Digital Image Processing Chapter 3: Intensity Transformations and Spatial Filtering.
-
Upload
claire-franklin -
Category
Documents
-
view
252 -
download
1
Transcript of Digital Image Processing Chapter 3: Intensity Transformations and Spatial Filtering.
![Page 1: Digital Image Processing Chapter 3: Intensity Transformations and Spatial Filtering.](https://reader035.fdocuments.net/reader035/viewer/2022062217/56649cf35503460f949c1106/html5/thumbnails/1.jpg)
Digital Image Processing
Chapter 3: Intensity Transformations and Spatial Filtering
![Page 2: Digital Image Processing Chapter 3: Intensity Transformations and Spatial Filtering.](https://reader035.fdocuments.net/reader035/viewer/2022062217/56649cf35503460f949c1106/html5/thumbnails/2.jpg)
Background
Spatial domain process
where is the input image, is the processed image, and T is an operator on f, defined over some neighborhood of
)],([),( yxfTyxg ),( yxf ),( yxg
),( yx
![Page 3: Digital Image Processing Chapter 3: Intensity Transformations and Spatial Filtering.](https://reader035.fdocuments.net/reader035/viewer/2022062217/56649cf35503460f949c1106/html5/thumbnails/3.jpg)
Neighborhood about a point
![Page 4: Digital Image Processing Chapter 3: Intensity Transformations and Spatial Filtering.](https://reader035.fdocuments.net/reader035/viewer/2022062217/56649cf35503460f949c1106/html5/thumbnails/4.jpg)
Gray-level transformation function
where r is the gray level of and s is the gray level of at any point
)(rTs ),( yxf
),( yxg),( yx
![Page 5: Digital Image Processing Chapter 3: Intensity Transformations and Spatial Filtering.](https://reader035.fdocuments.net/reader035/viewer/2022062217/56649cf35503460f949c1106/html5/thumbnails/5.jpg)
Contrast enhancement For example, a thresholding function
![Page 6: Digital Image Processing Chapter 3: Intensity Transformations and Spatial Filtering.](https://reader035.fdocuments.net/reader035/viewer/2022062217/56649cf35503460f949c1106/html5/thumbnails/6.jpg)
Masks (filters, kernels, templates, windows) A small 2-D array in which the values of
the mask coefficients determine the nature of the process
![Page 7: Digital Image Processing Chapter 3: Intensity Transformations and Spatial Filtering.](https://reader035.fdocuments.net/reader035/viewer/2022062217/56649cf35503460f949c1106/html5/thumbnails/7.jpg)
Some Basic Gray Level Transformations
![Page 8: Digital Image Processing Chapter 3: Intensity Transformations and Spatial Filtering.](https://reader035.fdocuments.net/reader035/viewer/2022062217/56649cf35503460f949c1106/html5/thumbnails/8.jpg)
Image negatives
Enhance white or gray details
rLs 1
![Page 9: Digital Image Processing Chapter 3: Intensity Transformations and Spatial Filtering.](https://reader035.fdocuments.net/reader035/viewer/2022062217/56649cf35503460f949c1106/html5/thumbnails/9.jpg)
Log transformations
Compress the dynamic range of images with large variations in pixel values
)1log( rcs
![Page 10: Digital Image Processing Chapter 3: Intensity Transformations and Spatial Filtering.](https://reader035.fdocuments.net/reader035/viewer/2022062217/56649cf35503460f949c1106/html5/thumbnails/10.jpg)
From the range 0- to the range 0 to 6.2
6105.1
![Page 11: Digital Image Processing Chapter 3: Intensity Transformations and Spatial Filtering.](https://reader035.fdocuments.net/reader035/viewer/2022062217/56649cf35503460f949c1106/html5/thumbnails/11.jpg)
