You can try this

a=imread('a.jpg'); % change the file names

a=rgb2gray(a);

f=fft2(a);

p=f./abs(f);

imshow(abs(ifft2(p)),[])

Is it like a edge detection?

Let me know if you have any question.

Well this is a little bit hard to explain because is completly different to what we are normaly accustomed to see in image processing...as I see it....it becomes in signal processing intead of traditional image processing because all the filters and transformations you perform in your image will be through the sine and cosine components of the image....you surely know that to apply this type of image processing you must first use FFT (Fast Fourier Transform) to represent the image in the frequency domain.....check this links.....they may be of help

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

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

http://photo.stackexchange.com/questions/21762/how-to-analyze-images-with-fast-fourier-transform-method

@Luis Alberto Rodríguez Rodríguez 

Thank U sir for your suggestions! Yeah u r right, it's about signal processing.  I have studied FFT, DCT, DWT. Applied those to images (both using using the functions already available in  MATLAB as well as written my own codes for FFT, DCT and Haar DWT ) but still somehow fail to visualize things in a properer way !

Can you give an example of image you want to process ?

It could be more easy to answer ;-)

Frequency domain results are hard to imagine in general when it comes to 2 D subjects (1 D is much easier).

What you might be able to imagine: if you have a repeated pattern 1D or 2D in your image, this will be expressed in raised amplitudes for the fundamental and harmonics of this pattern.

A more generalized image may or may not exhibit such frequency peaks. The other way round: if you get peaks in the frequency domain, this indicates periodic patterns in the spatial domain.

Much more than this rather basic interpretation of frequency domain results is beyond my imaginative capabilities :)

Images are just signals of dimensions 2 (grayscale) and 3 (Color). The transformation to the frequency domain involves the Fourier Transform (DFT). So the images are now represented as a linear combination of sinusoids (you will need a basic review of Linear Algebra here). When you take the FFT of an image in a software such as MATLAB and visualize the result, you get a pattern. This result actually contains the magnitude, phase and of course, the spatial frequencies from 0 to the Nyquist frequency (depending on the resolution of your image). 

For a more clear understanding, take the attached picture as an example. The "magnitude" is seen as "how much the darkest black band differs from the brightest white band". The "phase" can be seen as a shift in these bands to the left or right. The number of bands would give you a rough idea about the "spatial frequencies". More the number of bands, more the frequency.

The 2nd picture (example2) shows the 1st picture in the Fourier domain. Here there are 3 pixels - the central one is the DC and there are 2 pixels on the either side depicting the frequencies. If there existed only a few bands in the original picture, then the 2 pixels would be closer to the center (indicating lower frequencies). The "magnitude" is to be seen as "how bright the pixels are". 

Hope this helps!

Thank u all for your valuable comments!

let's say I have three different images and I have taken the fft for those three ( using the inbuilt fft2 function of MATLAB) and displayed using imshow . The displays look something as attached. What interpretation regarding the original pictures I can make from these?

First of all you must realize that spatial and FFT representations are not the same but supplement. In spatial representation you can see what occured - in the meaning of position/place and amplitude of signal. In frequency domain you can see periodic matters (presented frequency and their "energy"). If you want locate when frequency occured you need to use STFT (short time fourier transform)

In layman's terms, spatial frequency means: How many times would a given part of the image fit inside the space of the whole image? Simply put, you can imagine an image to consist of large areas with small details. There is only a small number of large areas in a picture, so this corresponds to a low spatial frequency. There can be a large number of small details in a picture, so this corresponds to a high spatial frequency.

'interpretation' is a bit too much.

What do I see:

The topmost shows some symmetry in the corners - indicating some symmetry for higher frequencies diagonally in the original image.

The middle one seems to be synthetic. How to Interpret the 2 missing frequency bands (dark horizontal lines): ???

The lower spectrum shows similar indicating of missing frequencies - this time showing up in the Form of vertical lines. Between these lines the contents seem to repeat - though they could be shifted slightly.

I hope you'll supply the original images as well - I'm really keen to see what I can learn from this little 'puzzle'. :)

Thank U all!

@U. Dreher, it was not exactly a puzzle. .I am trying  to learn and understand the  frequency domain concepts. .

the figures are

 While the top and bottom images were not too surprising, the square really is: the Geometric symmetry in the spatial Domain is hardly reflected in the frequency Domain.

I too am (still) learning.

Dear Mishra

i am doing this part but in part of image filter in frequency domin.

see this sample code "indicate low pass filter in frequency domain":

>>HLP=@(d) double(d> a=fft2 (Original image);

>> [U V]=CreateFreqGrid ;

>> D=Sqrt (U.^2+ V.^2);

>>H=HLP(D);

>>G=H.*F;

>>g=ifft2(G);

----------------------------------------------

Best Regards,

Ehsan Nowroozi

Let's stay in the analog domain( long story short): When images are captured , lens does a low pass filtering of the scene  that has a reflective aspect of the object. Lens also partially does anti-aliasing (blurring ) of the image. Net level of processing is another story.

 DSLRs (digital -pixels in the CCDs ) with lens focusing the reflective aspects in a digital # formats, the frequency aspect is in the form of "contrast"  (use just noticeably difference (JND)) . This contrast in monochrome is a range of gray levels (8- bit = 256 shades). In RGB(Simpler-  8 bit each = 2 ^ 24 colors) . In the gray scale - Mach band /Moire pattern /line pairs per mm (MTF) etc etc are used for correlation (visual ) . 

Now, with digital #s relating it to frequency is based on statistical variance /covariance etc etc of the image #s [100 200 ...] , to get a magnitude for whole range of #s and relating it to spatial frequency we can use FFT  or any transformation that explains and characterizes image- as they say "beyond what meets the eye".

Again , transformation commonly done for secondary analysis , say compression. Image data is highly correlated set of signals and results in a good compression ratio.

The significance of the magnitude  are illustrated well in these answers. I'd like to add that the phase information (there are complex numbers in FFT2 results ) is also useful sometimes.

The three result images listed before were probably only magnitude of the FFT2 results and lost some important information. Ordinary filters (Low pass filter) can be constructed by magnitude information but You cannot get many features of an image by using magnitude of FFT2 results alone.

You can make a simple experiment in which  the basic feature ( e.g. edges) can be restored by using phase information alone to compare with the result of using magnitude without phase.

@Chao Xing you are right, the complex numbers couldnt be ploted. 

edge restoration ???using phase info???

how to write such programs? Would u mind sharing some MATLAB code and experimental results plz??? I know how to detect edges using operators such as  robot , sobel, prewitt, canny etc but no idea about edge restoration!!!

A lot to read and understand . .

You can try this

a=imread('a.jpg'); % change the file names

a=rgb2gray(a);

f=fft2(a);

p=f./abs(f);

imshow(abs(ifft2(p)),[])

Is it like a edge detection?

Let me know if you have any question.

Thanks Chao Xing !

No the results are not same but a bit similar! Please explain.

Generally we can divide frequency components into three parts: low, middle and high , which can be imagined as smooth region, edge and noise individually. The low frequency part has larger magnitude than  middle and high part in an ordinary image.

We attenuate low frequency part and enhance middle and high frequency part  when we remove magnitude information after unitization. It is not a good edge detection method because the noise( high frequency part) is also amplified.

On the other hand, it (p=f./abs(f)) can be explained as filtering the image f (frequency domain) with (high pass ) filter 1./abs(f).

@Chao Xing

The above fft image is kinda similar to the LH, HL, HH sub-bands of DWT?