Digital Image Processing R.Gonzales R.Woods.
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Transcript of Digital Image Processing R.Gonzales R.Woods.
Tutorial 1Basic Image Processing Concepts
Alexandre Kassel
Introduction to Medical Imaging
046831
Tutorial Overview 2D Fourier Transform Some Basic Filters Some Matlab functions and definitions Introduction to Image Reconstruction
2D Fourier Transforms: Definition Continuous
Discrete
Inverse
𝐹 (𝑢 ,𝑣)=∬𝛺
𝑓 (𝑥 , 𝑦 )⋅𝑒¿ ¿¿
𝐹 (𝑢 ,𝑣)=∑𝑥=0
𝑀 −1
.∑𝑦=0
𝑁−1
𝑓 (𝑥 , 𝑦 )⋅ 𝑒− 2𝜋 𝑗 (𝑢𝑥𝑀 + 𝑣𝑦
𝑁 )𝑑𝑥𝑑𝑦
𝑓 (𝑥 , 𝑦)=1
𝑀𝑁 ∑𝑢=0
𝑀 −1
⋅∑𝑣=0
𝑁−1
𝐹 (𝑢 ,𝑣 )⋅𝑒2 𝑗 𝜋 (𝑢𝑥𝑀 +𝑣𝑦
𝑁 )
DFT Properties Summary
Digital Image ProcessingR.GonzalesR.Woods
Convolution and Correlation Convolution
Correlation
Digital Image ProcessingR.GonzalesR.Woods
DFT
DFT is insensitive to rotation
The sinc function main direction in Frequency space is orthogonal to the rectangle main direction.
Basic Filters : LPF
1/16 2/16 1/16
2/16 4/16 2/16
1/16 2/16 1/16
1/9 1/9 1/9
1/9 1/9 1/9
1/9 1/9 1/9
Average
Gaussian
Basic Filters : Mean vs Median
Average [3x3]
Median [3x3]
Basic Filters : Laplacian (HPF)
-1 -1 -1
-1 8 -1
-1 -1 -1
(Laplacian)
0 -1 0
-1 4 -1
0 -1 0
Another conventional form of Laplacian operator :
Basic Filters : Laplacian of Gaussian (BPF)
Laplacian Operator :
Laplacian of Gaussian :
0
5
10
15
20
02468101214161820-4
-3.5
-3
-2.5
-2
-1.5
-1
-0.5
0
0.5
1
x 10-3
Laplacian of Gaussian
Basic Filters : Laplacian of GaussianFiltered with Laplacian of Gaussian (absolute value)
Filtered with Laplacian of Gaussian (absolute value)
Basic Filters : Difference of Gaussians (DoG)
Very good approximation of LoG
Why is it a Band Pass Filter ?
Basic Filters : Gradient operators(Horizontal)
-1
1
-1 -1 -1
0 0 0
1 1 1
-1 -2 -1
0 0 0
1 2 1
Gradient Pewitt Sobel
Basic Filters : Gradient operators Similarly, there are vertical
operators We can (and should)
combine both Horizontal and Vertical operators
Beware the noise !Vetical and Horizontal absolute response to
Sobel Filter , threshold and combined
> threshold
Matlab : DICOM files Digital Imaging and Communications in Medicine
Universal standard file for medical images.dcm filedicominfo( ) : load the
DICOM structuredicomread( ) : load the
DICOM file imagedicomwrite ( ) : create a
DICOM file
Matlab : Shepp-Logan phantom
Human head model Standard test image Widely used in Image
Reconstruction testing Matlab function : phantom( )
Matlab : Data classes
Most used data classes in Image Processing double : Double-precision floating-point numbers
uint8 : Unsigned 8-bit integers [0,255]
logical : Black and White image [0,1]
Attention Be careful when using ‘==‘ with double data
Be careful with mathematical operation and filtering on uint8 data.
To show ‘double’ images use : imshow(I,[])
Matlab : Some Useful basic IP Functionsfft2 ( ), ifft2 : 2D Fourier transform , and inverse 2D Fourier transform
fspecial ( ) : Create a linear filter (convolution kernel) , includes some “built-in” basic filters (Average, Laplacian, LoG, Sobel …..)
imfilter ( ) : Image filtering with a kernel.
imadjust ( ) : Gamma correction
histeq( ) : Histogram equalization
medfilt2 ( ) : median filtering
imrotate ( ) : Image rotation
Imresize ( ) : Image resizing
imnoise ( ) : add different type of noise (Gaussian, uniform “Salt & Pepper”, Poisson)
interp2 ( ) : 2D interpolation
Next weeks in
Introduction to Medical Imaging Tutorials
Image Reconstruction
Teaser : Image Reconstruction
Regular Image :
Object LensReceptors Object
Image
Processing
photograph a slice of the human body !
But one does not simply…
We need to “build” the image
Teaser : Image ReconstructionIn X-Ray CT recomstruction , all we have is X-Ray absorption.
Unknown
Our goal is to “reconstruct”
an image from this raw data(We do many more
than 2 angles)
Teaser : Image Reconstruction
In MRI reconstruction, we reconstruct the image from 1D Radio-Frequence signal.
`
MRI devicePatient
Magnetic field generator
RFRF
Reconstruction
See you next week!