Author Topic: Fourier transform study  (Read 6177 times)

Offline elevenaugust

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Fourier transform study
« on: June 12, 2008, 02:10:30 pm »
I've noticed that a slight gaussian blur tends to create the effect you want, if I understood you correctly?
In my tests, I didn't try to apply gaussian blur (yet). Sorry if I badly explained myself :P

A brief description about the Fourier Analysis:
The Fourier Transform is an important image processing tool which is used to decompose an image into its sine and cosine components. The output of the transformation represents the image in the Fourier or frequency domain, while the input image is the spatial domain equivalent. In the Fourier domain image, each point represents a particular frequency contained in the spatial domain image.

The Fourier Transform is used in a wide range of applications, such as image analysis, image filtering, image reconstruction and image compression.

I try to reproduce the same effects on the Fourier transform seen on the Raj's pict n17, with various enhancements, improvements, etc....
We already know that JPEG compression didn't affect it; so what could it be?

COLOR CORRECTIONS
  • brightness adjustment
  • contrast adjustment
  • exposure adjustment
  • saturation adjustment
  • color balance adjustment

FILTERS
  • smooth
  • sharpen
  • noise reduction
  • median filter

MORPHOLOGICAL OPERATIONS
  • erosion
  • dilatation
  • open
  • close

OTHER
  • noise adjustment
  • convert to 256 color
  • resizing
  • drawing/insert object inside photo
  • JPEG compression artifact


And also, of course, could be any combination of these...  :-\ :P
My first intempts are to find the same circular halo shape (a "donut" shape) as one can see it in Raj's original ft picture:


My "test" photograph:

Then, secondly, I will try to reproduce the other characteristics. (width of the central disc and of the "donut", brightness of the pixels, etc....)

« Last Edit: June 12, 2008, 05:27:31 pm by elevenaugust »
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Offline elevenaugust

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Re: Fourier transform study
« Reply #1 on: June 12, 2008, 04:18:41 pm »
1) COLOR CORRECTIONS
  • Brightness adjustment
All color plane:


Luminance:


Green channel:


The results are the same for the red and the blue channel.

The shape is oval, no match with the original Raj's ft photo.
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Offline elevenaugust

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Re: Fourier transform study
« Reply #2 on: June 12, 2008, 08:09:13 pm »
  • Contrast adjustment
All color plane:


Luminance:


Green channel:


The results are almost the same for the other channels.

Still no match....
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Offline nekitamo

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Re: Fourier transform study
« Reply #3 on: June 13, 2008, 08:31:07 am »
Here's how high pass filter affects the FFT diagram:



Gaussian blur (=low pass filter) does the same at the edges of the diagram:



This does seem pretty similar with Raj's images, here are the FFT diagrams for "various size grain" noise patterns that I mentioned in the other thread:



For example, FFT diagram for noise sample from my camera looks like this:

« Last Edit: June 13, 2008, 08:47:25 am by nekitamo »

Offline nekitamo

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Re: Fourier transform study
« Reply #4 on: June 13, 2008, 09:23:39 am »
I just thought of one more test - here are some totally random samples with their respective FFT diagrams from various images I took with my camera in which I managed to find an uniform-colour 256x256 square :



Camera's distinct noise signature seems to be recognizable in most of the samples, but not all. Perhaps it would be better if I did separate FFT analysis for each color...

Offline nekitamo

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Re: Fourier transform study
« Reply #5 on: June 13, 2008, 10:47:41 am »
Here's yet another FFT comparison...
I did separate analysis for each color channel of noise samples from my camera, Raj's PICT14 and DiMageX sample selected by elevenaugust. The procedure was the same for each sample (color separation->high-pass->autocontrast->desaturate->FFT), except that for two top rows I used 512x512 samples and the bottom one is 256x256 (no adequate uniform area):



As you can see, there are noticeable differences in noise FFT between color channels for both cameras, but almost none in sample taken from Raj's image.

Offline nekitamo

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Re: Fourier transform study
« Reply #6 on: June 13, 2008, 01:38:50 pm »
Here's a comparison of three different blue-sky samples shot with EOS350D camera with samples from Stephen's images:



Again, no match... not to mention that "halo" in image 060 is very similar with Raj's PICT14 sample - both look like somewhat filtered uniform noise.

Offline nekitamo

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Re: Fourier transform study
« Reply #7 on: June 13, 2008, 03:05:00 pm »
Here's how JPEG quality affects FFT diagram - same noise sample was saved with various quality levels, then FFT analysed:



Actually, the "original" can be also considered as JPEG with ~95% quality, as it also came in JPG format from the camera.

Offline elevenaugust

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Re: Fourier transform study
« Reply #8 on: June 13, 2008, 04:34:28 pm »
Hi Neki! Once again, great work.
It help me to try again with Image Analyzer and, after a few tries, I think I got a good match:


The left is Raj PICT0016 proceed as usual: 256*256 square of blue sky----->convert to grayscale----->highpass filter both direction radius 3px------>Fourier transform----->Complex map representation square root method with color range 0>x>0.4

The right is the blue sky portion of my image test proceed like this:
1- Add Noise intensity 20 and saturation 200
2- Save as JPEG 70% (!!)
Then, with Image Analyzer, the usual process:
Convert to grayscale----->highpass filter both direction radius 3px------>Fourier transform----->Complex map representation square root method with color range 0>x>0.4.

NOTE: I haven't add any Gaussian blur, since the differences between the results of various radius test are not very obvious, however maybe you can try it, using the same process as mine?

We can try to refine this, maybe with a complete study including split color plane (RGB) and recombine fft.

What could be the conclusion of these results?
1- There's (maybe) a slight addition of Gaussian blur, need to be confirmed.
2- Jtp was wrong when he said that jpeg compression doesn't affect the fft.
3- It's a combination of noise and jpeg compression artifact that gives this fft shape of Raj's PICT0016 picture.
4- The noise added is consequent (Intensity 20 and color saturation +/-200). The question is why the hell Raj or his brother-in-law added this noise? Unless there is an automatic process that can add it....
5- The Jpeg compression is somewhere around 70-80%.

Another consequence of this is that, but we need to verify the fft in full colors, we can say that Raj effectively used a Minolta DimageX, but that the fft was degraded by addition of noise and by saving the picture in jpeg at 70-80%.
« Last Edit: June 13, 2008, 04:57:19 pm by elevenaugust »
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Offline nekitamo

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Re: Fourier transform study
« Reply #9 on: June 13, 2008, 05:52:09 pm »
Well, what you just described seems like a great way for hiding any camera signature. :)
Here's what the same process does with the signature of my camera - it also looks like Raj's in the end:



Actually, I remember reading about this somewhere - found it, here.

In short, the author recommends cleaning EXIF data, cropping, resizing, adding noise and saving with low jpeg quality as means for destruction of camera signature. Certainly fits Raj's images - remember my speculation about resizing being the reason for various sizes of noise grain? So did Raj and Stephen use described methods to hide signatures of their cameras? Did Chad and Ty use printing and scanning back for the same purpose?

Also, be sure to visit the link mentioned in step 1 - actually, I already visited it before reading this, as spf33 mentioned it on OM forum - especially the titles of publications:

- Determining Digital Image Origin Using Sensor Imperfections
- Digital Camera Identification from Sensor Noise
- Detecting Digital Image Forgeries Using Sensor Pattern Noise
...