# Image-Guided Maze Construction

AI and Robotics

Oct 29, 2013 (4 years and 6 months ago)

126 views

Image
-
Guided Maze
Construction

논문

세미나

고려대학교

그래픽스

연구실

윤종철

2007.10.18

1

목차

Abstract

Introduction

Maze basics

Related work

Maze textures

Directional mazes

Spiral and vortex mazes

Random mazes

User
-
defined lines

User
-
specified solution paths

Tone reproduction

Foreshortening

Implementation and results

Conclusions and Future Work

2

Abstract

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

3

Introduction

4

Introduction

Mazes and labyrinths have enjoyed a
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

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

Maze basics

Kruskal’s

algorithm

1. graph

모든

edge

가중치로

오름차순

정렬

2.
가중치가

가장

작은

곳에

edge

삽입
,

이때

cycle

형성하는

edge

삽입할

없으므로

가중치가

작은

edge

삽입

3. n
-
1
개의

edge

삽입할

때까지

2

반복

4. edge

n
-
1
개가

되면

spanning

tree

완성

7

Maze basics

Kruskal’s

algorithm

Cycle
판별

a

b
라는

노드가

선택되었을

,

1) a

b

서로

다른

집합이면

a

b

연결해도

cycle

생기지

않는다
.

2) a

b

서로

같은

집합에

속해

있다면

a

b

연결하

cycle

생긴다
.

1
번의

경우

edge

연결하고

a

속한

집합과

b

속한

합을

합쳐주고
, 2
번의

경우에는

edge

선택하지

않는다
.

8

Maze basics

9

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

10

11

12

13

Perfect maze :

When each of these paths is unique

then the maze contains no cycles and is called perfect

14

Segmentation

15

not automate the segmentation,

Intelligent Scissors [Mortensen 1995]

Maze textures

Maze textures

Directional mazes

Spiral and vortex mazes

Random mazes

User
-
defined lines

16

Maze textures

(a) directional region

(b) spiral region,

(c) random region

(d) user
-
defined lines

17

18

Vortex texture

1
9

20

21

Random texture

22

Random texture

23

User
-
specified solution paths

24

User
-
specified solution paths

25

User
-
specified solution paths

26

User
-
specified solution paths

27

User
-
specified solution paths

28

A B C

A

B

C

1

1

1

1

1

1

2

2

User
-
specified solution paths

29

α

β

A B C

A

B

C

2

2

1

1

1

1

>

(O)

User
-
specified solution paths

30

User
-
specified solution paths

31

User
-
specified solution paths

32

Avoidance direct passages

33

Tone reproduction

Foreshortening

34

Tone reproduction

35

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

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

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

Foreshortening

39

40

Implementation and results

C++, CGAL library

Design process requires only a few
minutes of user interaction

Multi
-

41

Results

42

Results

43

Results

44

Results

45

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