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Transportation Informatics Group, ALPEN-ADRIA University of Klagenfurt
Machine VisionMachine VisionTransportation Informatics Group
University of Klagenfurt
Alireza Fasih, 2009
12/24/2009 1Address: L4.2.02, Lakeside Park, Haus B04, Ebene 2, Klagenfurt-Austria
Transportation Informatics Group, ALPEN-ADRIA University of Klagenfurt
Image Processing & Transforms
Most image transform of interests are invertible
• the original image can be reconstructed from the transform without loss of information.
12/24/2009 2Ref: CCU Vision Laboratory
Transportation Informatics Group, ALPEN-ADRIA University of Klagenfurt
Image Transformations
1. Image Transformation are alternative ways of representing the information in an image
To exploit some image properties which are not available inTo exploit some image properties which are not available in the image domain.
Most commonly used in image processing, image compression, image editing.compression, image editing.
2. Common image transforms:
Fourier transform
Cosine transform
Wavelet transform
The most commonly used is the Fourier Transform !
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Transportation Informatics Group, ALPEN-ADRIA University of Klagenfurt
Fast Fourier Transform
The image is represented as a weighted set of spatial frequency.
The individual spatial frequencies are know as basis function.
There is no information lost in transforming an image into the Fourier domain.
One point in the Fourier domain representation of an image contains information about the entire imageinformation about the entire image.
The value of the point tells us how much of spatial frequency is in the image.
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Transportation Informatics Group, ALPEN-ADRIA University of Klagenfurt
Fourier Transform
You should have learned the basic of fourier transform from thecourse such as “signals and systems”, “differential equations” andg y“Electronic Circuit”
Only discrete Fourier transformation transform (DFT) related to 2-D image processing will be taught in detail2-D image processing will be taught in detail
DFT
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Transportation Informatics Group, ALPEN-ADRIA University of Klagenfurt
Introduction
Almost every function of practical interest can be expressed as a superposition of sinusoids
The form taken by superposition into sinusoidal components depends on whether the signal is periodic
Fourier series for periodic signalFourier series for periodic signal
Fourier transformation for aperiodic signals
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Transportation Informatics Group, ALPEN-ADRIA University of Klagenfurt
Fourier Transformation
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Transportation Informatics Group, ALPEN-ADRIA University of Klagenfurt
FFT in Matlab
• fft2 (x)This function return the two-dimensional discrete Fourier transformation of x.
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Filtering in Fourier Domain
Transportation Informatics Group, ALPEN-ADRIA University of Klagenfurt
Filtering in Fourier Domain
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High Pass Filtering by FFT
Transportation Informatics Group, ALPEN-ADRIA University of Klagenfurt
High-Pass Filtering by FFT
Input ImageHigh frequency domain
Mask
Mask
Input Image FFT Result after using Inverse FFT
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Transportation Informatics Group, ALPEN-ADRIA University of Klagenfurt
Low-Pass Filtering by FFTInput Image FFT Filtering Result after using Inverse FFT
Input Image FFT
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Transportation Informatics Group, ALPEN-ADRIA University of Klagenfurt
Low-Pass Filtering by FFT
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Shape Matching
Transportation Informatics Group, ALPEN-ADRIA University of Klagenfurt
Shape Matching
• Correlation Based Template Matching• FFT Based Template Matching• Geometric Based Shape Matching (Scale variant and Rotation
Variant )
Geometric Based Shape Matching
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Geometric Based Shape Matching
Template Matching
Transportation Informatics Group, ALPEN-ADRIA University of Klagenfurt
Template Matching
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Transportation Informatics Group, ALPEN-ADRIA University of Klagenfurt
FFT in Matlab and Template matchingRead in the sample imageRead in the sample image.
bw = imread('text.png');
Create a template for matching by extracting the letter "a" from the imageCreate a template for matching by extracting the letter a from the image.
a = bw(32:45,88:98);
You can also create the template image by using the interactive version of imcropYou can also create the template image by using the interactive version of imcrop.
The following figure shows both the original image and the template.
imshow(bw);imshow(bw);figure, imshow(a);
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Transportation Informatics Group, ALPEN-ADRIA University of Klagenfurt
FFT in Matlab and Pattern matching
C = real(ifft2( fft2(bw) .* fft2(rot90(a,2) ,256,256) ));
figure, imshow(C,[]) % Scale image to appropriate display range.
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FFT i M tl b d P tt t hi
Transportation Informatics Group, ALPEN-ADRIA University of Klagenfurt
FFT in Matlab and Pattern matching
T i th l ti f th t l t i th i fi d th i i l l d th d fi• To view the locations of the template in the image, find the maximum pixel value and then define a threshold value that is less than this maximum. The locations of these peaks are indicated by the white spots in the threshold correlation image. (To make the locations easier to see in this figure, the thresholded image has been dilated to enlarge the size of the points.)
max(C(:))
ans =
68.0000
thresh = 60; % Use a threshold that's a little less than max.thresh 60; % Use a threshold that s a little less than max.
figure, imshow(C > thresh)% Display showing pixels over
th h ldthreshold.
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Transportation Informatics Group, ALPEN-ADRIA University of Klagenfurt
Th k f tt tiThank you for your attention
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Transportation Informatics Group, ALPEN-ADRIA University of Klagenfurt
AppendixAppendix
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Transportation Informatics Group, ALPEN-ADRIA University of Klagenfurt
Discrete Fourier Transform
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Transportation Informatics Group, ALPEN-ADRIA University of Klagenfurt
2D - DFT
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