Investigate circles in Fourier domain of the estimated PRNU #76

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opened 2024-05-16 01:34:23 +02:00 by Benjamin_Loison · 5 comments

Benjamin_Loison commented 2024-05-16 01:34:23 +02:00

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In Fourier domain

leads to

in the image domain, so as shown for instance in the estimated PRNU using the non-local means denoiser (see issues/69#issuecomment-1884) we notice a radial gradient so all the circles we notice in the FFT are equivalent to this smooth radial gradient.

With wavelet and bilateral especially denoisers, and to some extent initial images we also significantly notice circles in the estimated PRNU, see issues/59#issuecomment-1721.

Related to #70 and #74.

In Fourier domain  leads to  in the image domain, so as shown for instance in the estimated PRNU using the non-local means denoiser (see [issues/69#issuecomment-1884](https://gitea.lemnoslife.com/Benjamin_Loison/Robust_image_source_identification_on_modern_smartphones/issues/69#issuecomment-1884)) we notice a radial gradient so all the circles we notice in the FFT are equivalent to this smooth radial gradient. With wavelet and bilateral especially denoisers, and to some extent initial images we also significantly notice circles in the estimated PRNU, see [issues/59#issuecomment-1721](https://gitea.lemnoslife.com/Benjamin_Loison/Robust_image_source_identification_on_modern_smartphones/issues/59#issuecomment-1721). Related to #70 and #74.

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Benjamin_Loison commented 2024-05-16 01:39:56 +02:00

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Let us consider the FFT considering a centered crop of 800x800 of the estimated PRNU.

RESOLUTION = 800
padHeight, padWidth = [(dimension - RESOLUTION) // 2 for dimension in image.shape]
image = image[padHeight:-padHeight, padWidth:-padWidth]

Cropped PRNU:

FFT:

Zoom 100x100:

We still notice circles in the FFT but less significant it seems than without cropping, see issues/70#issuecomment-1886.

As it seems we were able to guess the sizes of circles when considering the whole image, do we find the same sizes for this crop?

Let us consider the FFT considering a centered crop of 800x800 of the estimated PRNU. ```python RESOLUTION = 800 padHeight, padWidth = [(dimension - RESOLUTION) // 2 for dimension in image.shape] image = image[padHeight:-padHeight, padWidth:-padWidth] ``` Cropped PRNU:  FFT:  Zoom 100x100:  We still notice circles in the FFT but less significant it seems than without cropping, see [issues/70#issuecomment-1886](https://gitea.lemnoslife.com/Benjamin_Loison/Robust_image_source_identification_on_modern_smartphones/issues/70#issuecomment-1886). As it seems we were able to guess the sizes of circles when considering the whole image, do we find the same sizes for this crop?

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Benjamin_Loison commented 2024-05-16 01:59:34 +02:00

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Should generare a white image with vignetting and see how the FFT looks like, see #69.

Let us consider a 2D degree 2 polynomial y(r) = ar^2 + br + c matching the center and corner conditions of Rafael 23/04/24 first image being DSC03294:

After GIMP Image > Mode > Grayscale:

Top left pixel: 31,8
Center pixel: 42,0

Distance both of these pixels: d = \sqrt{3000^2 + 2000^2} = 3605.55.

We have y(0) = c = 42 and y(d) = ad^2 + bd = 31.8

So c = 42. Is not there an infinity of possibilities of pairs of a and b?

ad + b = 31.8 / d does not help much and seems to confirm the infinity of solutions.

Maybe could force b = 0.

FFT from artificial vignetting using 3 points to establish a degree 2 polynomial.

Resolution issue leading to significant axes in the Fourier domain when we consider artificial vignetting.

It indeed seems that if we consider an odd resolution artificial vignetting we get a far more consistent Fourier transform:

Resolution issue leading to significant axes in the Fourier domain when we consider artificial vignetting. The axes are still significant but the overall Fourier transform looks consistent. Well in fact I am unable to reproduce the inconsistent previous result.

Should generare a white image with vignetting and see how the FFT looks like, see #69. Let us consider a 2D degree 2 polynomial $y(r) = ar^2 + br + c$ matching the center and corner conditions of Rafael 23/04/24 first image being `DSC03294`:  After GIMP `Image` > `Mode` > `Grayscale`:  Top left pixel: 31,8 Center pixel: 42,0 Distance both of these pixels: $d = \sqrt{3000^2 + 2000^2} = 3605.55$. We have $y(0) = c = 42$ and $y(d) = ad^2 + bd = 31.8$ So $c = 42$. Is not there an infinity of possibilities of pairs of $a$ and $b$? $ad + b = 31.8 / d$ does not help much and seems to confirm the infinity of solutions. Maybe could force $b = 0$. FFT from artificial vignetting using 3 points to establish a degree 2 polynomial.    Resolution issue leading to significant axes in the Fourier domain when we consider artificial vignetting. It indeed seems that if we consider an odd resolution artificial vignetting we get a far more consistent Fourier transform: <img width="4321" alt="vignetting_odd" src="/attachments/b4a41686-e516-4b53-9b6f-e9b96735ddad"> <img width="4321" alt="vignetting_odd_fft" src="/attachments/5401d5ca-dade-4664-b8c1-e622c2c846ff"> Resolution issue leading to significant axes in the Fourier domain when we consider artificial vignetting. The axes are still significant but the overall Fourier transform looks consistent. Well in fact I am unable to reproduce the inconsistent previous result.

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Benjamin_Loison referenced this issue 2024-05-16 11:22:55 +02:00

Investigate rays in Fourier domain for the estimated PRNU #77

Benjamin_Loison commented 2024-05-16 11:30:35 +02:00

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Crop (of above crop) without small circles:

Crop (of above crop) without small circles: 

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Benjamin_Loison commented 2024-05-16 12:56:42 +02:00

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Could check what circle in image domain results in in Fourier domain and for circle in FFT what it results back in FFT if shifts the image in the image domain.

Could check what circle in image domain results in in Fourier domain and for circle in FFT what it results back in FFT if shifts the image in the image domain.

Benjamin_Loison closed this issue 2024-05-16 12:56:44 +02:00

Benjamin_Loison reopened this issue 2024-05-16 12:56:48 +02:00

Benjamin_Loison referenced this issue 2024-05-16 12:59:14 +02:00

Investigate rays in Fourier domain for the estimated PRNU #77

Benjamin_Loison commented 2024-05-31 16:38:37 +02:00

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How to remove circles? Related to #70.

How to remove circles? Related to #70.

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Reference: Benjamin_Loison/Robust_image_source_identification_on_modern_smartphones#76

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