• Ei tuloksia

Distance Transforms on Gray-Level Surfaces

N/A
N/A
Info
Lataa
Protected

Academic year: 2022

Jaa "Distance Transforms on Gray-Level Surfaces"

Copied!
130
0
0

Kokoteksti

(1)

!

"# $! $%

& '$ (()$ *

(2)

!"

#

$

%

& % '

#

'! ()*+*,-+*./+(

'! ()*+*,-+*.0+012

!,-)/+--(,

*../

(3)

3*../

,F* 5

*-.

5

'! ()*+*,-+*./+(

'! ()*+*,-+*.0+012

! ,-)/+--(,

+ 3

# 1&#25

+5 &# A 3

5 & &#

< G &#1G&#2 D 3

@ H < 3 +

5 #

3 I 3 +

@3 D HI 5

&# A +

@ 3 3 5

3 3

&# @ 5 H

5

H H I

3 6 3 5

H +

3 A

5

&# H 3

3 5

7 C 3+ 3 +

33 3

# ..-5(F*5*C ..-5(*,

(4)

G(p) %+ Hp

X XC #

N4(p) -+ H p1I

@J 2

N8(p) 4 Hp1- 3-H 2

N8(p)\N4(p) H Hp1 2

d(pi, pi−1) I Hpi pi−1

∆(p) Hp H

F(x) Hx

F1(x) xI

F(x) x

Fa(x) x Ha

FA(x) x H A

DR(x) Fa(x) +Fb(x)FA(x) +FB(x)

R(a, b) Hab

R(A, B) HA B

(5)

*

F

&# #

@@

%B$ %+ $ H

$$ $ $

!! !!

7K L K

I

G&# G #

(6)

5 3537 3653 35379 9 3853 M# +

N3

33 3+

)+43*...3()0+(/.5

5 353 3 53 M 8 $ %+

N3 !" " "

!#$$ 3!33!,(O*,3

*..F3F.4OF,/5

5 353 353 M ' %++

N3 % " & 365 ,)3 !5,3*..)3

,()O,(45

65 3 53 3 53 M 6 8 +

%+ N3" ' " 365*F3

!5*3*..)3,FFO,-,5

65 353M HP % N3

!" "" !#$(

3 33 ,F+,)3*..)3**4O*F(5

65 353 353M !! %+

HP N &

' "&'#)

3 3' 3*.+*F3*..)3F.4OF,)5

3 * 3* 3*

3 * '3* ' * '5

(7)

! "

*5, ' $ 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 ,)

*5* 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 ,4

*5F &#G&# 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 ,(

*5- &# 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 *,

*5) % 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 **

*5/ %+ 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 *F

*50 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 *-

# $ %

F5, #$ 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 *0

F5* & &# 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 F.

F5F #6 &# 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 FF

F5- &# % 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 F-

& ! '()! #%

-5, I 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 F4

-5* & 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 -.

-5F HP 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 -*

-5- !! 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 -0

" ) &*

)5, &# 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 -(

)5* & 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 )*

+ ,,' ""

/5, # 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 ))

/5* $ 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 )/

% "*

- +#

./'(,)0 +"

1/' %

(8)
(9)

5 @ >

> 3

@ 5 3

,(//@Q-0R3 3

3 H3 H5 3

123 3 3

H H3

A5

>3 H H @3

>3 >5

A 5

33 5

3

H5 A

3 3 <

5

$ 1$$2 Q/*3

5,R5 >3

5 $$

@ > 3 3

3 5 & 3 $$ A <

3 I H $$ 5

3 3 = = H

>3 3 H>3 5

3 I 3

H>3 A 5

3

+5 3 # 1&#2

(10)

3 5 &#3 Q/4R3Q/(R3 H+

+3 +

5 3 +1

H2 3 + 1 H2

5 A 3 3

5 H

H3

A 3 @

= H5

%+3 &# A3

3

5 F> >H3

F3H

H Q-/R5 H F > ** H

,5,5 >I @3×3×43 H

F >5 H3

H ) 3 ) H F

>5 + F @

,5,5 + 3×3

H3 H 5

+ FH 3 F>

+ 3

H A z+ Q/FR5 3 >

H L3

3 z > (x, y)5

> > z+H 3

> 3&# 5

&# + 3 H

(11)

+ z (x, y)

3 5 3 3

A3*,J* 3A 3

I 3 Q0,35,/3-,R5

3 H3

5 3 3

+ = +

@ H5 3

= @ 5

&++ H3 +

3 3

5 5

& 3 3 5

&# A @5

& 3H3 3

5 & 3

3

&#5

3

H

5 3 A

H L 5 3

+ 5 &#

+3 H +

A 5 3&# A

H 5 3 H

I &# 3

D 3I 125

@ 3

H5

A3 &#5

&# 3

Q/4R3 Q0.R5

@ 3

5

5 #*H

3 A &#3 + 5

# F 3

A &#A 5 #- +

3 HI

&#3 H 3 5 #+

)3 &# A +

3 5

@ &#3 3

#/5 #0 3#4

(12)

* 3 &# 5 #

5 6

7 : 3H 3 5

* &# A

5 +

3 3 5

G&#

&#3

2+&# <

L + =5

5

* 3&# A

+ 5 A

12 5

&*..-5 >

3 : 3

5

; 3 5

* ' H> * +

3 H

2+&#3 5 3 &#

A 3F+-+&#3&

&#5 H H

5 'A +

F 5

5

3 5

* ' D HI

&#5 HI

5 3 @

5

* '3 5

* '3 HI H

1!!2 5 !!

