dr. z. r. ghassabi [email protected] tehran shomal university spring 2015...
TRANSCRIPT
![Page 2: Dr. Z. R. Ghassabi z.r.ghassabi@gmail.com Tehran shomal University Spring 2015 z.r.ghassabi@gmail.com Digital Image Processing Session 3 1](https://reader033.vdocuments.us/reader033/viewer/2022061604/56649e855503460f94b882b3/html5/thumbnails/2.jpg)
2
Outline
• Introduction• Digital Image Fundamentals• Intensity Transformations and Spatial Filtering• Filtering in the Frequency Domain• Image Restoration and Reconstruction• Color Image Processing • Wavelets and Multi resolution Processing• Image Compression• Morphological Operation• Object representation• Object recognition
![Page 3: Dr. Z. R. Ghassabi z.r.ghassabi@gmail.com Tehran shomal University Spring 2015 z.r.ghassabi@gmail.com Digital Image Processing Session 3 1](https://reader033.vdocuments.us/reader033/viewer/2022061604/56649e855503460f94b882b3/html5/thumbnails/3.jpg)
Outline of Chapter 3
• Basic Intensity Transformation Functions• Negative, Log, Gamma
• Piecewise-Linear Transformation Functions• Contrast stretching, contrast slicing, bit-plane slicing
• Histogram Processing• Histogram Stretching, Histogram Shrink, Histogram Sliding, Histogram
equalization, adaptive local histogram, histogram matching, local histogram equalization, histogram statistics
• Fundamentals of Spatial Filtering• Smoothing Spatial Filters, Sharpening Spatial Filters, Combining Spatial
Enhancement Tools
![Page 4: Dr. Z. R. Ghassabi z.r.ghassabi@gmail.com Tehran shomal University Spring 2015 z.r.ghassabi@gmail.com Digital Image Processing Session 3 1](https://reader033.vdocuments.us/reader033/viewer/2022061604/56649e855503460f94b882b3/html5/thumbnails/4.jpg)
Image Enhancement
• Methods– Spatial Domain:
• Linear• Nonlinear
– Frequency Domain:• Linear• Nonlinear
![Page 5: Dr. Z. R. Ghassabi z.r.ghassabi@gmail.com Tehran shomal University Spring 2015 z.r.ghassabi@gmail.com Digital Image Processing Session 3 1](https://reader033.vdocuments.us/reader033/viewer/2022061604/56649e855503460f94b882b3/html5/thumbnails/5.jpg)
Image Enhancement
• Spatial Domain
, ,g x y T f x y
![Page 6: Dr. Z. R. Ghassabi z.r.ghassabi@gmail.com Tehran shomal University Spring 2015 z.r.ghassabi@gmail.com Digital Image Processing Session 3 1](https://reader033.vdocuments.us/reader033/viewer/2022061604/56649e855503460f94b882b3/html5/thumbnails/6.jpg)
Image Enhancement
• Example: Image Subtraction for enhancing Differences
, , ,g x y f x y h x y
![Page 7: Dr. Z. R. Ghassabi z.r.ghassabi@gmail.com Tehran shomal University Spring 2015 z.r.ghassabi@gmail.com Digital Image Processing Session 3 1](https://reader033.vdocuments.us/reader033/viewer/2022061604/56649e855503460f94b882b3/html5/thumbnails/7.jpg)
Image Enhancement
• Frequency Domain
![Page 8: Dr. Z. R. Ghassabi z.r.ghassabi@gmail.com Tehran shomal University Spring 2015 z.r.ghassabi@gmail.com Digital Image Processing Session 3 1](https://reader033.vdocuments.us/reader033/viewer/2022061604/56649e855503460f94b882b3/html5/thumbnails/8.jpg)
Image Transforms
![Page 9: Dr. Z. R. Ghassabi z.r.ghassabi@gmail.com Tehran shomal University Spring 2015 z.r.ghassabi@gmail.com Digital Image Processing Session 3 1](https://reader033.vdocuments.us/reader033/viewer/2022061604/56649e855503460f94b882b3/html5/thumbnails/9.jpg)
Image Enhancement in spatial Domain (Transformation)
• For 11 neighborhood: – Contrast Enhancement/Stretching/Point process
• For w w neighborhood:– Filtering/Mask/Kernel/Window/Template Processing
s T r
![Page 10: Dr. Z. R. Ghassabi z.r.ghassabi@gmail.com Tehran shomal University Spring 2015 z.r.ghassabi@gmail.com Digital Image Processing Session 3 1](https://reader033.vdocuments.us/reader033/viewer/2022061604/56649e855503460f94b882b3/html5/thumbnails/10.jpg)
Image Enhancement in spatial Domain
Input gray level, r
Ou
tpu
t gr
ay le
vel,
s
Negative
Log
nth root
Identity
nth power
Inverse Log Some Basic Intensity Transformation Functions
