Image processing - convolution & fourier

[m~ray]

it might sound a bit hilarious.. some where i read about image processing where on the original image some operations were done (dealing with something related to convolution may be ) and say image A was obtained.. again another set of operations ( dealing with Fourier transform on the image plus something)were done on the original image and say image B was obtained. its found that image A and image B are almost same..
i can't remember where i have seen it, but i need to know the entire process now..Has anybody come across such sort of thing?? if yes, please describe me the operations.. sorry for a silly question, your help would be much appreciated..

 

[zhermes]

This question is too vague to really give an answer too.

Image processing/manipulation, more often than not, involves convolution with the image itself or the transformed version.

"Almost the same" doesn't really mean much. If the operations performed on the image are similar, the results will look similar. If you're 'looking' at the phase-space representation of the images, many transformations would 'look' "almost the same"...

 

[cosmik debris]

IT is common in image processing to Fourier transform an image, filter it usually using convolution as it easier in the Fourier domain, and then inverse transforming to get back to the filtered image in the time domain.

 

[m~ray]

yes its too vague i agree.. these r wat i remember there was some image say f(x,y).. apply FFT get F(u,v). then from the image get f(lambda in superscript)(z in subscript) ( i have no idea what this f lambda thing is all about.. does it have any standard meaning ?? then multiply it with F(u,v). after that one needs to do further operations like inverse FFT..

 

[Andy Resnick]

it might sound a bit hilarious.. some where i read about image processing where on the original image some operations were done (dealing with something related to convolution may be ) and say image A was obtained.. again another set of operations ( dealing with Fourier transform on the image plus something)were done on the original image and say image B was obtained. its found that image A and image B are almost same..
i can't remember where i have seen it, but i need to know the entire process now..Has anybody come across such sort of thing?? if yes, please describe me the operations.. sorry for a silly question, your help would be much appreciated..

It could be related to the convolution theorem:

http://en.wikipedia.org/wiki/Convolution_theorem

For example, (under suitable conditions) the image field is the object field convolved with the point spread function. Also, the FT of the image is the FT of the object multiplied by the FT of the point spread function.

There are some subtleties: the FT is complex, for example. This leads to a distinction between the optical transfer function and modulation transfer function, and to differences between coherent vs. incoherent imaging.

Does that sound about right?

 

[DragonPetter]

OP, is this some new method or just standard digital image processing you're talking about?

It sounds you're just talking about filtering the image. They use a 2-d shape of weighted pixels, say a 3x3 square, and convolve it with the image to get a new image, or they take the 2-D FFT of the image and of the filter, which the filters are some kind of guassian distribution or butterworth LPF for example. The filters look kind of cool in the frequency domain. They multiply the image with the filter before taking the inverse 2-D FFT.

From what I remember, the phase information is not that important in reconstructing the image.

 

[m~ray]

yes thanks for the help... i think it deals with the convolution theorem.. in that we need two functions f and g.. now the given image say f(x,y) is the function f. and i need to take g as the function f(lambda in superscript)(z in subscript).. now i have no what this is. does it a any special meaning ??