image-guided maze construction 논문 세미나 고려대학교 그래픽스 연구실 윤종철...
TRANSCRIPT
Image-Guided Maze Construction
논문 세미나고려대학교 그래픽스 연구실
윤종철2007.10.18
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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
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Abstracta set of graphical and combinato-
rial algorithms for designing mazes based on images
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Introduction
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IntroductionMazes and labyrinths have en-
joyed a long, venerable tradition in the history of art and design.
They have been used as pure visual art, as architectural deco-ration, and as cultural and reli-gious artifacts
An interactive application that lets a designer author a maze at a high level.
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Related workVortex maze construc-
tion [Jie Xu 2006]◦ Technique for drawing abstract
geometric mazes based on ar-rangements of vortices
Organic Labyrinths and Mazes [Pedersen 2006]◦ Single paths with no branch
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Maze basicsKruskal’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 다음 가중치가 작은 edge 삽입
◦ 3. n-1 개의 edge 를 삽입할 때까지 2 반복◦ 4. edge 가 n-1 개가 되면 spanning tree 완성
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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 집합을 합쳐주고 , 2 번의 경우에는 edge 를 선택하지 않는다 .
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Maze basics
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Maze basicsex) To bias maze construction
◦0<a<b<1◦Assign horizontal walls weights cho-
sen from the interval [0,b], and ver-tical walls weights from [a,1]
Horizontal walls are therefore more likely to be deleted first
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Perfect maze : When each of these paths is unique then the maze contains no cycles and is called perfect
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Segmentation
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not automate the segmenta-tion,Intelligent Scissors [Mortensen 1995]
Maze texturesMaze textures
◦Directional mazes◦Spiral and vortex mazes◦Random mazes◦User-defined lines
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Maze textures
(a) directional region(b) spiral region,(c) random region(d) user-defined lines
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Vortex texture
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Random texture
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Random texture
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User-specified solution paths
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User-specified solution paths
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User-specified solution paths
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User-specified solution paths
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User-specified solution paths
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A B C A
B
C 1
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1
11
2
2
User-specified solution paths
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α
β
A B C A
B
C 2
2
1 1
1
1
>(O)
User-specified solution paths
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User-specified solution paths
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User-specified solution paths
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Avoidance direct passages
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Additional effectsTone reproductionForeshortening
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Tone reproduction
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Tone reproductionLightness G = (S-W)/S
◦ S : the spacing between the centres of the lines◦ W : line Width
◦ P : passage width S-W
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S
W
P
Tone reproductionWe define
◦minimum line width Wmin
◦minimum passage width Pmin
◦The largest acceptable line spacing Smax
The darkest tone : ◦S = Smax, S−W = Pmin
◦lightness Gmin = Pmin/Smax Similarly, the lightest available
tone is Gmax = (Smax−Wmin)/Smax
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Tone reproductionBoth passage width and line
width are minimized◦Gthresh = Pmin / Pmin+Wmin
◦G’ is computed by mapping G into the range [Gmin,Gmax]
When G’<=Gthresh, S=Pmin/G’, W=Pmin(1-G’)/G’
When G>Gthresh, S=Wmin(1-G’), W=Wmin
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Foreshortening
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Implementation and re-sultsC++, CGAL libraryDesign process requires only a
few minutes of user interactionMulti-thread
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Results
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Results
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Results
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Results
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Conclusions and Future WorkA 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 hu-man psychology 46
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