![Page 11: Dr. Z. R. Ghassabi z.r.ghassabi@gmail.com Tehran shomal University Spring 2015 z.r.ghassabi@gmail.com Digital Image Processing Session 3 1](https://reader033.vdocuments.us/reader033/viewer/2022061604/56649e855503460f94b882b3/html5/thumbnails/11.jpg)
Image Negatives
• Image Negatives: 1s L r L x0
L
y
y=L-x
![Page 12: Dr. Z. R. Ghassabi z.r.ghassabi@gmail.com Tehran shomal University Spring 2015 z.r.ghassabi@gmail.com Digital Image Processing Session 3 1](https://reader033.vdocuments.us/reader033/viewer/2022061604/56649e855503460f94b882b3/html5/thumbnails/12.jpg)
Image Negatives
![Page 13: Dr. Z. R. Ghassabi z.r.ghassabi@gmail.com Tehran shomal University Spring 2015 z.r.ghassabi@gmail.com Digital Image Processing Session 3 1](https://reader033.vdocuments.us/reader033/viewer/2022061604/56649e855503460f94b882b3/html5/thumbnails/13.jpg)
Log Transformation
![Page 14: Dr. Z. R. Ghassabi z.r.ghassabi@gmail.com Tehran shomal University Spring 2015 z.r.ghassabi@gmail.com Digital Image Processing Session 3 1](https://reader033.vdocuments.us/reader033/viewer/2022061604/56649e855503460f94b882b3/html5/thumbnails/14.jpg)
Log Transformation
)1(log10 xcy
c=100
L x0
y
![Page 15: Dr. Z. R. Ghassabi z.r.ghassabi@gmail.com Tehran shomal University Spring 2015 z.r.ghassabi@gmail.com Digital Image Processing Session 3 1](https://reader033.vdocuments.us/reader033/viewer/2022061604/56649e855503460f94b882b3/html5/thumbnails/15.jpg)
Log TransformationRange Compression
![Page 16: Dr. Z. R. Ghassabi z.r.ghassabi@gmail.com Tehran shomal University Spring 2015 z.r.ghassabi@gmail.com Digital Image Processing Session 3 1](https://reader033.vdocuments.us/reader033/viewer/2022061604/56649e855503460f94b882b3/html5/thumbnails/16.jpg)
Power-Law(Gamma) Transformations
s c r
![Page 17: Dr. Z. R. Ghassabi z.r.ghassabi@gmail.com Tehran shomal University Spring 2015 z.r.ghassabi@gmail.com Digital Image Processing Session 3 1](https://reader033.vdocuments.us/reader033/viewer/2022061604/56649e855503460f94b882b3/html5/thumbnails/17.jpg)
Power-Law(Gamma) Transformations
Gamma Correction:
1.8 2.5r
11.8 2.5r
1.8 2.5r
![Page 18: Dr. Z. R. Ghassabi z.r.ghassabi@gmail.com Tehran shomal University Spring 2015 z.r.ghassabi@gmail.com Digital Image Processing Session 3 1](https://reader033.vdocuments.us/reader033/viewer/2022061604/56649e855503460f94b882b3/html5/thumbnails/18.jpg)
Power-Law(Gamma) Transformations (Effect of decreasing gamma)
Original =0.6
=0.4 =0.3
![Page 19: Dr. Z. R. Ghassabi z.r.ghassabi@gmail.com Tehran shomal University Spring 2015 z.r.ghassabi@gmail.com Digital Image Processing Session 3 1](https://reader033.vdocuments.us/reader033/viewer/2022061604/56649e855503460f94b882b3/html5/thumbnails/19.jpg)
Power-Law(Gamma) Transformations(Effect of increasing gamma)
![Page 20: Dr. Z. R. Ghassabi z.r.ghassabi@gmail.com Tehran shomal University Spring 2015 z.r.ghassabi@gmail.com Digital Image Processing Session 3 1](https://reader033.vdocuments.us/reader033/viewer/2022061604/56649e855503460f94b882b3/html5/thumbnails/20.jpg)
Power-Law(Gamma) Transformations
• Medical Example
![Page 21: Dr. Z. R. Ghassabi z.r.ghassabi@gmail.com Tehran shomal University Spring 2015 z.r.ghassabi@gmail.com Digital Image Processing Session 3 1](https://reader033.vdocuments.us/reader033/viewer/2022061604/56649e855503460f94b882b3/html5/thumbnails/21.jpg)
Piecewise-Linear Transformation Functions
• Contrast Stretching• Contrast slicing• Bite-Plane slicing
![Page 22: Dr. Z. R. Ghassabi z.r.ghassabi@gmail.com Tehran shomal University Spring 2015 z.r.ghassabi@gmail.com Digital Image Processing Session 3 1](https://reader033.vdocuments.us/reader033/viewer/2022061604/56649e855503460f94b882b3/html5/thumbnails/22.jpg)
Contrast Stretching
Lxbybx
bxayax
axx
y
b
a
)(
)(
0
Lx
0 a b
ya
yb
200,30,1,2,2.0,150,50 ba yyba
y
![Page 23: Dr. Z. R. Ghassabi z.r.ghassabi@gmail.com Tehran shomal University Spring 2015 z.r.ghassabi@gmail.com Digital Image Processing Session 3 1](https://reader033.vdocuments.us/reader033/viewer/2022061604/56649e855503460f94b882b3/html5/thumbnails/23.jpg)