Power-law transformations or
maps a narrow range of dark input values into a wider range of output values, while maps a narrow range of bright input values into a wider range of output values
: gamma, gamma correction
crs )( rcs
1
1
![Page 12: Digital Image Processing Chapter 3: Intensity Transformations and Spatial Filtering.](https://reader035.fdocuments.net/reader035/viewer/2022062217/56649cf35503460f949c1106/html5/thumbnails/12.jpg)
![Page 13: Digital Image Processing Chapter 3: Intensity Transformations and Spatial Filtering.](https://reader035.fdocuments.net/reader035/viewer/2022062217/56649cf35503460f949c1106/html5/thumbnails/13.jpg)
Monitor, 5.2
![Page 14: Digital Image Processing Chapter 3: Intensity Transformations and Spatial Filtering.](https://reader035.fdocuments.net/reader035/viewer/2022062217/56649cf35503460f949c1106/html5/thumbnails/14.jpg)
![Page 15: Digital Image Processing Chapter 3: Intensity Transformations and Spatial Filtering.](https://reader035.fdocuments.net/reader035/viewer/2022062217/56649cf35503460f949c1106/html5/thumbnails/15.jpg)
![Page 16: Digital Image Processing Chapter 3: Intensity Transformations and Spatial Filtering.](https://reader035.fdocuments.net/reader035/viewer/2022062217/56649cf35503460f949c1106/html5/thumbnails/16.jpg)
Piecewise-linear transformation functions The form of piecewise functions can be
arbitrarily complex
![Page 17: Digital Image Processing Chapter 3: Intensity Transformations and Spatial Filtering.](https://reader035.fdocuments.net/reader035/viewer/2022062217/56649cf35503460f949c1106/html5/thumbnails/17.jpg)
Contrast stretching
![Page 18: Digital Image Processing Chapter 3: Intensity Transformations and Spatial Filtering.](https://reader035.fdocuments.net/reader035/viewer/2022062217/56649cf35503460f949c1106/html5/thumbnails/18.jpg)
Gray-level slicing
![Page 19: Digital Image Processing Chapter 3: Intensity Transformations and Spatial Filtering.](https://reader035.fdocuments.net/reader035/viewer/2022062217/56649cf35503460f949c1106/html5/thumbnails/19.jpg)
![Page 20: Digital Image Processing Chapter 3: Intensity Transformations and Spatial Filtering.](https://reader035.fdocuments.net/reader035/viewer/2022062217/56649cf35503460f949c1106/html5/thumbnails/20.jpg)
Bit-plane slicing
![Page 21: Digital Image Processing Chapter 3: Intensity Transformations and Spatial Filtering.](https://reader035.fdocuments.net/reader035/viewer/2022062217/56649cf35503460f949c1106/html5/thumbnails/21.jpg)
![Page 22: Digital Image Processing Chapter 3: Intensity Transformations and Spatial Filtering.](https://reader035.fdocuments.net/reader035/viewer/2022062217/56649cf35503460f949c1106/html5/thumbnails/22.jpg)
![Page 23: Digital Image Processing Chapter 3: Intensity Transformations and Spatial Filtering.](https://reader035.fdocuments.net/reader035/viewer/2022062217/56649cf35503460f949c1106/html5/thumbnails/23.jpg)
![Page 24: Digital Image Processing Chapter 3: Intensity Transformations and Spatial Filtering.](https://reader035.fdocuments.net/reader035/viewer/2022062217/56649cf35503460f949c1106/html5/thumbnails/24.jpg)
![Page 25: Digital Image Processing Chapter 3: Intensity Transformations and Spatial Filtering.](https://reader035.fdocuments.net/reader035/viewer/2022062217/56649cf35503460f949c1106/html5/thumbnails/25.jpg)
Histogram Processing
Histogram
where is the kth gray level and is the number of pixels in the image having gray level
