Image-Guided Maze Construction

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29 Οκτ 2013 (πριν από 3 χρόνια και 7 μήνες)

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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


Additional effects


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
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

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

Additional effects


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
-
thread

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
no dead ends at all


Mathematical structure and human
psychology

46

END

47