Comments on: Fourier transforms – where to go from here http://blogs.mathworks.com/steve/2010/05/10/fourier-transforms-where-to-go-from-here/ Steve Eddins manages the Image & Geospatial development team at The MathWorks and coauthored Digital Image Processing Using MATLAB. He writes here about image processing concepts, algorithm implementations, and MATLAB. Fri, 17 May 2013 16:28:28 +0000 hourly 1 http://wordpress.org/?v=3.2.1 By: Steve http://blogs.mathworks.com/steve/2010/05/10/fourier-transforms-where-to-go-from-here/#comment-23738 Steve Wed, 24 Nov 2010 15:24:02 +0000 http://blogs.mathworks.com/steve/2010/05/10/fourier-transforms-where-to-go-from-here/#comment-23738 Jenny—A high-pass filter would eliminate the low-frequency stuff that is not of interest. There are some two-dimensional filter design routines in the Image Processing Toolbox, but using them does require some knowledge about digital filtering. Most textbooks on image processing would have information on lowpass and highpass filtering. Jenny—A high-pass filter would eliminate the low-frequency stuff that is not of interest. There are some two-dimensional filter design routines in the Image Processing Toolbox, but using them does require some knowledge about digital filtering. Most textbooks on image processing would have information on lowpass and highpass filtering.

]]> By: Jenny Devaud http://blogs.mathworks.com/steve/2010/05/10/fourier-transforms-where-to-go-from-here/#comment-23731 Jenny Devaud Tue, 23 Nov 2010 21:35:44 +0000 http://blogs.mathworks.com/steve/2010/05/10/fourier-transforms-where-to-go-from-here/#comment-23731 Hi Steve, I have an image that has high frequency data on top of low frequency data..think nano-scale roughness on top of macroroughness. I want to look at the average roughness of ONLY the nano-scale roughness. Is there a way to do this? It would seem to be related to FFT somehow, but I have x, y and z data. Any help appreciated. Hi Steve, I have an image that has high frequency data on top of low frequency data..think nano-scale roughness on top of macroroughness. I want to look at the average roughness of ONLY the nano-scale roughness. Is there a way to do this? It would seem to be related to FFT somehow, but I have x, y and z data. Any help appreciated.

]]> By: matteo http://blogs.mathworks.com/steve/2010/05/10/fourier-transforms-where-to-go-from-here/#comment-23498 matteo Fri, 17 Sep 2010 00:31:39 +0000 http://blogs.mathworks.com/steve/2010/05/10/fourier-transforms-where-to-go-from-here/#comment-23498 Thank you Steve I found an online example, but yet not much detail on the justification. http://www.imagemagick.org/Usage/fourier/#contrast Matteo Thank you Steve
I found an online example, but yet not much detail on the justification.
http://www.imagemagick.org/Usage/fourier/#contrast
Matteo

]]> By: Steve http://blogs.mathworks.com/steve/2010/05/10/fourier-transforms-where-to-go-from-here/#comment-23494 Steve Thu, 16 Sep 2010 16:06:38 +0000 http://blogs.mathworks.com/steve/2010/05/10/fourier-transforms-where-to-go-from-here/#comment-23494 Matteo—I'm not familiar with this technique. I'll think about it. My initial reaction is that it seems like an awful lot of computation to go through in order to increase contrast. Matteo—I’m not familiar with this technique. I’ll think about it. My initial reaction is that it seems like an awful lot of computation to go through in order to increase contrast.

]]> By: Matteo http://blogs.mathworks.com/steve/2010/05/10/fourier-transforms-where-to-go-from-here/#comment-23492 Matteo Thu, 16 Sep 2010 14:26:17 +0000 http://blogs.mathworks.com/steve/2010/05/10/fourier-transforms-where-to-go-from-here/#comment-23492 Hi Steve I was reading on a book that if you fourier transform an image, separate magnitude and phase, increase or decrease the magnitude by adjusting its exponent, say to 1.2 or 0.98, and recombine with phase through inverse fourier, this amounts to changing the contrast. THe source however was uniquely ppor in details. Would you care to elaborate on why this works? Thank you Matteo Hi Steve

I was reading on a book that if you fourier transform an image, separate magnitude and phase, increase or decrease the magnitude by adjusting its exponent, say to 1.2 or 0.98, and recombine with phase through inverse fourier, this amounts to changing the contrast. THe source however was uniquely ppor in details. Would you care to elaborate on why this works?
Thank you

Matteo

]]> By: Martin Offterdinger http://blogs.mathworks.com/steve/2010/05/10/fourier-transforms-where-to-go-from-here/#comment-23207 Martin Offterdinger Mon, 21 Jun 2010 14:39:11 +0000 http://blogs.mathworks.com/steve/2010/05/10/fourier-transforms-where-to-go-from-here/#comment-23207 For me it would be particularly interesting how to do image registration based on Fourier Transforms? Thanx Martin For me it would be particularly interesting how to do image registration based on Fourier Transforms?

