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Image-Guided Maze Construction. 논문 세미나 고려대학교 그래픽스 연구실 윤종철 2007.10.18. 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
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Image-Guided Maze Construction 논문 세미나 고려대학교 그래픽스 연구실 윤종철 2007.10.18
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
Abstract • a set of graphical and combinatorial algorithms for designing mazes based on images
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.
Related work • Vortex maze construction [JieXu 2006] • Technique for drawing abstract geometric mazes based on arrangements of vortices • Organic Labyrinths and Mazes [Pedersen 2006] • Single paths with no branch
Maze basics • Kruskal’s algorithm • 1. graph의모든 edge를 가중치로 오름차순 정렬 • 2. 가중치가 가장 작은 곳에 edge를 삽입, 이때 cycle을 형성하는 edge는 삽입할 수 없으므로 다음 가중치가 작은 edge 삽입 • 3. n-1개의 edge를 삽입할 때까지 2 반복 • 4. edge가 n-1개가 되면 spanningtree 완성
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 cycle이 생기지 않는다. • 2) a 와 b 가 서로 같은 집합에 속해 있다면 a 와 b 를 연결하면 cycle이 생긴다. • 1번의 경우 edge를 연결하고 a 가 속한 집합과 b 가 속한 집합을 합쳐주고, 2번의 경우에는 edge를 선택하지 않는다.
Maze basics • 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
Perfect maze : When each of these paths is unique then the maze contains no cycles and is called perfect
Segmentation not automate the segmentation, Intelligent Scissors [Mortensen 1995]
Maze textures • Maze textures • Directional mazes • Spiral and vortex mazes • Random mazes • User-defined lines
Maze textures • (a) directional region • (b) spiral region, • (c) random region • (d) user-defined lines
User-specified solution paths A B C A B C 1 1 1 1 2 1 1 2
User-specified solution paths A B C A B C 1 1 β 1 2 α 1 2 > (O)
Additional effects • Tone reproduction • Foreshortening
Tone reproduction • Lightness G = (S-W)/S • S : the spacing between the centres of the lines • W : line Width • P : passage width • S-W W S P
Tone reproduction • We 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
Tone reproduction • Both 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
Implementation and results • C++, CGAL library • Design process requires only a few minutes of user interaction • Multi-thread
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