&# H

H3 5

3

3 L 5

5

(13)

3

3 H H5

H A H3 3

H5 3

>3 H

3 > H 5

H 3 3 A

3 H @3 5

3 H H3

5 A

H 3 5

H A 3

I3 H5

A 3

&#5 # 3 H 3 +

#F5

3 3 5 +

3

+ &#5

&#H 3 + +

+5

5

# -5

3 3 3

H3 Q-)3 5 *.(R5 < P = (x, y)

(14)

b a

b a

a b 0 a b

P P

P P P

nw

P

n

P

ne

c

P

P

w c

P

e

se s

sw

P P P P

P P

se s sw

e w

P

nw

P

n

P

ne

Mask M1

Mask M2

!"

Q= (u, v)3 xy 15 uv2 HP 15 Q23 C

de(P, Q) =

(x−u)2+ (y−v)2 1*5,2

3

< 5 3$ 3 A C

d4(P, Q) =|x−u|+|y−v| 1*5*2

C

d8(P, Q) =max(|x−u|,|y−v|) 1*5F2

de3 d8 d4 A

H >

= H H 5 8 3

H 3

H H3

5 A

H5 *5,

*5*5 3×3

3 a b H3

0 3 *5,5 83 H

a H3 H b

H 5 3

I 3H 5

d83 4+ 3

a = b = 13

a = 1 b =5 -+ 3

H3 3 5 +

3 H <

Q)R5 3

< 3

= 5

A @ *5*5 I

(15)

P

City block distance Q

Euclidean distance

Chessboard distance Euclidean distance

P

Q

# !

$

A5 H3 -

= 3 A5 <

H

3 3

5 a = 1 b =

2

< 3

3H H H

5 <

H *5*5 3 3

1 + 3

2 5.24 -5

< F5,5

A H 5

3 H5

H3 3 H 3 @5

H H3

H 3

A5 H3 3 3 H

@3 X3

H3XC3 5

*5F 3 = 5 <

H

A 5 # *5F 12

H I 4+ I 5

H

*5F 12 123 < @

*5F125 < H

< *5F 125 !

H 3 3 &# <

A 3 G&#3 5 $ H

I +< F5,5

(16)

3 2 2 2 2 2 3 4

2 2 1 1 1 2 3 3

2 1 1 0 1 2 2 2

2 1 0 0 1 1 1 1

2 1 1 0 1 1 0 1

2 2 1 0 0 0 0 1

3 2 1 1 1 1 1 1

3 2 2 2 2 2 2 2

3.83 2.83 2.41 2.00 2.41 2.83 3.83 4.41 2.83 2.41 1.41 1.00 1.41 2.41 3.00 3.41 2.41 1.41 1.00 0.00 1.00 2.00 2.00 2.41 2.00 1.00 0.00 0.00 1.00 1.41 1.00 1.41 2.41 1.41 1.00 0.00 1.00 1.00 0.00 1.00 2.83 2.00 1.00 0.00 0.00 0.00 0.00 1.00 3.41 2.41 1.41 1.00 1.00 1.00 1.00 1.41 3.83 2.83 2.41 2.00 2.00 2.00 2.00 2.41

3.61 2.83 2.24 2.00 2.24 2.83 3.61 4.12 2.83 2.24 1.41 1.00 1.41 2.24 3.00 3.16 2.24 1.41 1.00 0.00 1.00 2.00 2.00 2.24 2.00 1.00 0.00 0.00 1.00 1.41 1.00 1.41 2.24 1.41 1.00 0.00 1.00 1.00 0.00 1.00 2.83 2.00 1.00 0.00 0.00 0.00 0.00 1.00 3.16 2.24 1.41 1.00 1.00 1.00 1.00 1.41 3.61 2.83 2.24 2.00 2.00 2.00 2.00 2.24

@Q-0R3

H H H

5 3 H =

3 3

3 H 5 3 A

3 a b 5 3

H *5,3

+ 5 A

M1 = {pnw, pn, pne, pw}

3 H pc3 F(pc)3

C

F1(pc) = min[F(pc), min

p∈M1

(∆(p) +F1(p))] 1*5-2

A H M1 3

Hpc5

H pc H5 ∆(p) H

p H pc A 5

a ppc 3b H

Viittaukset

LIITTYVÄT TIEDOSTOT

The predation risk of the golden eagle was modeled as a function of territory density, density of fledglings produced, and distance to nearest active eagle territory, with

Measuring supply by two distinct variables, the distance to the nearest SPRA and the total area of such areas in the respondent’s home municipality, we can compare the impacts

Population density and such variables as distance to the nearest city, urbanization level and housing value are usually included in land value models to indicate the urban pressure

It would seem that k-nearest-neighbor methods would be more appropriate for the mixture Scenario 2 described above, while for Gaussian data the decision boundaries of

The new European Border and Coast Guard com- prises the European Border and Coast Guard Agency, namely Frontex, and all the national border control authorities in the member

The US and the European Union feature in multiple roles. Both are identified as responsible for “creating a chronic seat of instability in Eu- rope and in the immediate vicinity

Indeed, while strongly criticized by human rights organizations, the refugee deal with Turkey is seen by member states as one of the EU’s main foreign poli- cy achievements of

However, the pros- pect of endless violence and civilian sufering with an inept and corrupt Kabul government prolonging the futile fight with external support could have been