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What does frequency domain denote in case of images?

If we look deeply into Digital Images they are purely generated by the pixels distributed in rows and coloumn and the pixel consists of number of certain bits which define the complete Image.

Then what is the role of Frequency in generating Digital Images ? like many people says that in Digital Image processing and Image Compression, Wavelets is much more efficient than Discrete Cosine Transform as Wavelets gives the information of both time and Frequency.

I want to know what role does frequency and time plays in producing a Digital image, does it has to do something with pixels?


1 Answer 1


You can take images as 2D discrete signals. The "time" in 1D signals is actually two spatial dimensions in images (2D signals).

You can measure "frequency" as well - imagine a line of white pixels with regular spacing. The spacing represents period $p$, and frequency is given by $1/p$. Hence the maximum frequency the discrete signal can contain is limited by the sampling rate.

When creating a digital image, sampling can cause new frequencies to appear due to aliasing. See Nyquist frequency.

Fourier and wavelet transforms have discrete variants to work with discrete signals - very simply said: integrals are replaced by sums.

Wavelets are more efficient in image compression, because they can deal with localized redundancies. Simply look of DFT of a grey square on black background and then on DWT of that square.

DWT will exploit transitions of the square shape in high fequency layer, and other layers will be almost clear. The sharp 1px transition would be best described with Haar wavelet without any remainder.

On the other hand, DFT or DCT will result in many cosine functions which summed together form the edge without visible ringing artifacts (Gibbs effect).

Wavelet have its artifacts too, but these are better localized, hence does not corrupt rest of the image (or rest of the macroblock in case of JPEG/DCT compression).


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