Assignment for digital image processing

1. ASSIGNMENT 3
(FOURIER)
NAME : MUHAMAD AMINUDDIN BIN MOHD JAMAL
MATRIC NO : 2200255
CLASS : 3TSI
LECTURER : PROF MADYA TS DR. SUZAIMAH BTE RAMLI

2. 1. Give three(3) steps to filter an image in the frequency domain
All frequency filters can also be implemented in the spatial domain and, if there exists
a simple kernel for the desired filter effect, it is computationally less expensive to
perform the filtering in the spatial domain. Frequency filtering is more appropriate if
no straightforward kernel can be found in the spatial domain, and may also be more
efficient.
1. Compute F(u,v) the Discrete Fourier transform (DFT) of the Image.
2. Multiply F(u,v) by a filter function H(u,v)
3. Compute the inverse Discrete Fourier Transform of the result.
2. Figure 1 show an image and it’s Fourier spectrum and a series of ideal low
pass filters of radius 5, 15, 30, 80 and 230 superimposed on top of it. Give
your justification on the result of filtering with ideal low pass filter of radius 5
and ideal low pass filter of radius 230.

3. An ideal low pass filter is the one which transmits all the signal of frequencies less
than a certain frequency ωc radians per second without any distortion and blocks all
the signals of frequencies above ωc radians per second. Where, the frequency ωc
radians per second is called the cut-off frequency.
Simply cut off all high frequency components that are a specified distance D0 from
the origin of the transform. changing the distance changes the behaviour of the filter
The transfer function for the ideal low pass filter can be given as:
where D(u,v) is given as:
This is the result of the filtering with ideal low pass filter of radius 5
This is the result of the filtering with ideal low pass filter of
radius 230.

4. Figure 1
3. Run this Matlab Code by used any image with this specification:
a. Only 1 object/person in the image with no background
b. Only 1 object/person in the image with scenery background
c. More than 2 object in the image with scenery background
d. More than 2 object + noise(refer Slide 35: Chap 3, Fourier)
- Explain what the output you get and what are the differences between a,b and c.
clear all
%I=zeros(10);
I= imread('D:qqqrrrxx.jpg')
%I=
imread('D:BackupACERJul2019DataBackupJun2019BackupNotbkSu_Jan2010Kerja
HusnaInkedOIPicture_LI3.jpg')
figure(3), imshow(I)
I=rgb2gray(I);
[r, c] = size(I)
%imshow(I);
for i=1:r
X(i,:) = fft(I(i,:));
end
for j=1:c
Y(:,j) = fft(X(:,j));
end
figure(1), imshow(I)
M=Y;
M=fftshift(M);
Ab=abs(M);
Ab = (Ab-min(min(Ab)))./(max(max(Ab))).*255;
figure(2),imshow(Ab)

5. a.
b.
c.