Contrast stretching
Original
C. S. THR.
![Page 24: Dr. Z. R. Ghassabi z.r.ghassabi@gmail.com Tehran shomal University Spring 2015 z.r.ghassabi@gmail.com Digital Image Processing Session 3 1](https://reader033.vdocuments.us/reader033/viewer/2022061604/56649e855503460f94b882b3/html5/thumbnails/24.jpg)
Contrast Stretching
![Page 25: Dr. Z. R. Ghassabi z.r.ghassabi@gmail.com Tehran shomal University Spring 2015 z.r.ghassabi@gmail.com Digital Image Processing Session 3 1](https://reader033.vdocuments.us/reader033/viewer/2022061604/56649e855503460f94b882b3/html5/thumbnails/25.jpg)
Contrast Stretching
Lxbab
bxaax
ax
y
)(
)(
00
L x0 a b
2,150,50 ba
yClipping:
![Page 26: Dr. Z. R. Ghassabi z.r.ghassabi@gmail.com Tehran shomal University Spring 2015 z.r.ghassabi@gmail.com Digital Image Processing Session 3 1](https://reader033.vdocuments.us/reader033/viewer/2022061604/56649e855503460f94b882b3/html5/thumbnails/26.jpg)
MATLAB Tutorial
• imadjust(I, [low-in, high-in],[low-out, high-out])
low-in high-in
low-out
high-out
Output Image
Input Image
![Page 27: Dr. Z. R. Ghassabi z.r.ghassabi@gmail.com Tehran shomal University Spring 2015 z.r.ghassabi@gmail.com Digital Image Processing Session 3 1](https://reader033.vdocuments.us/reader033/viewer/2022061604/56649e855503460f94b882b3/html5/thumbnails/27.jpg)
چیست؟ مقدار ترین مناسب
MATLAB Tutorial
• imadjust(I, [low-in, high-in],[low-out, high-out], gamma)
• imadjust(I, [0.1, 0.7],[0, 1], gamma)
low-in high-in
low-out
high-out
Output Image
Input Image
![Page 28: Dr. Z. R. Ghassabi z.r.ghassabi@gmail.com Tehran shomal University Spring 2015 z.r.ghassabi@gmail.com Digital Image Processing Session 3 1](https://reader033.vdocuments.us/reader033/viewer/2022061604/56649e855503460f94b882b3/html5/thumbnails/28.jpg)
MATLAB Tutorial
• Use Min and Max gray-levels– Low-in: Double(min(I(:))/255)– max-in: Double(max(I(:))/255)
• Use stretchlim(I) imadjust(I,stretchlim(I) ,[low-out, high-out], gamma)
![Page 29: Dr. Z. R. Ghassabi z.r.ghassabi@gmail.com Tehran shomal University Spring 2015 z.r.ghassabi@gmail.com Digital Image Processing Session 3 1](https://reader033.vdocuments.us/reader033/viewer/2022061604/56649e855503460f94b882b3/html5/thumbnails/29.jpg)
MATLAB Tutorial
low-in high-in
low-out
high-out
Output Image
Input Image
Y= )
Y= )
Y= )
![Page 30: Dr. Z. R. Ghassabi z.r.ghassabi@gmail.com Tehran shomal University Spring 2015 z.r.ghassabi@gmail.com Digital Image Processing Session 3 1](https://reader033.vdocuments.us/reader033/viewer/2022061604/56649e855503460f94b882b3/html5/thumbnails/30.jpg)
Gray-level Slicing
![Page 31: Dr. Z. R. Ghassabi z.r.ghassabi@gmail.com Tehran shomal University Spring 2015 z.r.ghassabi@gmail.com Digital Image Processing Session 3 1](https://reader033.vdocuments.us/reader033/viewer/2022061604/56649e855503460f94b882b3/html5/thumbnails/31.jpg)
Gray-level Slicing
![Page 32: Dr. Z. R. Ghassabi z.r.ghassabi@gmail.com Tehran shomal University Spring 2015 z.r.ghassabi@gmail.com Digital Image Processing Session 3 1](https://reader033.vdocuments.us/reader033/viewer/2022061604/56649e855503460f94b882b3/html5/thumbnails/32.jpg)
Gray-level Slicing
![Page 33: Dr. Z. R. Ghassabi z.r.ghassabi@gmail.com Tehran shomal University Spring 2015 z.r.ghassabi@gmail.com Digital Image Processing Session 3 1](https://reader033.vdocuments.us/reader033/viewer/2022061604/56649e855503460f94b882b3/html5/thumbnails/33.jpg)
Gray-level Slicing
![Page 34: Dr. Z. R. Ghassabi z.r.ghassabi@gmail.com Tehran shomal University Spring 2015 z.r.ghassabi@gmail.com Digital Image Processing Session 3 1](https://reader033.vdocuments.us/reader033/viewer/2022061604/56649e855503460f94b882b3/html5/thumbnails/34.jpg)
Gray-level Slicing
![Page 35: Dr. Z. R. Ghassabi z.r.ghassabi@gmail.com Tehran shomal University Spring 2015 z.r.ghassabi@gmail.com Digital Image Processing Session 3 1](https://reader033.vdocuments.us/reader033/viewer/2022061604/56649e855503460f94b882b3/html5/thumbnails/35.jpg)
Bit-plane Slicing
Highlighting the contribution made to total image appearance by specific bitsSuppose each pixel is represented by 8 bitsHigher-order bits contain the majority of the visually significant dataUseful for analyzing the relative importance played by each bit of the image
![Page 36: Dr. Z. R. Ghassabi z.r.ghassabi@gmail.com Tehran shomal University Spring 2015 z.r.ghassabi@gmail.com Digital Image Processing Session 3 1](https://reader033.vdocuments.us/reader033/viewer/2022061604/56649e855503460f94b882b3/html5/thumbnails/36.jpg)
Bit-plane Slicing
![Page 37: Dr. Z. R. Ghassabi z.r.ghassabi@gmail.com Tehran shomal University Spring 2015 z.r.ghassabi@gmail.com Digital Image Processing Session 3 1](https://reader033.vdocuments.us/reader033/viewer/2022061604/56649e855503460f94b882b3/html5/thumbnails/37.jpg)
Bit-plane Slicing
The (binary) image for bit-plane 7 can be obtained by processing the input image with a thresholding gray-level transformation.
