The Statistical Fingerprint of AI-Generated Images - Revision history

Mikesomm: /* Photometric Statistics: Signal-Dependent Noise */

2026-01-02T03:26:14Z

Photometric Statistics: Signal-Dependent Noise

← Older revision		Revision as of 03:26, 2 January 2026
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	=== Photometric Statistics: Signal-Dependent Noise ===		=== Photometric Statistics: Signal-Dependent Noise ===

	[[File:Localnoiseresponse.pn\|thumb\|right\|600px\|Figure 9: Photometric Statistics. Left: The Camera simulation (Set B) shows a strong correlation between signal intensity and local variance (slope = 1.94), consistent with photon shot noise processed through a non-linear gamma curve. Right: The GenAI (Set C) shows a much weaker relationship (slope = 0.80), indicating that the noise is a uniform texture rather than a physical signal-dependent phenomenon.]]		[[File:Localnoiseresponse.png\|thumb\|right\|600px\|Figure 9: Photometric Statistics. Left: The Camera simulation (Set B) shows a strong correlation between signal intensity and local variance (slope = 1.94), consistent with photon shot noise processed through a non-linear gamma curve. Right: The GenAI (Set C) shows a much weaker relationship (slope = 0.80), indicating that the noise is a uniform texture rather than a physical signal-dependent phenomenon.]]

	In a physical imaging system, noise is signal-dependent. Photon shot noise follows a Poisson distribution where the variance <math>\sigma^2</math> increases linearly with the mean intensity <math>\mu</math>.[[#ref12\|<sup>[12]</sup>]] To test for this physical signature, local variance was analyzed against local mean intensity in non-overlapping <math>8 \times 8</math> pixel blocks. The relationship is modeled as:		In a physical imaging system, noise is signal-dependent. Photon shot noise follows a Poisson distribution where the variance <math>\sigma^2</math> increases linearly with the mean intensity <math>\mu</math>.[[#ref12\|<sup>[12]</sup>]] To test for this physical signature, local variance was analyzed against local mean intensity in non-overlapping <math>8 \times 8</math> pixel blocks. The relationship is modeled as:

Mikesomm: /* Feature Extraction and Results */

2026-01-02T03:25:56Z

Feature Extraction and Results

← Older revision		Revision as of 03:25, 2 January 2026
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	=== Photometric Statistics: Signal-Dependent Noise ===		=== Photometric Statistics: Signal-Dependent Noise ===

	[[File:Localnoiseresponse.~~png~~\|thumb\|right\|600px\|Figure 9: Photometric Statistics. Left: The Camera simulation (Set B) shows a strong correlation between signal intensity and local variance (slope = 1.94), consistent with photon shot noise processed through a non-linear gamma curve. Right: The GenAI (Set C) shows a much weaker relationship (slope = 0.80), indicating that the noise is a uniform texture rather than a physical signal-dependent phenomenon.]]		[[File:Localnoiseresponse.pn\|thumb\|right\|600px\|Figure 9: Photometric Statistics. Left: The Camera simulation (Set B) shows a strong correlation between signal intensity and local variance (slope = 1.94), consistent with photon shot noise processed through a non-linear gamma curve. Right: The GenAI (Set C) shows a much weaker relationship (slope = 0.80), indicating that the noise is a uniform texture rather than a physical signal-dependent phenomenon.]]

	In a physical imaging system, noise is signal-dependent. Photon shot noise follows a Poisson distribution where the variance <math>\sigma^2</math> increases linearly with the mean intensity <math>\mu</math>.[[#ref12\|<sup>[12]</sup>]] To test for this physical signature, local variance was analyzed against local mean intensity in non-overlapping <math>8 \times 8</math> pixel blocks. The relationship is modeled as:		In a physical imaging system, noise is signal-dependent. Photon shot noise follows a Poisson distribution where the variance <math>\sigma^2</math> increases linearly with the mean intensity <math>\mu</math>.[[#ref12\|<sup>[12]</sup>]] To test for this physical signature, local variance was analyzed against local mean intensity in non-overlapping <math>8 \times 8</math> pixel blocks. The relationship is modeled as:

Mikesomm: /* Summary */

2025-12-14T09:41:55Z

Summary

← Older revision		Revision as of 09:41, 14 December 2025
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	== Conclusion ==		== Conclusion ==

