lecture eight matlab for spatial filtering and intro to dfts figures from gonzalez and woods,...

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Lecture Eight Matlab for spatial filtering and intro to DFTs Figures from Gonzalez and Woods, Digital Image Processing, Copyright 2002, Gonzalez, Woods, and Eddins, Digital Image Processing with MATLAB, Copyright, 2004, and Jahne, Digital Image Processing, 4 th Edition, Copyright, 1997

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Page 1: Lecture Eight Matlab for spatial filtering and intro to DFTs Figures from Gonzalez and Woods, Digital Image Processing, Copyright 2002, Gonzalez, Woods,

Lecture Eight

Matlab for spatial filtering and intro to DFTsFigures from Gonzalez and Woods, Digital Image Processing, Copyright 2002, Gonzalez,

Woods, and Eddins, Digital Image Processing with MATLAB, Copyright, 2004, and

Jahne, Digital Image Processing, 4th Edition, Copyright, 1997

Page 2: Lecture Eight Matlab for spatial filtering and intro to DFTs Figures from Gonzalez and Woods, Digital Image Processing, Copyright 2002, Gonzalez, Woods,

Imadjust

g=imadjust(f,[low_in,high_in],[low_out,high_out],gamma)

Includes various contract transformations.

Page 3: Lecture Eight Matlab for spatial filtering and intro to DFTs Figures from Gonzalez and Woods, Digital Image Processing, Copyright 2002, Gonzalez, Woods,

Chapter 3Intensity Transformations

and Spatial Filtering

Chapter 3Intensity Transformations

and Spatial Filtering

Page 4: Lecture Eight Matlab for spatial filtering and intro to DFTs Figures from Gonzalez and Woods, Digital Image Processing, Copyright 2002, Gonzalez, Woods,

Logarithmic and Constrast Transformations

g=c*log(1+double(f))

gs=im2uint8(mat2gray(g)); % to range [0,1] and to gray scale

Contrast transformation

g=1./(1+(m./(double(f)+eps)).^E)

Use of eps prevents overflow if f has any zero values

m is turning point

Page 5: Lecture Eight Matlab for spatial filtering and intro to DFTs Figures from Gonzalez and Woods, Digital Image Processing, Copyright 2002, Gonzalez, Woods,

Chapter 3Intensity Transformations

and Spatial Filtering

Chapter 3Intensity Transformations

and Spatial Filtering

Page 6: Lecture Eight Matlab for spatial filtering and intro to DFTs Figures from Gonzalez and Woods, Digital Image Processing, Copyright 2002, Gonzalez, Woods,

Stem and plot

Find out syntax from typing help stem and help plot in MATLAB.

Page 7: Lecture Eight Matlab for spatial filtering and intro to DFTs Figures from Gonzalez and Woods, Digital Image Processing, Copyright 2002, Gonzalez, Woods,

Chapter 3Intensity Transformations

and Spatial Filtering

Chapter 3Intensity Transformations

and Spatial Filtering

Page 8: Lecture Eight Matlab for spatial filtering and intro to DFTs Figures from Gonzalez and Woods, Digital Image Processing, Copyright 2002, Gonzalez, Woods,

Histeq command

g=histeq(f,hspec)

hspec is a specified histogram.

If you do

g=histeq(f,256) you get histogram equalization.

Page 9: Lecture Eight Matlab for spatial filtering and intro to DFTs Figures from Gonzalez and Woods, Digital Image Processing, Copyright 2002, Gonzalez, Woods,

Chapter 3Intensity Transformations

and Spatial Filtering

Chapter 3Intensity Transformations

and Spatial Filtering

Page 10: Lecture Eight Matlab for spatial filtering and intro to DFTs Figures from Gonzalez and Woods, Digital Image Processing, Copyright 2002, Gonzalez, Woods,

Chosen Histgram

small one large, one peaks,Gaussian edconcentrat Two

05.0 ,75.0 ,15.0 ,07.0a ,1a

chosen Values

)2/)(exp(2

)2/)(exp(2

)(

212121

222

2

2211

1

1

kza

za

zp

Page 11: Lecture Eight Matlab for spatial filtering and intro to DFTs Figures from Gonzalez and Woods, Digital Image Processing, Copyright 2002, Gonzalez, Woods,

Chapter 3Intensity Transformations

and Spatial Filtering

Chapter 3Intensity Transformations

and Spatial Filtering

Page 12: Lecture Eight Matlab for spatial filtering and intro to DFTs Figures from Gonzalez and Woods, Digital Image Processing, Copyright 2002, Gonzalez, Woods,

Spatial Filters

g=imfilter(f,w,mode,bndry,size)

Mode= ‘corr’ correlation—standard

‘conv’ convolution, w rotated

180 degrees

Page 13: Lecture Eight Matlab for spatial filtering and intro to DFTs Figures from Gonzalez and Woods, Digital Image Processing, Copyright 2002, Gonzalez, Woods,

