Under Supervision of Dr. Kamel A. ArramEng. Lamiaa Said

Wed. 14-04-2010

Wed. 14-04-2010

Lecture Main Points

Introduction to Image Transforms

Distance Transform

Fourier Transform

Hough Transform

Conclusion & Questions

Wed. 14-04-2010

Lecture Main Points

Introduction to Image Transforms

Distance Transform

Fourier Transform

Hough Transform

Conclusion & Questions

1. Introduction

• What is the language meaning of Image Transform ?

1. Introduction

• Image Transform :

changing the way of the image representation.

1. Introduction

• What is the physical meaning of Image Transform ?

1. Introduction

• 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

1. Introduction

• 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.

Wed. 14-04-2010

Lecture Main Points

Introduction to Image Transforms

Distance Transform

Fourier Transform

Hough Transform

Conclusion & Questions

2. Distance Transform

• 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.

2. Distance Transform

Input (Binary Image ) Output (gray Image )

2. Distance Transform

• How it works ?

Input (Binary Image ) Output (gray Image )

2. Distance Transform

• How it works ?

Input Matrix Output Matrix

2. Distance Transform

• 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).

2. Distance Transform

• How it works ?

Input Matrix Output Matrix

2. Distance Transform

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

Input Matrix

0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 1 1 1 1 1 1 1 1 1 0 0

0 0 1 1 1 1 1 1 1 1 1 0 0

0 0 1 1 1 1 1 1 1 1 1 0 0

0 0 1 1 1 1 1 1 1 1 1 0 0

0 0 1 1 1 1 1 1 1 1 1 0 0

0 0 1 1 1 1 1 1 1 1 1 0 0

0 0 1 1 1 1 1 1 1 1 1 0 0

0 0 1 1 1 1 1 1 1 1 1 0 0

0 0 1 1 1 1 1 1 1 1 1 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0

2. Distance Transform

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

Input Matrix

0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 1 1 1 1 1 1 1 1 1 0 0

0 0 1 2 2 2 2 2 2 2 1 0 0

0 0 1 2 3 3 3 3 3 2 1 0 0

0 0 1 2 3 4 4 4 3 2 1 0 0

0 0 1 2 3 4 5 4 3 2 1 0 0

0 0 1 2 3 4 4 4 3 2 1 0 0

0 0 1 2 3 3 3 3 3 2 1 0 0

0 0 1 2 2 1 2 2 2 2 1 0 0

0 0 1 1 1 1 1 1 1 1 1 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 1 1 1 1 1 1 1 1 1 0 0

0 0 1 1 1 1 1 1 1 1 1 0 0

0 0 1 1 1 1 1 1 1 1 1 0 0

0 0 1 1 1 1 1 1 1 1 1 0 0

0 0 1 1 1 1 1 1 1 1 1 0 0

0 0 1 1 1 1 1 1 1 1 1 0 0

0 0 1 1 1 1 1 1 1 1 1 0 0

0 0 1 1 1 1 1 1 1 1 1 0 0

0 0 1 1 1 1 1 1 1 1 1 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0

Output Matrix

2. Distance Transform

What if the image was a gray image ??

2. Distance Transform

What if the image was a gray image ??

Output (gray Image )Intermediate (Binary Image )

Input (gray Image )

2. Distance Transform

• D.T applications : 1) Blurring.

Input Image Output Blurred Image

2. Distance Transform

• D.T applications : 2) Skeletonizing

Input Image Output Skeleton

Wed. 14-04-2010

Lecture Main Points

Introduction to Image Transforms

Distance Transform

Fourier Transform

Hough Transform

Conclusion & Questions

3. Fourier Transform

• What is Fourier Transform ?

3. 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 or frequency 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.

3. Fourier Transform

• Fast Fourier Transform 2D Equation :

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

3. Fourier Transform

• Fast Fourier Transform 2D :

A Box and its DFT

3. Fourier Transform

• 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

3. Fourier Transform

• 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 ?

3. Fourier Transform

• 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

3. Fourier Transform

• Fourier Transform Code:

A C# Fourier Transform Code http://www.codeproject.com/KB/GDI/FFT.aspx

Wed. 14-04-2010

Lecture Main Points

Introduction to Image Transforms

Distance Transform

Fourier Transform

Hough Transform

Conclusion & Questions

4. Hough Transform

• What is Hough Transform ?

4. 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.

4. Hough Transform

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

4. Hough Transform

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

4. Hough Transform

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

4. Hough Transform

• Hough Theory :

4. Hough Transform

• Hough Theory :

Edge detection for the shape

4. Hough Transform

• Hough Theory :

Determine the points at the ends of the lines

4. Hough Transform

• 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.

4. Hough Transform

• Hough Theory :

• Then calculate the value of theta from the equation :

4. Hough Transform

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

4. Hough Transform

• 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.

Wed. 14-04-2010

Lecture Main Points

Introduction to Image Transforms

Distance Transform

Fourier Transform

Hough Transform

Conclusion & Questions

5. Conclusion

1

2 3

Image Transform

s

Distance Transform

Fourier Transform

Hough Transform

5. Conclusion

Distance

Transform

Quite similar to the binary images erosion.Input : Binary Image Output : Gray Image Uses : Skeleton , Binary Blurring

5. Conclusion

Fourier

Transform

Used to convert the image to a series of Sin and Cosine WavesInput : Spatial domain Image Output : frequency domain Image Uses : Image Filtering , Image Analysis

5. Conclusion

Hough

Transform

Used to extract features form the shapes in the imageInput : edge detected imageOutput : edge detected image + (r , theta) for every pointUses : features extraction.

6. Questions

7. References

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

8. Assignment

Prepared and Presented By

NaDeR Mostafa 4th year , C.S Department

Wed. 14-04-2010