Tutorial 1Basic Image Processing Concepts

Alexandre Kassel

Introduction to Medical Imaging

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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!