paths 24

25. User-specified solution paths 25

26. User-specified solution paths 26

27. User-specified solution paths 27

28. User-specified solution paths 28 A B C ABCABC 1 11 1 11 2 2

29. User-specified solution paths 29 α β A B C ABCABC 2 2 11 1 1 > (O)

30. User-specified solution paths 30

31. User-specified solution paths 31

32. User-specified solution paths 32

33. Avoidance direct passages 33

34. Additional effects Tone reproduction Foreshortening 34

35. Tone reproduction 35

36. Tone reproduction Lightness G = (S-W)/S ◦ S : the spacing between the centres of the lines ◦ W : line Width ◦ P : passage width  S-W 36 S W P

37. Tone reproduction We define ◦ minimum line width W min ◦ minimum passage width P min ◦ The largest acceptable line spacing S max The darkest tone : ◦ S = S max, S−W = P min ◦ lightness G min = P min /S max Similarly, the lightest available tone is G max = (S max −W min )/S max 37

38. Tone reproduction Both passage width and line width are minimized ◦ G thresh = P min / P min +W min ◦ G’ is computed by mapping G into the range [G min,G max ] When G’<=G thresh, S=P min /G’, W=P min (1-G’)/G’ When G>G thresh, S=W min (1-G’), W=W min 38

39. Foreshortening 39

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41. Implementation and results C++, CGAL library Design process requires only a few minutes of user interaction Multi-thread 41

42. Results 42

43. Results 43

44. Results 44

45. Results 45

46. Conclusions and Future Work A system for designing mazes that are stylized line drawings of images The perfect mazes we construct here are but one possible maze topology. ◦ It is also possible to construct mazes containing cycles, or indeed mazes with no dead ends at all Mathematical structure and human psychology 46

47. END 47