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In the context of image manipulation i need to learn about 2D fourier transforms, especially about the discrete version. Can somebody recommend a book that starts at the basics and treats some practical examples?

I would like the emphasis to be on the theoretical side, as there are enough people around me that know how to apply things, but not a lot that actually know the foundations. But just to have a bit more context: practical skills i need to master are for example extracting the most prevalent orientation in an image, splitting an image into high and low frequency bands, etc.

Background knowledge can be assumed, i finished my msc in math recently (graduated in algebraic geometry but also did quite some courses on analysis). This question is because of my internship in neuroscience (vision research).

Thanks a lot!

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A lot of books which cover this are under the name "image processing".

Gonzales and Woods' Digital Image Processing is the standard reference for image processing.

Lim's Two-Dimensional Signal and Image Processing is also a good book, but is quite old (early 1980s).

Some people I know also like Bovik's The Essential Guide to Image Processing.

The relevant 1-d analogues can be found in Oppenheim's Discrete-Time Signal Processing or Mitra's Digital Signal Processing or Proakis' Digital Signal Processing texts. You will probably want one of these books as a supplement if you are not familiar with the 1 dimensional DFT to begin with.

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  • $\begingroup$ Thanks a bunch, i'll take a look now. $\endgroup$ – Joachim Mar 11 '14 at 10:48
  • $\begingroup$ I borrowed Gonzales and Woods, it is very nice. However, do you know where to find something about directional and orientation filters? $\endgroup$ – Joachim Mar 16 '14 at 9:39

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