Document

```University of UD
Image processing
(spatial &frequency domain)
College of Science
Computer Science Department
2013-2014
E-mail: [email protected]
Computer
Graphics
Image process inspatial &frequency domain
Faculty of Physical and Basic Education
Computer Science Dep.
2014-2015
E-mail:
[email protected]
[email protected]
Lecturer: 14
Azhee W. MD.
Outline
 Image processing
 Image processing(spatial &frequency domain)
 Spatial Domain
 frequency domain
 Image Filtering in Spatial Domain
 Linear spatial filtering
 nonlinear spatial filtering
 median filter
 Image Filtering in Frequency Domain
 Low Pass Filtering
 Gaussian Low pass Filters
University of sulaimanyiah - Faculty of Physical and Basic Education - Computer Dep. 2012-2013
3
Image processing
 A technique in which the data from an image are
digitized and various mathematical operations are
applied to the data.
 generally with a digital computer, in order to
create an enhanced image that is more useful or
for special purpose like security , traffic ,
face recoganization ).
 or to perform some of the interpretation and
recognition tasks usually performed by humans,
also known as picture processing
University of sulaimanyiah - Faculty of Physical and Basic Education - Computer Dep. 2014-2015
4
Image processing(spatial &frequency domain)
The following diagram shows the image processing method in both spatial
and frequency domain.
LPF = Low Pass Filter (like, Ideal, Gaussian)
HPF= High Pass Filter (like, Ideal, Laplacian)
BPF= Band Pass Filter (like, Ideal, Stop)
University of sulaimanyiah - Faculty of Physical and Basic Education - Computer Dep. 2014-2015
5
Image processing (Spatial Domain)
 Spatial domain processing means that we are
performing operations on the intensity values
f(x, y) on the image .
Two principle categories:
Intensity transformation (Point independent)
Spatial filtering (Point dependent)
 Intensity transformation works on single pixels
independent of other pixels.
 Spatial filtering works on a neighborhood of
every pixel.
University of sulaimanyiah - Faculty of Physical and Basic Education - Computer Dep. 2014-2015
6
Image Filtering in Spatial Domain
 The value of a pixel with coordinates (x,y) in the
enhanced image is the result of performing some
operation on the pixels in the neighborhood of (x,y) in
the input image.
 F. Spatial filtering is performed by convolving the image
with a mask or a kernel. Spatial filters include
sharpening, smoothing, edge detection, noise removal,
etc.
 In general, linear filtering of an image f of size M x N
with filter size m x n is given by the expression, where
g(x,y) is enhanced image, f(x,y) is input image and w(s,t)
is mask or filter which is applying on input image.
University of sulaimanyiah - Faculty of Physical and Basic Education - Computer Dep. 2014-2015
7
Image Filtering in Spatial Domain
University of sulaimanyiah - Faculty of Physical and Basic Education - Computer Dep. 2014-2015
8
Image Filtering in Spatial Domain cont’s
The general block diagram of image filtering in spatial domain illustrates
below:
University of sulaimanyiah - Faculty of Physical and Basic Education - Computer Dep. 2014-2015
9
Image Filtering in Spatial Domain
1-
University of sulaimanyiah - Faculty of Physical and Basic Education - Computer Dep. 2014-2015
1
Image Filtering in Spatial Domain
2-
University of sulaimanyiah - Faculty of Physical and Basic Education - Computer Dep. 2014-2015
1
Example
University of sulaimanyiah - Faculty of Physical and Basic Education - Computer Dep. 2014-2015
12
Example cont’s
University of sulaimanyiah - Faculty of Physical and Basic Education - Computer Dep. 2014-2015
1
Example cont’s
University of sulaimanyiah - Faculty of Physical and Basic Education - Computer Dep. 2014-2015
1
Image Filtering in Spatial Domain
University of sulaimanyiah - Faculty of Physical and Basic Education - Computer Dep. 2014-2015
1
Image Filtering in Spatial Domain Median filter
University of sulaimanyiah - Faculty of Physical and Basic Education - Computer Dep. 2014-2015
1
Example
University of sulaimanyiah - Faculty of Physical and Basic Education - Computer Dep. 2014-2015
1
Example cont’s
University of sulaimanyiah - Faculty of Physical and Basic Education - Computer Dep. 2014-2015
1
Example cont’s
University of sulaimanyiah - Faculty of Physical and Basic Education - Computer Dep. 2014-2015
1
Example
University of sulaimanyiah - Faculty of Physical and Basic Education - Computer Dep. 2014-2015
20
Image Filtering in Frequency Domain
 In frequency domain, the low frequency components are
generally the approximation and while high frequency
components are generally details, edges, and/or noise.
 One can take the discrete Fourier transform of an image,
modify the Fourier transform, and take the inverse
discrete Fourier transform to obtain the modified image
according to the following model.
University of sulaimanyiah - Faculty of Physical and Basic Education - Computer Dep. 2014-2015
2
Image Filtering in Frequency Domain
The general block diagram of image filtering in frequency domain
illustrates as:
University of sulaimanyiah - Faculty of Physical and Basic Education - Computer Dep. 2014-2015
2
Image processing (frequency domain )
 The coefficients corresponding to the new
domain (frequency domain) are the transform
coefficients.
 Image processing operations that process
transform coefficients are called transform
domain processing.
 Low frequency means that the sine/cosine curves
are slowly varying (or even constant).
 High frequency means that the sine/cosine
curves are rapidly changing.
University of sulaimanyiah - Faculty of Physical and Basic Education - Computer Dep. 2014-2015
2
Low‐Pass Filtering:
 ILPF:
The Ideal Low-pass Filter is the simplest low pass filter
that “cuts off” all high frequency component of the DFT
that are at a certain distance from the center of the DFT.
University of sulaimanyiah - Faculty of Physical and Basic Education - Computer Dep. 2014-2015
2
Gaussian Low pass Filters:
The Gaussian Lowpass Filter (GLPF) with cutoff frequency
at distance D0 is defined as:
University of sulaimanyiah - Faculty of Physical and Basic Education - Computer Dep. 2014-2015
2
Example1
Find the output of applying smoothing filter on the pixel
(2,2) shown in block of image:
University of sulaimanyiah - Faculty of Physical and Basic Education - Computer Dep. 2014-2015
2
Example1
Solution: since the index of image width and height
starts with (0,0), then the value of pixel (2,2)= 9. Now the
smoothing filter must be centered on this value to
change its value.
Pixel(2,2)= (1/9)*(8*1+5*1+5*1+2*1+9*1+4*1+2*1+9*1+4*1)=round(48/9)=5
University of sulaimanyiah - Faculty of Physical and Basic Education - Computer Dep. 2014-2015
2
Example2
Find the output of applying sharpening filter on the pixel
(3,4) shown in block of image:
University of sulaimanyiah - Faculty of Physical and Basic Education - Computer Dep. 2014-2015
2
Example2
Solution: since the index of image width and height strats
with (0,0), then the value of pixel (4,3)= 3. Now the
sharpening filter must be centered on this value to
change its value
Pixel(3,4)=(1/9)*(4*-1+4*-1+6*-1+3*-1
+3*8+5*-1+2*-1+3*-1+4*-1) 
round(abs((-7/9))=1
University of sulaimanyiah - Faculty of Physical and Basic Education - Computer Dep. 2014-2015
29
```