Hi,
I've been trying to understand more on frequency plots of images.
1. Assuming a 1d example of just a strip of an image; in the frequency map there
are 'same' no. of frequencies as there are pixels. What is the reason
for this? Does this have something to do with the Nyquist theorom.
2. What you see in the frequency domain is just a plot of all the spatial
frequencies and thier amplitude corresponds to the coefficient of that
frequency? Is this correct?
3. Now if in the 1d example, i see a one recurring pattern...
0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1
How would this map to the frequency domain? So for example, i see the sequence
'0 0 0 1' 4 times. What can i make out of this?
4. In 2d all the points near the center are the lower frequencies and away from
the center are higher frequencies. What can be said about the image if we get
higher amplitudes in the lower freqencies as compared to the higher frequencies.
What does this mean? Can we say that simpler (or more complicated) images will
not peak at the center like this? [PS:- i do know that lower frequencies capture
the general aspects of the image whereas the higher frequencies capture the more
'detailed' aspects (e.g. edges)]
Thanks
Neville
Images in the frequency domain..
Started by ●February 2, 2009
Reply by ●February 3, 20092009-02-03
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(1)well, as one dimensional DFT has same length as x[n] has.If u take inverse of dft with less coefficients then aliasing will be there (not follow nyquist rule),if coefficients are more , some zero padding interpolation is there.So,to get original image we require same no of coefficients.
Or,In linear algebra terms the frequicies are integral multiple of exp(j*2*pi)/m*n are orthogonal basis so its trasformation matrix is invertiable.
(2)yes.
(3)No, it is not periodic but it find dft of 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1 as one cycle.
Hi,
I've been trying to understand more on frequency plots of images.
1. Assuming a 1d example of just a strip of an image; in the frequency map there are 'same' no. of frequencies as there are pixels. What is the reason for this? Does this have something to do with the Nyquist theorom.
2. What you see in the frequency domain is just a plot of all the spatial frequencies and thier amplitude corresponds to the coefficient of that frequency? Is this correct?
3. Now if in the 1d example, i see a one recurring pattern...
0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1
How would this map to the frequency domain? So for example, i see the sequence '0 0 0 1' 4 times. What can i make out of this?
4. In 2d all the points near the center are the lower frequencies and away from the center are higher frequencies. What can be said about the image if we get higher amplitudes in the lower freqencies as compared to the higher frequencies. What does this mean? Can we say that simpler (or more complicated) images will not peak at the center like this? [PS:- i do know that lower frequencies capture the general aspects of the image whereas the higher frequencies capture the more 'detailed' aspects (e.g. edges)]
Thanks
Neville
(1)well, as one dimensional DFT has same length as x[n] has.If u take inverse of dft with less coefficients then aliasing will be there (not follow nyquist rule),if coefficients are more , some zero padding interpolation is there.So,to get original image we require same no of coefficients.
Or,In linear algebra terms the frequicies are integral multiple of exp(j*2*pi)/m*n are orthogonal basis so its trasformation matrix is invertiable.
(2)yes.
(3)No, it is not periodic but it find dft of 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1 as one cycle.
Hi,
I've been trying to understand more on frequency plots of images.
1. Assuming a 1d example of just a strip of an image; in the frequency map there are 'same' no. of frequencies as there are pixels. What is the reason for this? Does this have something to do with the Nyquist theorom.
2. What you see in the frequency domain is just a plot of all the spatial frequencies and thier amplitude corresponds to the coefficient of that frequency? Is this correct?
3. Now if in the 1d example, i see a one recurring pattern...
0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1
How would this map to the frequency domain? So for example, i see the sequence '0 0 0 1' 4 times. What can i make out of this?
4. In 2d all the points near the center are the lower frequencies and away from the center are higher frequencies. What can be said about the image if we get higher amplitudes in the lower freqencies as compared to the higher frequencies. What does this mean? Can we say that simpler (or more complicated) images will not peak at the center like this? [PS:- i do know that lower frequencies capture the general aspects of the image whereas the higher frequencies capture the more 'detailed' aspects (e.g. edges)]
Thanks
Neville