Normalized histogram
kk nrh )(
kr kn
kr
nnrp kk /)(
![Page 26: Digital Image Processing Chapter 3: Intensity Transformations and Spatial Filtering.](https://reader035.fdocuments.net/reader035/viewer/2022062217/56649cf35503460f949c1106/html5/thumbnails/26.jpg)
![Page 27: Digital Image Processing Chapter 3: Intensity Transformations and Spatial Filtering.](https://reader035.fdocuments.net/reader035/viewer/2022062217/56649cf35503460f949c1106/html5/thumbnails/27.jpg)
Histogram equalization10 ),( rrTs
10 ),(1 ssTr
![Page 28: Digital Image Processing Chapter 3: Intensity Transformations and Spatial Filtering.](https://reader035.fdocuments.net/reader035/viewer/2022062217/56649cf35503460f949c1106/html5/thumbnails/28.jpg)
![Page 29: Digital Image Processing Chapter 3: Intensity Transformations and Spatial Filtering.](https://reader035.fdocuments.net/reader035/viewer/2022062217/56649cf35503460f949c1106/html5/thumbnails/29.jpg)
Probability density functions (PDF)
ds
drrpsp rs )()(
r
r dwwpLrTs0
)()1()(
)()1()()1()(
0rpLdwwp
dr
dL
dr
rdT
dr
dsr
r
r
1
1)(
L
sps
![Page 30: Digital Image Processing Chapter 3: Intensity Transformations and Spatial Filtering.](https://reader035.fdocuments.net/reader035/viewer/2022062217/56649cf35503460f949c1106/html5/thumbnails/30.jpg)
1,...,2,1,0 ,)1()()1()(00
Lkn
nLrpLrTs
k
j
jk
jjrkk
![Page 31: Digital Image Processing Chapter 3: Intensity Transformations and Spatial Filtering.](https://reader035.fdocuments.net/reader035/viewer/2022062217/56649cf35503460f949c1106/html5/thumbnails/31.jpg)
![Page 32: Digital Image Processing Chapter 3: Intensity Transformations and Spatial Filtering.](https://reader035.fdocuments.net/reader035/viewer/2022062217/56649cf35503460f949c1106/html5/thumbnails/32.jpg)
![Page 33: Digital Image Processing Chapter 3: Intensity Transformations and Spatial Filtering.](https://reader035.fdocuments.net/reader035/viewer/2022062217/56649cf35503460f949c1106/html5/thumbnails/33.jpg)
![Page 34: Digital Image Processing Chapter 3: Intensity Transformations and Spatial Filtering.](https://reader035.fdocuments.net/reader035/viewer/2022062217/56649cf35503460f949c1106/html5/thumbnails/34.jpg)
![Page 35: Digital Image Processing Chapter 3: Intensity Transformations and Spatial Filtering.](https://reader035.fdocuments.net/reader035/viewer/2022062217/56649cf35503460f949c1106/html5/thumbnails/35.jpg)
![Page 36: Digital Image Processing Chapter 3: Intensity Transformations and Spatial Filtering.](https://reader035.fdocuments.net/reader035/viewer/2022062217/56649cf35503460f949c1106/html5/thumbnails/36.jpg)
![Page 37: Digital Image Processing Chapter 3: Intensity Transformations and Spatial Filtering.](https://reader035.fdocuments.net/reader035/viewer/2022062217/56649cf35503460f949c1106/html5/thumbnails/37.jpg)
Histogram matching (specification)
r
r dwwpLrTs0
)()1()(
z
z sdttpLzG0
)()1()(
)]([)( 11 rTGsGz
)(zpz is the desired PDF
![Page 38: Digital Image Processing Chapter 3: Intensity Transformations and Spatial Filtering.](https://reader035.fdocuments.net/reader035/viewer/2022062217/56649cf35503460f949c1106/html5/thumbnails/38.jpg)
1,...,2,1,0 ,)1()()1()(00
Lkn
nLrpLrTs
k
j
jk
jjrkk
1,...,2,1,0 ,)()1()(0
LkszpLzGv k
k
iizkk
1,...,2,1,0 )],([1 LkrTGz kk
![Page 39: Digital Image Processing Chapter 3: Intensity Transformations and Spatial Filtering.](https://reader035.fdocuments.net/reader035/viewer/2022062217/56649cf35503460f949c1106/html5/thumbnails/39.jpg)