Thanx

Martin

]]> By: Steve http://blogs.mathworks.com/steve/2010/05/10/fourier-transforms-where-to-go-from-here/#comment-23137 Steve Thu, 20 May 2010 13:45:11 +0000 http://blogs.mathworks.com/steve/2010/05/10/fourier-transforms-where-to-go-from-here/#comment-23137 Fen—Once aliasing has occurred, you can't get rid of it with filtering. Fen—Once aliasing has occurred, you can’t get rid of it with filtering.

]]> By: Fen http://blogs.mathworks.com/steve/2010/05/10/fourier-transforms-where-to-go-from-here/#comment-23114 Fen Sat, 15 May 2010 04:35:45 +0000 http://blogs.mathworks.com/steve/2010/05/10/fourier-transforms-where-to-go-from-here/#comment-23114 Hi Steve, great to see the FT theme will be continuing. All the topics you suggest sound very interesting- I hope you get to cover them all at some point! Although it's already a pretty big list. I think I suggested a few blogs ago that I'd be interested in Gibbs phenomenon and ringing (and I guess this fits in nicely with filtering). Also phase sounds like a good one (as I work a lot with this at the moment)- I've seen some cool examples of images reconstructed just from the phase info to demonstrate it's importance to vision. And how about aliasing/anti-aliasing images. How does one best pick the right cut-off frequency for low-pass filtering any given aliased image? Thanks, Fen Hi Steve, great to see the FT theme will be continuing.

All the topics you suggest sound very interesting- I hope you get to cover them all at some point! Although it’s already a pretty big list.

I think I suggested a few blogs ago that I’d be interested in Gibbs phenomenon and ringing (and I guess this fits in nicely with filtering).

Also phase sounds like a good one (as I work a lot with this at the moment)- I’ve seen some cool examples of images reconstructed just from the phase info to demonstrate it’s importance to vision.

And how about aliasing/anti-aliasing images. How does one best pick the right cut-off frequency for low-pass filtering any given aliased image?

Thanks,

Fen

]]> By: Jez http://blogs.mathworks.com/steve/2010/05/10/fourier-transforms-where-to-go-from-here/#comment-23111 Jez Thu, 13 May 2010 17:51:31 +0000 http://blogs.mathworks.com/steve/2010/05/10/fourier-transforms-where-to-go-from-here/#comment-23111 I've always been interested in DFTs to find the frequency of single pure sinusoids. I usually think of this as a MATLAB vector multiply of a section of sinusoid with several different frequencies of complex exponential and seeing which 'comes out on top' as most similar. You'd expect this to work if the exponential is bang on the right frequency, what I find puzzling about the DFT is that it also works if the frequency is a bit out - and if you interpolate the output you can get a useful answer. What I find surprising is that this doesn't seem to work in general. For example when I took a section of linear chirp and MATLAB vector multiplied it by linear chirps of various frequencies and chirp rates (it would be a 2D grid) I got a nice spike if I hit the chirp parameters bang on but no nice 'near miss' behaviour to interpolate. So, what gives? What's so special in this respect about the DFT? The best explanation I've found so far is p164 of Rader and Gold. But any enlightenment you can offer would be great. I’ve always been interested in DFTs to find the frequency of single pure sinusoids. I usually think of this as a MATLAB vector multiply of a section of sinusoid with several different frequencies of complex exponential and seeing which ‘comes out on top’ as most similar. You’d expect this to work if the exponential is bang on the right frequency, what I find puzzling about the DFT is that it also works if the frequency is a bit out – and if you interpolate the output you can get a useful answer.

What I find surprising is that this doesn’t seem to work in general. For example when I took a section of linear chirp and MATLAB vector multiplied it by linear chirps of various frequencies and chirp rates (it would be a 2D grid) I got a nice spike if I hit the chirp parameters bang on but no nice ‘near miss’ behaviour to interpolate.

So, what gives? What’s so special in this respect about the DFT? The best explanation I’ve found so far is p164 of Rader and Gold. But any enlightenment you can offer would be great.

]]> By: Charles Kenny http://blogs.mathworks.com/steve/2010/05/10/fourier-transforms-where-to-go-from-here/#comment-23110 Charles Kenny Thu, 13 May 2010 13:49:19 +0000 http://blogs.mathworks.com/steve/2010/05/10/fourier-transforms-where-to-go-from-here/#comment-23110 Is there a way to extract phase info from spatial frequency plots that is not limited to mod 2 pi recycling? Is there a way to extract phase info from spatial frequency plots that is not limited to mod 2 pi recycling?

]]>