Map all levels between 0 and 127 to 0Map all levels between 129 and 255 to 255
![Page 38: Dr. Z. R. Ghassabi z.r.ghassabi@gmail.com Tehran shomal University Spring 2015 z.r.ghassabi@gmail.com Digital Image Processing Session 3 1](https://reader033.vdocuments.us/reader033/viewer/2022061604/56649e855503460f94b882b3/html5/thumbnails/38.jpg)
Bit-plane SlicingFractal Image
![Page 39: Dr. Z. R. Ghassabi z.r.ghassabi@gmail.com Tehran shomal University Spring 2015 z.r.ghassabi@gmail.com Digital Image Processing Session 3 1](https://reader033.vdocuments.us/reader033/viewer/2022061604/56649e855503460f94b882b3/html5/thumbnails/39.jpg)
Bit-plane SlicingFractal Image
Bit-plane 7 Bit-plane 6
Bit-plane 5 Bit-plane 4 Bit-plane 3
Bit-plane 2 Bit-plane 1 Bit-plane 0
![Page 40: Dr. Z. R. Ghassabi z.r.ghassabi@gmail.com Tehran shomal University Spring 2015 z.r.ghassabi@gmail.com Digital Image Processing Session 3 1](https://reader033.vdocuments.us/reader033/viewer/2022061604/56649e855503460f94b882b3/html5/thumbnails/40.jpg)
Bit-plane Slicing
![Page 41: Dr. Z. R. Ghassabi z.r.ghassabi@gmail.com Tehran shomal University Spring 2015 z.r.ghassabi@gmail.com Digital Image Processing Session 3 1](https://reader033.vdocuments.us/reader033/viewer/2022061604/56649e855503460f94b882b3/html5/thumbnails/41.jpg)
Histogram Processing
Enhancement based on statistical Properties: Local, Global
Histogram Definition
h(rk)=nk
Where rk is the kth gray level and nk is the number of pixels in the image having gray level rk
Normalized histogram:
P(rk)=nk/n
Histogram of an image represents the relative frequency of occurrence of various gray levels in the image
![Page 42: Dr. Z. R. Ghassabi z.r.ghassabi@gmail.com Tehran shomal University Spring 2015 z.r.ghassabi@gmail.com Digital Image Processing Session 3 1](https://reader033.vdocuments.us/reader033/viewer/2022061604/56649e855503460f94b882b3/html5/thumbnails/42.jpg)
Histogram Example
![Page 43: Dr. Z. R. Ghassabi z.r.ghassabi@gmail.com Tehran shomal University Spring 2015 z.r.ghassabi@gmail.com Digital Image Processing Session 3 1](https://reader033.vdocuments.us/reader033/viewer/2022061604/56649e855503460f94b882b3/html5/thumbnails/43.jpg)
MATLAB Tutorial
• Hist(double(I(:)),50)• imhist(I)
![Page 44: Dr. Z. R. Ghassabi z.r.ghassabi@gmail.com Tehran shomal University Spring 2015 z.r.ghassabi@gmail.com Digital Image Processing Session 3 1](https://reader033.vdocuments.us/reader033/viewer/2022061604/56649e855503460f94b882b3/html5/thumbnails/44.jpg)
Histogram Examples
• Histogram Visual Meaning:– Dark– Bright– Low Contrast– High Contrast
![Page 45: Dr. Z. R. Ghassabi z.r.ghassabi@gmail.com Tehran shomal University Spring 2015 z.r.ghassabi@gmail.com Digital Image Processing Session 3 1](https://reader033.vdocuments.us/reader033/viewer/2022061604/56649e855503460f94b882b3/html5/thumbnails/45.jpg)
Histogram Modification
• Histogram Stretching• Histogram Shrink• Histogram Sliding
![Page 46: Dr. Z. R. Ghassabi z.r.ghassabi@gmail.com Tehran shomal University Spring 2015 z.r.ghassabi@gmail.com Digital Image Processing Session 3 1](https://reader033.vdocuments.us/reader033/viewer/2022061604/56649e855503460f94b882b3/html5/thumbnails/46.jpg)
Histogram Stretching
Stretch (I(r,c))
is the largest gray-value in the image I(r,c)
is the smallest gray-level in I(r,c)
(for an 8-bit image these are 0 and 255)
![Page 47: Dr. Z. R. Ghassabi z.r.ghassabi@gmail.com Tehran shomal University Spring 2015 z.r.ghassabi@gmail.com Digital Image Processing Session 3 1](https://reader033.vdocuments.us/reader033/viewer/2022061604/56649e855503460f94b882b3/html5/thumbnails/47.jpg)
