edge detection & image sharpening -...

Edge Detection & Image Sharpening

김성영교수

금오공과대학교

컴퓨터공학과

2

학습 내용

Edge정의

Edge detection 개요및방법

Image sharpening 방법

3

Edge 정의

A large change in image brightness over a short spatial distance

4

Edge detection 개요

Most are based on discrete approximations to differential operators

Implemented with convolution masks

Return orientation or existence of an edge information

Used as a first step in the line detection or object outlines process

6

Edge detection 방법

darkbright

change of brightness

1st-order derivative

positivepeak

negativepeak

2nd-order derivative

Prewitt, Sobel, Roberts 등

Laplacian

777

∂∂

∂∂

=

=∇

yf

xf

G

Gf

y

x [ 1, ] [ , ], [ , 1] [ , ]x yG f x y f x y G f x y f x y≅ + − ≅ + −

2 2 max( , )x y x y x yG G G G G G G= + ≈ + ≈

1 (x, y) tan y

x

GG

α − =

1st-order derivative

Gx

G y

edge

line

888

−−−

=1 0 11 0 11 0 1

),( yxhx

−−−=

1 1 1 0 0 0 111

),( yxhy

[ 1, ] [ , ], [ , 1] [ , ]x yG f x y f x y G f x y f x y≅ + − ≅ + −

( , ) ( , ), ( , ) ( , )x x y yG h x y f x y G h x y f x y= ∗ = ∗

Prewitt

[ ]101111

−⋅

Simple box filter

Finite diff filter

999

−−−

=1 0 12 0 21 0 1

),( yxhx

−−−=

1 2 1 0 0 0 121

),( yxhy



Sobel

[ ]101121

−⋅

Simple Gaussian filter

Finite diff filter

101010

Roberts

−=

0 0 10 1 0 0 0 0

),( yxhx

−=

0 0 0 0 1 0 0 0 1

),( yxhy



No the orientation information

111111

(a) 원영상 (b) Prewitt

(c) Sobel (d) Roberts

121212

Laplacian

2

2

2

22

yf

xff

∂∂

+∂∂

=∇

2

2

( [ 1, ] [ , ]) [ 1, ] [ , ]xGf f x y f x y f x y f x yx x x x x

∂∂ ∂ + − ∂ + ∂= = = −

∂ ∂ ∂ ∂ ∂

( [ 1, ] [ , ]) ( [ , ] [ 1, ]) [ 1, ] 2 [ , ] [ 1, ]f x y f x y f x y f x y f x y f x y f x y= + − − − − = + − + −

[ ]2 ( , 1) ( 1, ) ( 1, ) ( , 1) 4 ( , )f f x y f x y f x y f x y f x y∇ = + + − + + + − −

2

2 [ , 1] 2 [ , ] [ , 1]f f x y f x y f x yy

∂= + − + −

∂

131313

0 1 01 4 10 1 0

−

0 1 01 4 10 1 0

− − − −

1 1 11 8 11 1 1

−

1 1 11 8 11 1 1

− − − − − − − −

common spatial convolution masks

141414

First vs. Second-order derivative

151515

• First-order derivatives generally produce thicker edges

• Second-order derivatives have a stronger response to fine detail, such as thin lines and isolated points

• First-order derivatives generally have a stronger response to a gray-level step

• Second-order derivatives produce a double response at step changes in gray level

In most applications, the second-order derivative is better suited than the first derivative for image enhancement

161616

Laplacian of Gaussian filtering

[ ] ),(),(),( 2 yxfyxhyxg ∗∇=

( )2

22

24

2222 ),( σ

σσ

yx

eyxyxh+

−

−+−=∇

171717

1.0

0.70 0 -1 0 00 -1 -2 -1 0-1 -2 16 -2 -10 -1 -2 -1 00 0 -1 0 0

LoG mask

181818

(a) 원영상(b) 4 방향라플라시안

(c) 8 방향라플라시안

(d) 가우시안의라플라시안

19

Image Sharpening

enhancing detail information in an imagetypically contained in the high spatial frequencycomponents of the image

done by various types of high boost filters and Laplacian-type filters

202020

High-pass filtering

),(),(),( yxfyxfyxf LH −=

1 1 11 1 8 19

1 1 1

− − − × − − − − −

=

−

111111111

91

000010000

212121

-10 -20 -10 -20 -10 0 0 0

-20 40 20 40 -20 0 0 0

-30 20 80 20 -30 0 0 0

-20 40 20 40 -20 0 0 0

-10 -20 -30 -20 -10 0 0 0

0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0

High-passfiltering

10 10 10 10 10 10 10 10

10 20 20 20 10 10 10 10

10 20 30 20 10 10 10 10

10 20 20 20 10 10 10 10

10 10 10 10 10 10 10 10

10 10 10 10 10 10 10 10

10 10 10 10 10 10 10 10

10 10 10 10 10 10 10 10

※이전슬라이드의마스크에서9로나누는것을제외하고계산

※경계외부는경계값으로채움

222222

High boost filtering

)1(19

11111111

1111191111

91

111111111

91

000010000

,111111111

91

≥−=∴

⇒

=

−

=

AA

--------

----A-----

A

fL

α

α

{ }{ }

),(),()1(),(),(

),()1(),(),(),(

yxfyxfAyxfyxf

yxfAyxfyxAfyxg

H

L

L

+−=−+

−=−=

High boost

232323

결과영상(α=9) Histogram equalization

242424

−−−

−

010151

010

−−−

−

121252

121

Original image Contrast-enhanced

Laplacian-type filtering

−−−

−

010151

010

000010000

−−−

−

010141

010+=

252525

InputImage

LowpassFilter

HistogramShrink

SubtractImages

HistogramStretch

ResultImage

+

−

Unsharp masking

262626

),(),()1()},(),({),(

),(),(),(

crLcrIcrLcrIcrI

crHcrIcrE

λλλλ

−+=−+=

+=

),( crI

),( crL

),(),( crLcrI −

)},(),({),(),( crLcrIcrIcrE −+= λ

272727

OriginalImage

Unsharpmaskinglower limit=0, upper=100,2% low andhigh clipping

Unsharpmaskinglower limit=0, upper=200,2% low andhigh clipping

Unsharpmasking

lower limit=0, upper=150,2% low and

high clipping

28

요약

Edge 짧은공간적인거리상에서영상의밝기혹은색상이급격하게변하는지점

Edge detection 개요 주로차분연산을이산적으로근사화하여사용 (마스크사용처리)

Edge의세기와방향을제공

Edge detection 방법 1차미분: Prewitt, Sobel, Roberts 등

2차미분: Laplacian (Laplacian of Gaussian)

29

Image Sharpening 영상의상세정보를강화

High-pass filtering, High boost filtering, Laplacian-type filtering, Unsharp masking

30

Reference

R. Gonzalez, R. Woods, Digital Image Processing (2nd Edition), Prentice Hall, 2002

Scott E Umbaugh, Computer Imaging, CRC Press, 2005

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