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Image Transforms

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Image Transforms

Under Supervision of

Dr. Kamel A. Arram

Eng. Lamiaa Said

Introduction to Image Transforms

Distance Transform

Fourier Transform

Hough Transform

Conclusion & Questions

Introduction to Image Transforms

Distance Transform

Fourier Transform

Hough Transform

Conclusion & Questions

- What is the language meaning of Image Transform ?

- Image Transform :
changing the way of the image representation.

- What is the physical meaning of Image Transform ?

- Image Transform :
Image transforms can be simple / complex mathematical operations on images which convert images from one representation to another.

The output images characteristics is generally quite different from the characteristics of the input images. This difference might be in the geometry of the information in the image or the nature of the information itself

- Why Image Transform ?
- The main purpose of applying a transformation is to extract some desired information that is hard to extract using the original representation.

Introduction to Image Transforms

Distance Transform

Fourier Transform

Hough Transform

Conclusion & Questions

- What is Distance Transform ?
- A Distance Transform ( D.T ), also known as distance map or distance field, is a derived representation of a digital image.
- D.T only applied to binary images. The result of the transform is a graylevel image that looks similar to the input image, except that the graylevel intensities of points inside foreground regions are changed to show the distance to the closest boundary from each point.

Input (Binary Image )

Output (gray Image )

- How it works ?

Input (Binary Image )

Output (gray Image )

- How it works ?

Input Matrix

Output Matrix

- How it works ?
- 1) Determine the number of pixel between the corners and the center of the foreground .
- 2) Then scaling the new pixel values according to this number. (ascending to the center).

- How it works ?

Input Matrix

Output Matrix

- Another example … what will be the output of the next matrix ?

Input Matrix

- Another example … what will be the output of the next matrix ?

Output Matrix

Input Matrix

What if the image was a gray image ??

What if the image was a gray image ??

Input (gray Image )

Intermediate (Binary Image )

Output (gray Image )

- D.T applications :
1) Blurring.

Output Blurred Image

Input Image

- D.T applications :
2) Skeletonizing

Output Skeleton

Input Image

Introduction to Image Transforms

Distance Transform

Fourier Transform

Hough Transform

Conclusion & Questions

- What is Fourier Transform ?

- What is Fourier Transform ?
- The Fourier Transform is an important image processing tool which is used to decompose an image into its sine and cosine components.
- The output of the transformation represents the image in the Fourier orfrequency domain, while the input image is the spatial domain equivalent. In the Fourier domain image, each point represents a particular frequency contained in the spatial domain image.

- Fast Fourier Transform 2D Equation :

Where M is the image Width and N in the Image Height

- Fast Fourier Transform 2D :

A Box and its DFT

- Why Fourier Transform ?
- The Fourier Transform allows us to perform tasks which would be impossible to perform any other way; its efficiency allows us to perform other tasks more quickly. The Fourier Transform provides, among other things, a powerful alternative to linear spatial filtering; it is more efficiency to use the Fourier transform than a spatial filter for a large filter. The Fourier Transform also allows us to isolate and process particular image frequencies and so perform low-pass and high-pass filtering with a great degree of precision.
Digital Image Processing using Matlab

Alasdair McAndrew

- Fourier Transform applications :
- 1) Filtering : Blurring – edge detection – Sharpening
- 2) Removing Noise Specially Salt & Paper Noise.
- 3) Image analysis :
- extraction of meaningful information from images … How ?

- Fourier Transform applications :
- 1) Filtering : ex. Blurring

Input Image in Spatial Domain

Input Image in Freq. Domain

Blurring Filter in Freq. Domain

Output Image in Spatial Domain

- Fourier Transform Code:
- A C# Fourier Transform Code

http://www.codeproject.com/KB/GDI/FFT.aspx

Introduction to Image Transforms

Distance Transform

Fourier Transform

Hough Transform

Conclusion & Questions

- What is Hough Transform ?

- What is Hough Transform ?
The Hough transform (pronounced /ˈhʌf/ ) is a feature extraction technique used in image analysis, computer vision, and digital image processing.

The Hough transform is a technique which can be used to isolate features of a particular shape within an image. Because it requires that the desired features be specified in some parametric form.

- What is the problem in defining the shapes with its corner pixels only (the old way) ?

- The problem is that if one pixel in a corner is missed the whole shape may change.

- The problem is that if one pixel in a corner is missed the whole shape may change.

- Hough Theory :

- Hough Theory :

Edge detection for the shape

- Hough Theory :

Determine the points at the ends of the lines

- Hough Theory :
- For every point we determine r value from the equation :
- Where a and b are the coordinates of the center of the circle and is the radius.

- Hough Theory :
- Then calculate the value of theta from the equation :

- Consider that a noise has effected the shape through transmission :

- Solution:
- From the r and theta and only one given point we will draw the lines.
- Any intersection between the lines it will be a missing point.

Introduction to Image Transforms

Distance Transform

Fourier Transform

Hough Transform

Conclusion & Questions

1

2

3

Image Transforms

Hough Transform

Distance Transform

Fourier Transform

Distance Transform

Quite similar to the binary images erosion.

Input : Binary Image

Output : Gray Image

Uses : Skeleton , Binary Blurring

Fourier Transform

Used to convert the image to a series of Sin and Cosine Waves

Input : Spatial domain Image

Output : frequency domain Image

Uses : Image Filtering , Image Analysis

Hough Transform

Used to extract features form the shapes in the image

Input : edge detected image

Output : edge detected image + (r , theta) for every point

Uses : features extraction.

http://www.wavemetrics.com/products/IGORPro/imageprocessing/imagetransforms.htm

http://homepages.inf.ed.ac.uk/rbf/HIPR2/tranops.htm

http://en.wikipedia.org/wiki/Distance_transform

http://www.mathworks.com/access/helpdesk/help/toolbox/images/bwdist.html

http://en.wikipedia.org/wiki/Topological_skeletons

http://en.wikipedia.org/wiki/Hough_transform#Example

http://homepages.inf.ed.ac.uk/rbf/HIPR2/hough.htm

http://rkb.home.cern.ch/rkb/AN16pp/node122.html

http://www.codeproject.com/KB/GDI/FFT.aspx

Thank You !

Prepared and Presented By

NaDeR Mostafa

4th year , C.S Department