Post on 31-May-2020
Image Enhancement in the Spatial Domain (Part 5)
Lecturer: Dr. Hossam Hassan Email : hossameldin.hassan@eng.asu.edu.eg
Computers and Systems Engineering
2
Correct the effect of featureless background
• easily by adding the original and Laplacian image.
• be careful with the Laplacian filter used
),(),(
),(),(),(
2
2
yxfyxf
yxfyxfyxg
if the center coefficient of the Laplacian mask is negative
if the center coefficient of the Laplacian mask is positive
Example
Input Image Laplacian Result
4
Mask of Laplacian + addition
• to simplify the computation, we can create a mask which does both operations, Laplacian Filter and Addition of the original image.
5
Mask of Laplacian + addition
)]1,()1,(
),1(),1([),(5
)],(4)1,()1,(
),1(),1([),(),(
yxfyxf
yxfyxfyxf
yxfyxfyxf
yxfyxfyxfyxg
0 -1 0
-1 5 -1
0 -1 0
6
Note
0 -1 0
-1 5 -1
0 -1 0
0 0 0
0 1 0
0 0 0
),(),(
),(),(),(
2
2
yxfyxf
yxfyxfyxg
= + 0 -1 0
-1 4 -1
0 -1 0
0 -1 0
-1 9 -1
0 -1 0
0 0 0
0 1 0
0 0 0
= + 0 -1 0
-1 8 -1
0 -1 0
7
Un-sharp Masking
• to subtract a blurred version of an image produces sharpening output image.
),(),(),( yxfyxfyxfs
sharpened image = original image – blurred image
A process used for many years in the publishing industry to sharpen images consists of subtracting a blurred version of an image from the image itself. This process, called unsharp masking, is expressed as:-
8
High-boost filtering
• generalized form of Unsharp masking
• A 1
),(),(),( yxfyxAfyxfhb
),(),()1(
),(),(),()1(),(
yxfyxfA
yxfyxfyxfAyxf
s
hb
9
High-boost filtering
• if we use Laplacian filter to create sharpen image fs(x,y) with addition of original image
),(),()1(),( yxfyxfAyxf shb
),(),(
),(),(),(
2
2
yxfyxf
yxfyxfyxfs
10
High-boost filtering
• yields
),(),(
),(),(),(
2
2
yxfyxAf
yxfyxAfyxfhb
if the center coefficient of the Laplacian mask is negative
if the center coefficient of the Laplacian mask is positive
11
High-boost Masks
A 1 if A = 1, it becomes “standard” Laplacian
sharpening
12
Example (1)
Example (2) Input Image Laplacian
A=1 A=1.2
https://docs.kde.org/development/en/extragear-graphics/showfoto/using-kapp.html
Example (3) Input Image Laplacian
A=1 A=1.1
15
Gradient Operator
• first derivatives are implemented using the magnitude of the gradient.
y
fx
f
G
Gf
y
x
21
22
21
22 ][)f(||||
y
f
x
f
GGmagf yx
the magnitude becomes nonlinear yx GGf ||||
commonly approx.
16
Gradient Mask
• simplest approximation, 2x2
z1 z2 z3
z4 z5 z6
z7 z8 z9
)( and )( 5658 zzGzzG yx
21
2
56
2
582
122 ])()[(][|||| zzzzGGf yx
5658|||| zzzzf
17
Gradient Mask
• Roberts cross-gradient operators, 2x2
z1 z2 z3
z4 z5 z6
z7 z8 z9
)( and )( 6859 zzGzzG yx
21
2
68
2
592
122 ])()[(][|||| zzzzGGf yx
6859|||| zzzzf
18
Gradient Mask
• Sobel operators, 3x3
z1 z2 z3
z4 z5 z6
z7 z8 z9
)2()2(
)2()2(
741963
321987
zzzzzzG
zzzzzzG
y
x
yx GGf ||||
the weight value 2 is to achieve smoothing by giving more importance to the center point
19
Note
• the summation of coefficients in all masks equals 0, indicating that they would give a response of 0 in an area of constant gray level.
20
Example
21
Edge Detection
• Why detect edge?
Edges characterize object boundaries and are
useful features for segmentation, registration
and object identification in scenes.
• What is edge (to human vision system)?
Intuitively, edge corresponds to singularities in the image
(i.e. where pixel value experiences abrupt change)
No rigorous definition exists
22
Gradient Operators
• Motivation: detect changes
change in the pixel value large gradient
Gradient
operator image Thresholding
edge
map x(m,n) g(m,n) I(m,n)
otherwise
thnmgnmI
0
|),(|1),(
23
Common Operators
Examples: 1. Roberts operator
01
10
g1 g2
10
01
),(),(),( 2
2
2
1 nmgnmgnmg
• Gradient operator
24
Common Operators (cont’d)
2. Prewitt operator 3. Sobel operator
101
101
101
111
000
111
101
202
101
121
000
121
vertical
horizontal
Input Image Vertical Component
Horizontal Component Prewit Gradient
Pre
witt
Gra
die
nt
Appro
xim
ation
Eff
ect
of
Thre
sho
ldin
g P
aram
eter
s
Input Image Sobel Gradient Magnitude
Threshold = 20% of Max Threshold = 50% of Max
27
Compass Operators
101
101
101
111
000
111
111
000
111
101
101
101
110
101
011
110
101
011
011
101
110
011
101
110
|}),({|max),( nmgnmg kk
Co
mp
ass
Op
erat
or
Ex
amp
le
Input Image Compass Gradient Operator Results
Threshold = 20% of Max Threshold = 50% of Max
Color Image: Image from Google HD
Compass Gradient Operator Results
Color Image: Image from Google HD
Compass Gradient Operator Results