Histogram Stretching
![Page 48: Dr. Z. R. Ghassabi z.r.ghassabi@gmail.com Tehran shomal University Spring 2015 z.r.ghassabi@gmail.com Digital Image Processing Session 3 1](https://reader033.vdocuments.us/reader033/viewer/2022061604/56649e855503460f94b882b3/html5/thumbnails/48.jpg)
Histogram Stretching
![Page 49: Dr. Z. R. Ghassabi z.r.ghassabi@gmail.com Tehran shomal University Spring 2015 z.r.ghassabi@gmail.com Digital Image Processing Session 3 1](https://reader033.vdocuments.us/reader033/viewer/2022061604/56649e855503460f94b882b3/html5/thumbnails/49.jpg)
Histogram Shrinking
Shrink (I(r,c))
is the largest gray-value in the image I(r,c)
is the smallest gray-level in I(r,c)
![Page 50: Dr. Z. R. Ghassabi z.r.ghassabi@gmail.com Tehran shomal University Spring 2015 z.r.ghassabi@gmail.com Digital Image Processing Session 3 1](https://reader033.vdocuments.us/reader033/viewer/2022061604/56649e855503460f94b882b3/html5/thumbnails/50.jpg)
Histogram Shrinking
![Page 51: Dr. Z. R. Ghassabi z.r.ghassabi@gmail.com Tehran shomal University Spring 2015 z.r.ghassabi@gmail.com Digital Image Processing Session 3 1](https://reader033.vdocuments.us/reader033/viewer/2022061604/56649e855503460f94b882b3/html5/thumbnails/51.jpg)
Histogram Sliding
![Page 52: Dr. Z. R. Ghassabi z.r.ghassabi@gmail.com Tehran shomal University Spring 2015 z.r.ghassabi@gmail.com Digital Image Processing Session 3 1](https://reader033.vdocuments.us/reader033/viewer/2022061604/56649e855503460f94b882b3/html5/thumbnails/52.jpg)
Histogram Equalization
بین بودن Uو xتناظر صعودی .CDFاکیدا هست تابع بودن صعودی اکیدا یعنی CDFبرای آن مشتق .PDFباید باشد صفر از بزرگتر همیشه
F: X-------->[0,1] U=F(X)
. دارد هم معکوس پس هست یک به یک تابع X=F-1(U)چون
x
1
0
CDF
U تصادفی متغیر
![Page 53: Dr. Z. R. Ghassabi z.r.ghassabi@gmail.com Tehran shomal University Spring 2015 z.r.ghassabi@gmail.com Digital Image Processing Session 3 1](https://reader033.vdocuments.us/reader033/viewer/2022061604/56649e855503460f94b882b3/html5/thumbnails/53.jpg)
Histogram Equalization
10 ),( rrTs
10 ),(1 ssTr
![Page 54: Dr. Z. R. Ghassabi z.r.ghassabi@gmail.com Tehran shomal University Spring 2015 z.r.ghassabi@gmail.com Digital Image Processing Session 3 1](https://reader033.vdocuments.us/reader033/viewer/2022061604/56649e855503460f94b882b3/html5/thumbnails/54.jpg)
Histogram Equalization
و همیشه x مستقل از مقدار uتوزیع آماری • و یک هست.0یکنواخت بین
• u~U(0,1)•X و یک توزیع میکند.0 های ورودی را بین
Uهیستوگرام
![Page 55: Dr. Z. R. Ghassabi z.r.ghassabi@gmail.com Tehran shomal University Spring 2015 z.r.ghassabi@gmail.com Digital Image Processing Session 3 1](https://reader033.vdocuments.us/reader033/viewer/2022061604/56649e855503460f94b882b3/html5/thumbnails/55.jpg)
Histogram Equalization
r
1
0
CDFS=T(r)
PDFPr
منحنی زیر سطح
S~U(0,1)
Uهیستوگرام
ورودی تصویر هیستوگرام
ورودی تصویر rروشنایی
𝑠=∫0
𝑟
𝑃𝑟 (𝜌 )𝑑 𝜌
![Page 56: Dr. Z. R. Ghassabi z.r.ghassabi@gmail.com Tehran shomal University Spring 2015 z.r.ghassabi@gmail.com Digital Image Processing Session 3 1](https://reader033.vdocuments.us/reader033/viewer/2022061604/56649e855503460f94b882b3/html5/thumbnails/56.jpg)
Histogram Equalization
r
1
0
CDFS=T(r)
PDFPr
ورودی تصویر rروشنایی
ورودی تصویر هیستوگرام
h 𝑖𝑠𝑡𝑜𝑔𝑟𝑎𝑚 :(𝑟 𝑗 ,𝑛 𝑗)
Pr {𝑟=𝑟 𝑗 }=𝑛 𝑗
𝑛𝑆 𝑗=∑
𝑘=0
𝑗 𝑛 𝑗
𝑛≤ 1
![Page 57: Dr. Z. R. Ghassabi z.r.ghassabi@gmail.com Tehran shomal University Spring 2015 z.r.ghassabi@gmail.com Digital Image Processing Session 3 1](https://reader033.vdocuments.us/reader033/viewer/2022061604/56649e855503460f94b882b3/html5/thumbnails/57.jpg)