![Page 40: Digital Image Processing Chapter 3: Intensity Transformations and Spatial Filtering.](https://reader035.fdocuments.net/reader035/viewer/2022062217/56649cf35503460f949c1106/html5/thumbnails/40.jpg)
Histogram matching Obtain the histogram of the given
image, T(r) Precompute a mapped level for each
level Obtain the transformation function G
from the given Precompute for each value of Map to its corresponding level ;
then map level into the final level
)(zpz
kskr
kz kskr ks
ks kz
![Page 41: Digital Image Processing Chapter 3: Intensity Transformations and Spatial Filtering.](https://reader035.fdocuments.net/reader035/viewer/2022062217/56649cf35503460f949c1106/html5/thumbnails/41.jpg)
![Page 42: Digital Image Processing Chapter 3: Intensity Transformations and Spatial Filtering.](https://reader035.fdocuments.net/reader035/viewer/2022062217/56649cf35503460f949c1106/html5/thumbnails/42.jpg)
![Page 43: Digital Image Processing Chapter 3: Intensity Transformations and Spatial Filtering.](https://reader035.fdocuments.net/reader035/viewer/2022062217/56649cf35503460f949c1106/html5/thumbnails/43.jpg)
![Page 44: Digital Image Processing Chapter 3: Intensity Transformations and Spatial Filtering.](https://reader035.fdocuments.net/reader035/viewer/2022062217/56649cf35503460f949c1106/html5/thumbnails/44.jpg)
![Page 45: Digital Image Processing Chapter 3: Intensity Transformations and Spatial Filtering.](https://reader035.fdocuments.net/reader035/viewer/2022062217/56649cf35503460f949c1106/html5/thumbnails/45.jpg)
![Page 46: Digital Image Processing Chapter 3: Intensity Transformations and Spatial Filtering.](https://reader035.fdocuments.net/reader035/viewer/2022062217/56649cf35503460f949c1106/html5/thumbnails/46.jpg)
![Page 47: Digital Image Processing Chapter 3: Intensity Transformations and Spatial Filtering.](https://reader035.fdocuments.net/reader035/viewer/2022062217/56649cf35503460f949c1106/html5/thumbnails/47.jpg)
![Page 48: Digital Image Processing Chapter 3: Intensity Transformations and Spatial Filtering.](https://reader035.fdocuments.net/reader035/viewer/2022062217/56649cf35503460f949c1106/html5/thumbnails/48.jpg)
Local enhancement Histogram using a local neighborhood,
for example 7*7 neighborhood
![Page 49: Digital Image Processing Chapter 3: Intensity Transformations and Spatial Filtering.](https://reader035.fdocuments.net/reader035/viewer/2022062217/56649cf35503460f949c1106/html5/thumbnails/49.jpg)
Histogram using a local 3*3 neighborhood
![Page 50: Digital Image Processing Chapter 3: Intensity Transformations and Spatial Filtering.](https://reader035.fdocuments.net/reader035/viewer/2022062217/56649cf35503460f949c1106/html5/thumbnails/50.jpg)
Use of histogram statistics for image enhancement denotes a discrete random
variable denotes the normalized histogram
component corresponding to the ith value of
Mean
)( irp
r
r
1
0
)(L
iii rprm
![Page 51: Digital Image Processing Chapter 3: Intensity Transformations and Spatial Filtering.](https://reader035.fdocuments.net/reader035/viewer/2022062217/56649cf35503460f949c1106/html5/thumbnails/51.jpg)
The nth moment
The second moment
1
0
)()()(L
ii
nin rpmrr
1
0
22 )()()(
L
iii rpmrr
![Page 52: Digital Image Processing Chapter 3: Intensity Transformations and Spatial Filtering.](https://reader035.fdocuments.net/reader035/viewer/2022062217/56649cf35503460f949c1106/html5/thumbnails/52.jpg)
