Image-Guided Maze Construction

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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A B C A

B

C 1

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1

11

2

2


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α

β

A B C A

B

C 2

2

1 1

1

1

>(O)


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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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Image-Guided Maze Construction