Histogram Equalization
![Page 58: Dr. Z. R. Ghassabi z.r.ghassabi@gmail.com Tehran shomal University Spring 2015 z.r.ghassabi@gmail.com Digital Image Processing Session 3 1](https://reader033.vdocuments.us/reader033/viewer/2022061604/56649e855503460f94b882b3/html5/thumbnails/58.jpg)
Histogram Equalization
![Page 59: Dr. Z. R. Ghassabi z.r.ghassabi@gmail.com Tehran shomal University Spring 2015 z.r.ghassabi@gmail.com Digital Image Processing Session 3 1](https://reader033.vdocuments.us/reader033/viewer/2022061604/56649e855503460f94b882b3/html5/thumbnails/59.jpg)
MATLAB Tutorial
• histeq(I)
![Page 60: Dr. Z. R. Ghassabi z.r.ghassabi@gmail.com Tehran shomal University Spring 2015 z.r.ghassabi@gmail.com Digital Image Processing Session 3 1](https://reader033.vdocuments.us/reader033/viewer/2022061604/56649e855503460f94b882b3/html5/thumbnails/60.jpg)
Histogram Equalization
![Page 61: Dr. Z. R. Ghassabi z.r.ghassabi@gmail.com Tehran shomal University Spring 2015 z.r.ghassabi@gmail.com Digital Image Processing Session 3 1](https://reader033.vdocuments.us/reader033/viewer/2022061604/56649e855503460f94b882b3/html5/thumbnails/61.jpg)
Adaptive Contrast Enhancement (ACE)
𝐴𝐶𝐸=𝑘1[ 𝑚𝐼 (𝑟 , 𝑐 )
𝜎𝐿 (𝑟 ,𝑐) ] [ 𝐼 (𝑟 ,𝑐 ) −𝑚𝐿(𝑟 ,𝑐 )]+𝑘2(𝑚𝐿(𝑟 ,𝑐 ))
𝑚𝐿 (𝑟 ,𝑐 ) :𝑚𝑒𝑎𝑛 𝑓𝑜𝑟 𝑡 h𝑒𝑒𝑛𝑡𝑖𝑟𝑒𝑖𝑚𝑎𝑔𝑒 𝐼 (𝑟 ,𝑐 )
: Local standard Deviation (in the window under consideration)
= Local mean (average mean in the window under consideration)
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Adaptive Contrast Enhancement (ACE)
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Adaptive Contrast Enhancement (ACE)
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MATLAB Tutorial
• I2=adapthisteq( I,'clipLimit',0.015,'Distribution','rayleigh');
clear all;close all;clc; [f1, pp1] = uigetfile('*.jpg', 'Pick a image');I1Name = sprintf('%s%s',pp1,f1); I=imread(I1Name); if ndims(I)==3 I1=rgb2gray(I);end I2=adapthisteq( I1,'clipLimit',0.015,'Distribution','rayleigh'); figure(); subplot(1,2,1); imshow(I1); subplot(1,2,2); imshow(I2);
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Adaptive Histogram Equalization
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Histogram Matchingpr
pz
𝜇
exp (Histeq(I,hgram)
exp (
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Histogram matching:Obtain the histogram of the given image, s=T(r)
Precompute a mapped level Sk for each level rk
Obtain the transformation function G from the given pz(z)
Precompute Zk for each value of rk
Map rk to its corresponding level Sk; then map level Sk into the final level Zk
Histogram Matching
1,...,2,1,0 )],([1 LkrTGz kk
r
S
0
CDFS=T(r)PDF
Pr
rهیستوگرام تصویر ورودی
0
pz
هیستوگرام دلخواه
1,...,2,1,0 ,)()1()(0
LkszpLzG k
k
iizk
1,...,2,1,0 ,)1()()1()(00
Lkn
nLrpLrTs
k
j
jk
jjrkk
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Histogram Matching (Specification)
هیستوگرام طوری تبدیل شود که دارای مقادیر مشخص شده 64*64برای یک تصویر باشد. bدر شکل
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Histogram Matching (Specification)
S0=1 , G(z3)=1, s0--- >z3هر پیکسلی که مقدارش در تصویر تعدیل هیستوگرام یک هست
.به مقداری برابر سه در هیستوگرام مشخص شده نگاشت می شود
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Image is dominated by large, dark areas, resulting in a histogram characterized by a large concentration of pixels in pixels in the dark end of the gray scale
Histogram Matching (Specification)
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Notice that the output histogram’s low end has shifted right toward the lighter region of the gray scale as desired.