Global enhancement: The global mean and variance are measured over an entire image
Local enhancement: The local mean and variance are used as the basis for making changes
![Page 53: Digital Image Processing Chapter 3: Intensity Transformations and Spatial Filtering.](https://reader035.fdocuments.net/reader035/viewer/2022062217/56649cf35503460f949c1106/html5/thumbnails/53.jpg)
is the gray level at coordinates (s,t) in the neighborhood
is the neighborhood normalized histogram component
mean:
local variance
tsr ,
)( ,tsrp
xy
xySts
tstsS rprm),(
,, )(
xy
xyxySts
tsStsS rpmr),(
,2
,2 )(][
![Page 54: Digital Image Processing Chapter 3: Intensity Transformations and Spatial Filtering.](https://reader035.fdocuments.net/reader035/viewer/2022062217/56649cf35503460f949c1106/html5/thumbnails/54.jpg)
are specified parameters is the global mean is the global standard deviation Mapping
210 ,,, kkkEGMGD
otherwise),(
and
if),(
),(21
0
yxf
DkDk
MkmyxfE
yxgGSG
GS
xy
xy
![Page 55: Digital Image Processing Chapter 3: Intensity Transformations and Spatial Filtering.](https://reader035.fdocuments.net/reader035/viewer/2022062217/56649cf35503460f949c1106/html5/thumbnails/55.jpg)
![Page 56: Digital Image Processing Chapter 3: Intensity Transformations and Spatial Filtering.](https://reader035.fdocuments.net/reader035/viewer/2022062217/56649cf35503460f949c1106/html5/thumbnails/56.jpg)
![Page 57: Digital Image Processing Chapter 3: Intensity Transformations and Spatial Filtering.](https://reader035.fdocuments.net/reader035/viewer/2022062217/56649cf35503460f949c1106/html5/thumbnails/57.jpg)
![Page 58: Digital Image Processing Chapter 3: Intensity Transformations and Spatial Filtering.](https://reader035.fdocuments.net/reader035/viewer/2022062217/56649cf35503460f949c1106/html5/thumbnails/58.jpg)
Fundamentals of Spatial Filtering
The Mechanics of Spatial Filtering
)1,1()1,1(
),1()0,1(
),()0,0(
),1()0,1(
)1,1()1,1(
yxfw
yxfw
yxfw
yxfw
yxfwR
![Page 59: Digital Image Processing Chapter 3: Intensity Transformations and Spatial Filtering.](https://reader035.fdocuments.net/reader035/viewer/2022062217/56649cf35503460f949c1106/html5/thumbnails/59.jpg)
Image size: Mask size:
and and
NM nm
a
as
b
bt
tysxftswyxg ),(),(),(
2/)1( ma 2/)1( nb1,...,2,1,0 Mx 1,...,2,1,0 Ny
![Page 60: Digital Image Processing Chapter 3: Intensity Transformations and Spatial Filtering.](https://reader035.fdocuments.net/reader035/viewer/2022062217/56649cf35503460f949c1106/html5/thumbnails/60.jpg)
![Page 61: Digital Image Processing Chapter 3: Intensity Transformations and Spatial Filtering.](https://reader035.fdocuments.net/reader035/viewer/2022062217/56649cf35503460f949c1106/html5/thumbnails/61.jpg)
![Page 62: Digital Image Processing Chapter 3: Intensity Transformations and Spatial Filtering.](https://reader035.fdocuments.net/reader035/viewer/2022062217/56649cf35503460f949c1106/html5/thumbnails/62.jpg)
Spatial Correlation and Convolution
![Page 63: Digital Image Processing Chapter 3: Intensity Transformations and Spatial Filtering.](https://reader035.fdocuments.net/reader035/viewer/2022062217/56649cf35503460f949c1106/html5/thumbnails/63.jpg)
![Page 64: Digital Image Processing Chapter 3: Intensity Transformations and Spatial Filtering.](https://reader035.fdocuments.net/reader035/viewer/2022062217/56649cf35503460f949c1106/html5/thumbnails/64.jpg)
9
1
992211
...