	=== Summary ===		=== Summary of Outcomes ===

	This project successfully established a radiometric forensic framework to distinguish between physically simulated photographs and artificially generated images. A triplet dataset including spectral radiance, simulated photography, and artificially generated imagery was created for a rigorous evaluation of generative AI's physical fidelity. The analysis revealed that while Stable Diffusion v1.5 is highly effective at mimicking the semantic appearance of a photograph, it often fails to respect the radiometric laws of physics. Specifically:		This project successfully established a radiometric forensic framework to distinguish between physically simulated photographs and artificially generated images. A triplet dataset including spectral radiance, simulated photography, and artificially generated imagery was created for a rigorous evaluation of generative AI's physical fidelity. The analysis revealed that while Stable Diffusion v1.5 is highly effective at mimicking the semantic appearance of a photograph, it often fails to respect the radiometric laws of physics. Specifically:

Mikesomm: /* Summary of Achievements */

2025-12-14T09:41:36Z

Summary of Achievements

← Older revision		Revision as of 09:41, 14 December 2025
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	== Conclusion ==		== Conclusion ==

	=== Summary ~~of Achievements~~ ===		=== Summary ===

	This project successfully established a radiometric forensic framework to distinguish between physically simulated photographs and artificially generated images. A triplet dataset including spectral radiance, simulated photography, and artificially generated imagery was created for a rigorous evaluation of generative AI's physical fidelity. The analysis revealed that while Stable Diffusion v1.5 is highly effective at mimicking the semantic appearance of a photograph, it often fails to respect the radiometric laws of physics. Specifically:		This project successfully established a radiometric forensic framework to distinguish between physically simulated photographs and artificially generated images. A triplet dataset including spectral radiance, simulated photography, and artificially generated imagery was created for a rigorous evaluation of generative AI's physical fidelity. The analysis revealed that while Stable Diffusion v1.5 is highly effective at mimicking the semantic appearance of a photograph, it often fails to respect the radiometric laws of physics. Specifically:

Mikesomm: /* Appendix */

2025-12-14T09:37:17Z

Appendix

← Older revision		Revision as of 09:37, 14 December 2025
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	== Appendix ==		== Appendix ==

	The dataset and code used in this project can be found at ~~[GitHub Link]~~.		The dataset and code used in this project can be found at https://github.com/mikesomms/The-Statistical-Fingerprint-of-AI-Generated-Images.git.

Mikesomm: Added appendix; need to add GitHub link.

2025-12-14T09:32:56Z

Added appendix; need to add GitHub link.

← Older revision		Revision as of 09:32, 14 December 2025
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	== References ==		== References ==

	<div id="ref1">[1] Glynn, B. P. (2023). Sony World Photography Award 2023: Winner refuses award after revealing AI creation. https://www.bbc.com/news/entertainment-arts-65296763. </div>		<div id="ref1">[1] Glynn, B. P. (2023). Sony World Photography Award 2023: Winner refuses award after revealing AI creation. https://www.bbc.com/news/entertainment-arts-65296763. </div>
	<div id="ref2">[2] Valyaeva, A. (2024). AI image statistics for 2024: How much content was created by AI. Everypixel Journal. https://journal.everypixel.com/ai-image-statistics. </div>		<div id="ref2">[2] Valyaeva, A. (2024). AI image statistics for 2024: How much content was created by AI. Everypixel Journal. https://journal.everypixel.com/ai-image-statistics. </div>
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	<div id="ref11">[11] Liu, Z., Shah, D., & Wandell, B. A. (2025). ISETHDR: A Physics-Based Synthetic Radiance Dataset for High Dynamic Range Driving Scenes. IEEE Sensors Journal, 25(9), 15261–15269. https://doi.org/10.1109/JSEN.2025.3550455. </div>		<div id="ref11">[11] Liu, Z., Shah, D., & Wandell, B. A. (2025). ISETHDR: A Physics-Based Synthetic Radiance Dataset for High Dynamic Range Driving Scenes. IEEE Sensors Journal, 25(9), 15261–15269. https://doi.org/10.1109/JSEN.2025.3550455. </div>
	<div id="ref12">[12] Wandell, B. (2025). Foundations of Image Systems Engineering. https://wandell.github.io/FISE-git/. </div>		<div id="ref12">[12] Wandell, B. (2025). Foundations of Image Systems Engineering. https://wandell.github.io/FISE-git/. </div>

			== Appendix ==

			The dataset and code used in this project can be found at [GitHub Link].