Histogram Matching (Specification)
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Desired
Initial CDF Modified CDF
Histogram Matching (Specification)
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Local Histogram Processing
a) Original image b) global histogram equalization c) local histogram equalization using 7x7 neighborhood.
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Histogram using a local 3*3 neighborhood
Local Histogram Processing
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Use of histogram statistics for image enhancement:r denotes a discrete random variable
P(ri) denotes the normalized histogram component corresponding to the i th value of r
Mean:
The nth moment:
The second moment:
1
0
)(L
iii rprm
1
0
)()()(L
ii
nin rpmrr
1
0
22 )()()(
L
iii rpmrr
Using Histogram Statistics
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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
Using Histogram Statistics
rs,t is the gray level at coordinates (s,t) in the neighborhood
P(rs,t) is the neighborhood normalized histogram component
mean:
local variance:
xy
xySts
tstsS rprm),(
,, )(
xy
xyxySts
tsStsS rpmr),(
,2
,2 )(][
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Mapping:
E,K0,K1,K2 are specified parameters
MG is the global mean
DG is the global standard deviation
Using Histogram Statistics
0 1 2. , , ,,
, .S G G S GE f x y m x y K M and k D x y k D
g x yf x y OW
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• A SEM sample images:
Using Histogram Statistics
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Local Mean Local Var E or one
Using Histogram Statistics
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• Enhanced Images:
Using Histogram Statistics
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Fundamental of Spatial Filtering
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Fundamental 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
yxfwyxg
a
as
b
bt
tysxftswyxg ),(),(),( -a
+a
-b +b
Image size: M×N, x= 0,1,2,…,M-1 and y= 0,1,2,…,N-1Mask size: m×n, a=(m-1)/2 and b=(n-1)/2
Correlation
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Fundamental of Spatial Filtering
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Spatial Correlation and Convolution
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Spatial Correlation and Convolution
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9
1
992211
...
iii zw
zwzwzwR
Vector Representation of Linear FilteringVector Representation of Linear Filtering
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Smoothing Linear Filters :Noise reductionSmoothing of false contoursReduction of irrelevant detail
9
19
1
iizR
Smoothing Spatial Filters
a
as
b
bt
a
as
b
bt
tsw
tysxftswyxg
),(
),(),(),(
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Image smoothing with masks of various sizes.
Smoothing Spatial Filters
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Smoothing Spatial FiltersSmoothing Spatial Filters
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MATLAB Tutorial
• W=repmat(1/9,3,3);• W=1/9*ones(3,3);
• a=2;• W=ones(2*a+1)• W=W/sum(W(:));
• Img1=imread(‘image1.jpg’);• Img2=imfilter(Img1,W);
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MATLAB Tutorial
• Img2=imfilter(Img1,W,’symmetric’);
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Order-statistic filters:Max
Min
Median filter: Replace the value of a pixel by the median of the gray levels in the neighborhood of that pixel
Noise-reduction
Order-Static (Nonlinear) Filters
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Median Filter
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The first-order derivative:
The second-order derivative
)()1( xfxfx
f
)(2)1()1(2
2
xfxfxfx
f
Sharpening Spatial Filters
Zero in flat regionNon-zero at start of step/ramp regionNon-zero along ramp
Zero in flat regionNon-zero at start/end of step/ramp regionZero along ramp
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Sharpening Spatial Filters
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Sharpening Spatial Filters
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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
Sharpening Spatial Filters
2 1, , 1 1, , 1 4 ,f f x y f x y f x y f x y f x y
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Sharpening Spatial Filters
Practically use:
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2
2
, ,,
, ,
f x y f x y signg x y
f x y f x y sign
0 1 0
1 5 1 90
0 1 0
isotropic
1 1 1
1 9 1 45
1 1 1
isotropic
Sharpening Spatial Filters
0 1 0
1 4 1 90
0 1 0
isotropic
1 1 1
1 8 1 45
1 1 1
isotropic