iii zw
zwzwzwR
Vector Representation of Linear Filtering
![Page 65: Digital Image Processing Chapter 3: Intensity Transformations and Spatial Filtering.](https://reader035.fdocuments.net/reader035/viewer/2022062217/56649cf35503460f949c1106/html5/thumbnails/65.jpg)
Smoothing Spatial Filters
Smoothing Linear Filters Noise reduction Smoothing of false contours Reduction of irrelevant detail
![Page 66: Digital Image Processing Chapter 3: Intensity Transformations and Spatial Filtering.](https://reader035.fdocuments.net/reader035/viewer/2022062217/56649cf35503460f949c1106/html5/thumbnails/66.jpg)
9
19
1
iizR
![Page 67: Digital Image Processing Chapter 3: Intensity Transformations and Spatial Filtering.](https://reader035.fdocuments.net/reader035/viewer/2022062217/56649cf35503460f949c1106/html5/thumbnails/67.jpg)
a
as
b
bt
a
as
b
bt
tsw
tysxftswyxg
),(
),(),(),(
![Page 68: Digital Image Processing Chapter 3: Intensity Transformations and Spatial Filtering.](https://reader035.fdocuments.net/reader035/viewer/2022062217/56649cf35503460f949c1106/html5/thumbnails/68.jpg)
![Page 69: Digital Image Processing Chapter 3: Intensity Transformations and Spatial Filtering.](https://reader035.fdocuments.net/reader035/viewer/2022062217/56649cf35503460f949c1106/html5/thumbnails/69.jpg)
![Page 70: Digital Image Processing Chapter 3: Intensity Transformations and Spatial Filtering.](https://reader035.fdocuments.net/reader035/viewer/2022062217/56649cf35503460f949c1106/html5/thumbnails/70.jpg)
Order-statistic filters median filter: Replace the value of a
pixel by the median of the gray levels in the neighborhood of that pixel
Noise-reduction
![Page 71: Digital Image Processing Chapter 3: Intensity Transformations and Spatial Filtering.](https://reader035.fdocuments.net/reader035/viewer/2022062217/56649cf35503460f949c1106/html5/thumbnails/71.jpg)
![Page 72: Digital Image Processing Chapter 3: Intensity Transformations and Spatial Filtering.](https://reader035.fdocuments.net/reader035/viewer/2022062217/56649cf35503460f949c1106/html5/thumbnails/72.jpg)
Sharpening Spatial Filters
Foundation The first-order derivative
The second-order derivative
)()1( xfxfx
f
)(2)1()1(2
2
xfxfxfx
f
![Page 73: Digital Image Processing Chapter 3: Intensity Transformations and Spatial Filtering.](https://reader035.fdocuments.net/reader035/viewer/2022062217/56649cf35503460f949c1106/html5/thumbnails/73.jpg)
![Page 74: Digital Image Processing Chapter 3: Intensity Transformations and Spatial Filtering.](https://reader035.fdocuments.net/reader035/viewer/2022062217/56649cf35503460f949c1106/html5/thumbnails/74.jpg)
![Page 75: Digital Image Processing Chapter 3: Intensity Transformations and Spatial Filtering.](https://reader035.fdocuments.net/reader035/viewer/2022062217/56649cf35503460f949c1106/html5/thumbnails/75.jpg)
Use of second derivatives for enhancement-The Laplacian Development of the method
),(2),1(),1(2
2
yxfyxfyxfx
f
2
2
2
22
y
f
x
ff
),(2)1,()1,(2
2
yxfyxfyxfy
f
![Page 76: Digital Image Processing Chapter 3: Intensity Transformations and Spatial Filtering.](https://reader035.fdocuments.net/reader035/viewer/2022062217/56649cf35503460f949c1106/html5/thumbnails/76.jpg)
),(4)]1,(
)1,(),1(),1([2
yxfyxf
yxfyxfyxff
positive is
mask Laplacian theof
tcoefficiencenter theif
),(),(
negative is
mask Laplacian theof
t coefficiencenter theif
),(),(
),(
2
2
yxfyxf
yxfyxf
yxg
![Page 77: Digital Image Processing Chapter 3: Intensity Transformations and Spatial Filtering.](https://reader035.fdocuments.net/reader035/viewer/2022062217/56649cf35503460f949c1106/html5/thumbnails/77.jpg)
![Page 78: Digital Image Processing Chapter 3: Intensity Transformations and Spatial Filtering.](https://reader035.fdocuments.net/reader035/viewer/2022062217/56649cf35503460f949c1106/html5/thumbnails/78.jpg)
![Page 79: Digital Image Processing Chapter 3: Intensity Transformations and Spatial Filtering.](https://reader035.fdocuments.net/reader035/viewer/2022062217/56649cf35503460f949c1106/html5/thumbnails/79.jpg)
Simplifications