Chapter 3Intensity Transformations

and Spatial Filtering

Chapter 3Intensity Transformations

and Spatial Filtering

Page 14: Lecture Eight Matlab for spatial filtering and intro to DFTs Figures from Gonzalez and Woods, Digital Image Processing, Copyright 2002, Gonzalez, Woods,

Chapter 3Intensity Transformations

and Spatial Filtering

Chapter 3Intensity Transformations

and Spatial Filtering

Page 15: Lecture Eight Matlab for spatial filtering and intro to DFTs Figures from Gonzalez and Woods, Digital Image Processing, Copyright 2002, Gonzalez, Woods,

Chapter 3Intensity Transformations

and Spatial Filtering

Chapter 3Intensity Transformations

and Spatial Filtering

Page 16: Lecture Eight Matlab for spatial filtering and intro to DFTs Figures from Gonzalez and Woods, Digital Image Processing, Copyright 2002, Gonzalez, Woods,

Chapter 3Intensity Transformations

and Spatial Filtering

Chapter 3Intensity Transformations

and Spatial Filtering

Page 17: Lecture Eight Matlab for spatial filtering and intro to DFTs Figures from Gonzalez and Woods, Digital Image Processing, Copyright 2002, Gonzalez, Woods,

Chapter 3Intensity Transformations

and Spatial Filtering

Chapter 3Intensity Transformations

and Spatial Filtering

Page 18: Lecture Eight Matlab for spatial filtering and intro to DFTs Figures from Gonzalez and Woods, Digital Image Processing, Copyright 2002, Gonzalez, Woods,

Chapter 3Intensity Transformations

and Spatial Filtering

Chapter 3Intensity Transformations

and Spatial Filtering

Page 19: Lecture Eight Matlab for spatial filtering and intro to DFTs Figures from Gonzalez and Woods, Digital Image Processing, Copyright 2002, Gonzalez, Woods,

Fourier Transforms

Based on notion Fourier introduced to Heat transfer that any periodic function can be written as a possibly infinite sum of sines and cosines. Important in

• Differential equations• Probability and statistics (characteristic functions, proof

of central limit theorem)• Almost any area of engineering you can name.

Page 20: Lecture Eight Matlab for spatial filtering and intro to DFTs Figures from Gonzalez and Woods, Digital Image Processing, Copyright 2002, Gonzalez, Woods,

Chapter 4Image Enhancement in the

Frequency Domain

Chapter 4Image Enhancement in the

Frequency Domain

Page 21: Lecture Eight Matlab for spatial filtering and intro to DFTs Figures from Gonzalez and Woods, Digital Image Processing, Copyright 2002, Gonzalez, Woods,

Chapter 4Image Enhancement in the

Frequency Domain

Chapter 4Image Enhancement in the

Frequency Domain

Page 22: Lecture Eight Matlab for spatial filtering and intro to DFTs Figures from Gonzalez and Woods, Digital Image Processing, Copyright 2002, Gonzalez, Woods,

Chapter 4Image Enhancement in the

Frequency Domain

Chapter 4Image Enhancement in the

Frequency Domain

Page 23: Lecture Eight Matlab for spatial filtering and intro to DFTs Figures from Gonzalez and Woods, Digital Image Processing, Copyright 2002, Gonzalez, Woods,

Chapter 4Image Enhancement in the

Frequency Domain

Chapter 4Image Enhancement in the

Frequency Domain

Page 24: Lecture Eight Matlab for spatial filtering and intro to DFTs Figures from Gonzalez and Woods, Digital Image Processing, Copyright 2002, Gonzalez, Woods,

Chapter 4Image Enhancement in the

Frequency Domain

Chapter 4Image Enhancement in the

Frequency Domain

Page 25: Lecture Eight Matlab for spatial filtering and intro to DFTs Figures from Gonzalez and Woods, Digital Image Processing, Copyright 2002, Gonzalez, Woods,

Chapter 4Image Enhancement in the

Frequency Domain

Chapter 4Image Enhancement in the

Frequency Domain

Page 26: Lecture Eight Matlab for spatial filtering and intro to DFTs Figures from Gonzalez and Woods, Digital Image Processing, Copyright 2002, Gonzalez, Woods,

Fourier Spectrum and Phase

Two images

• Mix up phase and amplitude

Page 27: Lecture Eight Matlab for spatial filtering and intro to DFTs Figures from Gonzalez and Woods, Digital Image Processing, Copyright 2002, Gonzalez, Woods,

Two pictures from another text

Page 28: Lecture Eight Matlab for spatial filtering and intro to DFTs Figures from Gonzalez and Woods, Digital Image Processing, Copyright 2002, Gonzalez, Woods,

Mix up amplitude and phase

Amplitude from 1, phase from 2, amplitude from 2, phase from one.