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Sharpening Spatial Filters
2
2
, ,,
, ,
f x y f x y signg x y
f x y f x y sign
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Sharpening Spatial FiltersTwo L. Mask
SEM image
a. Mask Result b. Mask Result
(Sharper)
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Unsharp maskingSubtract a blurred version of an image from the image itself
f(x,y) : The image, fN (x,y): The blurred image
High boost Filtering:
),(),(),( yxfyxfyxgmask
),(*),(),( yxgkyxfyxg mask 1, k
),(*),(),( yxgkyxfyxg mask 1, k
Unsharp Masking and Highboost Filtering
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Unsharp Masking and Highboost Filtering
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2
2
, ,,
, , , , 1
, 1 , ,
, ,HB
HB
HB S
Af x y f x
f x y Af x y f x y A
f x y A
y signf x y
Af x y f x y sig
f x y f x y
n
Unsharp Masking and Highboost Filtering
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Original Laplacian (A=0)
Laplacian (A=1) Laplacian (A=1.7)
Unsharp Masking and Highboost Filtering
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Using first-order derivatives for (nonlinear) image sharpening, The gradient:The gradient:
The magnitude is rotation invariant (isotropic)
y
fx
f
g
g
y
xf
2
122
21
22
)(mag),(
y
f
x
f
GGyxM yxf
yx ggyxM ),(
Using First-Order Derivative for (Nonlinear) Image Sharpening - The Gradient
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Roberts Cross Gradient
Sobel
(2 1 for prewitt)
)( 59 zzg x )( 68 zzg y and
21
268
259 )()(),( zzzzyxM
6859),( zzzzyxM
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Using the Gradient for Image Sharpening
Sobel Gradient
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Bone Scan Laplacian
Original +Laplacian Soble of
Original
Combining Spatial Enhancement Tools
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Smoothed Sobel (Orig. + L.)*S.Sobel
Orig.+
(Orig. + L.)*S.SobelApply Power-Law
Combining Spatial Enhancement Tools
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• Img0=im2double(img0);
• w=fspecial(type, parameters)• W=fspecial(‘disk’,3);• W=fspecial(‘gaussian’,101,10);• W=fspecial(‘laplacian’,0);• W=fspecial(‘log’,10,1);
• Img1=imfilter(Img0,W);• figure();imshow(normalize(Img1));• C=-1; figure();imshow(img0+C*Img1);
• Wp=fspecial(‘prewitt’); Ws=fspecial(‘prewitt’);• Img1=imfilter(Img0,Wp); Img2=imfilter(Img0,Ws);
• W=0.3*Wp+0.7*Ws; Img1=imfilter(Img0,W);
• Img1=imfilter(Img0,Wp); Img2=imfilter(Img0,Wp’);• Imshow(sqrt(Img1.^2+Img2.^2)
MATLAB Tutorial
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function XN=Normalize(X) Xmin=min(X(:)); Xmax=max(X(:)); XN=((X-Xmin)/(Xmax-Xmin)).^beta;end
MATLAB Tutorial
![Page 114: Dr. Z. R. Ghassabi z.r.ghassabi@gmail.com Tehran shomal University Spring 2015 z.r.ghassabi@gmail.com Digital Image Processing Session 3 1](https://reader033.vdocuments.us/reader033/viewer/2022061604/56649e855503460f94b882b3/html5/thumbnails/114.jpg)
Img0=im2double(imread(‘….’));M=3;N=5;Domain=ones(M,N);Img1=ordfilt2(img0,M*N, Domain);Img2=ordfilt2(img0,0, Domain);Img3=ordfilt2(img0,(M+N+1)/2, Domain);
figure(); subplot(1,3,1); imshow(Img1);subplot(1,3,2); imshow(Img2);subplot(1,3,3); imshow(Img3);
MATLAB Tutorial
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Img0=im2double(imread(‘….’));M=3;N=5;Domain=ones(M,N);Img1=imnoise(img0,’salt & pepper’);Img2=ordfilt2(img1,(M+N+1)/2, Domain);Img3=medfilt2(img1,[M N]);
figure(); subplot(2,2,1); imshow(Img0);subplot(2,2,2); imshow(Img1);subplot(2,2,3); imshow(Img2);subplot(2,2,3); imshow(Img3);
MATLAB Tutorial
![Page 116: Dr. Z. R. Ghassabi z.r.ghassabi@gmail.com Tehran shomal University Spring 2015 z.r.ghassabi@gmail.com Digital Image Processing Session 3 1](https://reader033.vdocuments.us/reader033/viewer/2022061604/56649e855503460f94b882b3/html5/thumbnails/116.jpg)
MATLAB Tutorial• MATLAB Command:
– Image Statistics:• means2, std2, corr2, imhist, regionprops
– Image Intensity Adjustment:• imadjust, histeq, adapthisteq, imnoise
– Linear Filter:• imfilter, fspecial, conv2, corr2,
– Nonlinear filter:• medfilt2, ordfilt2,
![Page 117: Dr. Z. R. Ghassabi z.r.ghassabi@gmail.com Tehran shomal University Spring 2015 z.r.ghassabi@gmail.com Digital Image Processing Session 3 1](https://reader033.vdocuments.us/reader033/viewer/2022061604/56649e855503460f94b882b3/html5/thumbnails/117.jpg)
MATLAB Tutorial
![Page 118: Dr. Z. R. Ghassabi z.r.ghassabi@gmail.com Tehran shomal University Spring 2015 z.r.ghassabi@gmail.com Digital Image Processing Session 3 1](https://reader033.vdocuments.us/reader033/viewer/2022061604/56649e855503460f94b882b3/html5/thumbnails/118.jpg)
End of Session 3