)]1,(
)1,(),1(),1([),(5
),(4)]1,(
)1,(),1(),1([),(),(
yxf
yxfyxfyxfyxf
yxfyxf
yxfyxfyxfyxfyxg
![Page 80: Digital Image Processing Chapter 3: Intensity Transformations and Spatial Filtering.](https://reader035.fdocuments.net/reader035/viewer/2022062217/56649cf35503460f949c1106/html5/thumbnails/80.jpg)
![Page 81: Digital Image Processing Chapter 3: Intensity Transformations and Spatial Filtering.](https://reader035.fdocuments.net/reader035/viewer/2022062217/56649cf35503460f949c1106/html5/thumbnails/81.jpg)
Unsharp masking and highboost filtering Unsharp masking
Substract a blurred version of an image from the image itself
: The image, : The blurred image
),(),(),( yxfyxfyxgmask
),( yxf ),( yxf
),(*),(),( yxgkyxfyxg mask 1, k
![Page 82: Digital Image Processing Chapter 3: Intensity Transformations and Spatial Filtering.](https://reader035.fdocuments.net/reader035/viewer/2022062217/56649cf35503460f949c1106/html5/thumbnails/82.jpg)
High-boost filtering
),(*),(),( yxgkyxfyxg mask 1, k
![Page 83: Digital Image Processing Chapter 3: Intensity Transformations and Spatial Filtering.](https://reader035.fdocuments.net/reader035/viewer/2022062217/56649cf35503460f949c1106/html5/thumbnails/83.jpg)
![Page 84: Digital Image Processing Chapter 3: Intensity Transformations and Spatial Filtering.](https://reader035.fdocuments.net/reader035/viewer/2022062217/56649cf35503460f949c1106/html5/thumbnails/84.jpg)
![Page 85: Digital Image Processing Chapter 3: Intensity Transformations and Spatial Filtering.](https://reader035.fdocuments.net/reader035/viewer/2022062217/56649cf35503460f949c1106/html5/thumbnails/85.jpg)
Using first-order derivatives for (nonlinear) image sharpening—The gradient
y
fx
f
G
G
y
xf
![Page 86: Digital Image Processing Chapter 3: Intensity Transformations and Spatial Filtering.](https://reader035.fdocuments.net/reader035/viewer/2022062217/56649cf35503460f949c1106/html5/thumbnails/86.jpg)
The magnitude is rotation invariant (isotropic)
2
122
21
22
)(mag
y
f
x
f
GGf yxf
yx GGf
![Page 87: Digital Image Processing Chapter 3: Intensity Transformations and Spatial Filtering.](https://reader035.fdocuments.net/reader035/viewer/2022062217/56649cf35503460f949c1106/html5/thumbnails/87.jpg)
Computing using cross differences, Roberts cross-gradient operators
)( 59 zzGx )( 68 zzGy and
21
268
259 )()( zzzzf
6859 zzzzf
![Page 88: Digital Image Processing Chapter 3: Intensity Transformations and Spatial Filtering.](https://reader035.fdocuments.net/reader035/viewer/2022062217/56649cf35503460f949c1106/html5/thumbnails/88.jpg)
Sobel operators A weight value of 2 is to achieve some
smoothing by giving more importance to the center point
)2()2(
)2()2(
741963
321987
zzzzzz
zzzzzzf
![Page 89: Digital Image Processing Chapter 3: Intensity Transformations and Spatial Filtering.](https://reader035.fdocuments.net/reader035/viewer/2022062217/56649cf35503460f949c1106/html5/thumbnails/89.jpg)
![Page 90: Digital Image Processing Chapter 3: Intensity Transformations and Spatial Filtering.](https://reader035.fdocuments.net/reader035/viewer/2022062217/56649cf35503460f949c1106/html5/thumbnails/90.jpg)
![Page 91: Digital Image Processing Chapter 3: Intensity Transformations and Spatial Filtering.](https://reader035.fdocuments.net/reader035/viewer/2022062217/56649cf35503460f949c1106/html5/thumbnails/91.jpg)
Combining Spatial Enhancement Methods
An example Laplacian to highlight fine detail Gradient to enhance prominent edges Smoothed version of the gradient
image used to mask the Laplacian image
Increase the dynamic range of the gray levels by using a gray-level transformation
![Page 92: Digital Image Processing Chapter 3: Intensity Transformations and Spatial Filtering.](https://reader035.fdocuments.net/reader035/viewer/2022062217/56649cf35503460f949c1106/html5/thumbnails/92.jpg)
![Page 93: Digital Image Processing Chapter 3: Intensity Transformations and Spatial Filtering.](https://reader035.fdocuments.net/reader035/viewer/2022062217/56649cf35503460f949c1106/html5/thumbnails/93.jpg)