[FRIAM] Fourier image space, duality, filtering and compression

[Frank Wimberly]

I taught digital signal processing once to MS and PhD students without
knowing the field.  For what it's worth, I validate Ed's observations.  (In
my defense, I got very good student evaluations)

---
Frank C. Wimberly
140 Calle Ojo Feliz,
Santa Fe, NM 87505

505 670-9918
Santa Fe, NM 87505

On Mon, Aug 15, 2022, 3:14 PM Angel Edward <edward.angel at gmail.com> wrote:

> Sorry I missed the discussion. I was in Vancouver all week for SIGGRAPH.
>
> A few comments after looking at the two websites. I taught Fourier
> transforms for many years both through digital signal processing and though
> optics as part of a course on hybrid processing at the Institute of Optics
> at Rochester.
>
> The main problem with these sites is that they fail to distinguish between
> the continuous Fourier transform and the discrete Fourier transform, which
> have major differences that affect what you see in the examples. In
> particular, you need to talk about sampling and reconstruction to talk
> about the DFT. The Nyqist sampling theorem is key to understanding the
> effects of windowing in space or frequency, the uncertainty principle for
> the transforms, the limits of displays and the artifacts due the windows.
> In the transforms in the second site, I’m pretty certain that all the
> dominant frequencies in the transforms are window artifacts and not due to
> the data. At least the first site gives you the option of applying a
> spatial window to the data although it doesn’t give you a way to understand
> some of the displays you can generate with window applied to band limited
> data.
>
> There is an Appendix in my books about the FT and I have some notes from a
> summer short course at the Institute of Optics that cover these issues.
>
> Ed
> __________
>
> Ed Angel
>
> Founding Director, Art, Research, Technology and Science Laboratory (ARTS
> Lab)
> Professor Emeritus of Computer Science, University of New Mexico
>
> 1017 Sierra Pinon
> Santa Fe, NM 87501
> 505-984-0136 (home)   edward.angel at gmail.com
> 505-453-4944 (cell)  http://www.cs.unm.edu/~angel
>
> On Aug 12, 2022, at 2:09 PM, Stephen Guerin <stephen.guerin at simtable.com>
> wrote:
>
> Jon, Mike and I were talking about fourier transforms on images, JPEG
> compression and filtering at this morning's FRIAM.
>
> Here's a nice site that lets you load an image, and its fourier transform
> (amplitude spectrum) in cartesian or log-polar.
>      https://www.djmannion.net/img_freq_web/
>
>  A menu allows you to pull up sample images, simple sine waves in various
> frequencies and orientation and a live webcam image to see their point
> dualities in fourier space.
>
> The lower panel lets you filter high and low cutoffs (much like jpeg
> compression) to see the impact on the image.
>
> links related to compression:
>
> https://blog.demofox.org/2020/11/04/frequency-domain-image-compression-and-filtering/
>
> https://micro.magnet.fsu.edu/primer/java/digitalimaging/processing/fouriertransform/
>
> different but related use of fourier transform for finding epicycles in a
> drawing:
>
>    - https://www.jezzamon.com/fourier/
>    - https://www.myfourierepicycles.com/
>
>
> -S
>
>
> _______________________________________________________________________
> Stephen.Guerin at Simtable.com <stephen.guerin at simtable.com>
> CEO, https://www.simtable.com <http://www.simtable.com/>
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