Mikesomm: /* Summary of Achievements */

2025-12-14T09:30:29Z

Summary of Achievements

← Older revision		Revision as of 09:30, 14 December 2025
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	This project successfully established a radiometric forensic framework to distinguish between physically simulated photographs and artificially generated images. A triplet dataset including spectral radiance, simulated photography, and artificially generated imagery was created for a rigorous evaluation of generative AI's physical fidelity. The analysis revealed that while Stable Diffusion v1.5 is highly effective at mimicking the semantic appearance of a photograph, it often fails to respect the radiometric laws of physics. Specifically:		This project successfully established a radiometric forensic framework to distinguish between physically simulated photographs and artificially generated images. A triplet dataset including spectral radiance, simulated photography, and artificially generated imagery was created for a rigorous evaluation of generative AI's physical fidelity. The analysis revealed that while Stable Diffusion v1.5 is highly effective at mimicking the semantic appearance of a photograph, it often fails to respect the radiometric laws of physics. Specifically:

	'''Spatial Statistics:''' The AI ~~successfully~~ learned the global blur characteristic of a lens, matching the <math>1/f^\alpha</math> power law slope of the camera simulation (-2.82 vs -2.93) rather than the sharper physical scene (-2.30).		'''Spatial Statistics:''' The AI learned the global blur characteristic of a lens, matching the <math>1/f^\alpha</math> power law slope of the camera simulation (-2.82 vs -2.93) rather than the sharper physical scene (-2.30).

	'''Photometric Statistics:''' The AI failed to replicate signal-dependent photon shot noise. While the camera simulation showed a strong intensity-to-variance relationship (slope = 1.94), the AI produced a uniform noise texture (slope = 0.80) unrelated to photon arrival statistics.		'''Photometric Statistics:''' The AI failed to replicate signal-dependent photon shot noise. While the camera simulation showed a strong intensity-to-variance relationship (slope = 1.94), the AI produced a uniform noise texture (slope = 0.80) unrelated to photon arrival statistics.

Mikesomm: /* Conclusion */

2025-12-14T09:29:41Z

Conclusion

← Older revision		Revision as of 09:29, 14 December 2025
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	'''Spatial Statistics:''' The AI successfully learned the global blur characteristic of a lens, matching the <math>1/f^\alpha</math> power law slope of the camera simulation (-2.82 vs -2.93) rather than the sharper physical scene (-2.30).		'''Spatial Statistics:''' The AI successfully learned the global blur characteristic of a lens, matching the <math>1/f^\alpha</math> power law slope of the camera simulation (-2.82 vs -2.93) rather than the sharper physical scene (-2.30).

	'''Photometric Statistics:''' The AI failed to replicate signal-dependent photon shot noise. While the camera simulation showed a strong ~~variance~~-to-~~intensity~~ relationship (~~Slope~~ = 1.94), the AI produced a uniform noise texture (~~Slope~~ = 0.80) unrelated to photon arrival statistics.		'''Photometric Statistics:''' The AI failed to replicate signal-dependent photon shot noise. While the camera simulation showed a strong intensity-to-variance relationship (slope = 1.94), the AI produced a uniform noise texture (slope = 0.80) unrelated to photon arrival statistics.

	'''Spectral Statistics:''' The AI exhibited high color channel correlation (<math>R^2 = 0.969</math>), suggesting it has learned the demosaicing artifacts present in its training data of internet photographs.		'''Spectral Statistics:''' The AI exhibited high color channel correlation (<math>R^2 = 0.969</math>), suggesting it has learned the demosaicing artifacts present in its training data of internet photographs.

Mikesomm: /* Summary of Achievements */

2025-12-14T09:28:31Z

Summary of Achievements

← Older revision		Revision as of 09:28, 14 December 2025
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	=== Summary of Achievements ===		=== Summary of Achievements ===

	This project successfully established a radiometric forensic framework to distinguish between physically simulated photographs and artificially generated images. ~~By controlling the entire imaging pipeline—from~~ spectral radiance ~~to optical irradiance to sensor voltage—a ground truth dataset~~ was created ~~that allowed~~ for a rigorous evaluation of generative AI's physical fidelity. The analysis revealed that while Stable Diffusion v1.5 is highly effective at mimicking the semantic appearance of a photograph, it often fails to respect the radiometric laws of physics. Specifically:		This project successfully established a radiometric forensic framework to distinguish between physically simulated photographs and artificially generated images. A triplet dataset including spectral radiance, simulated photography, and artificially generated imagery was created for a rigorous evaluation of generative AI's physical fidelity. The analysis revealed that while Stable Diffusion v1.5 is highly effective at mimicking the semantic appearance of a photograph, it often fails to respect the radiometric laws of physics. Specifically:

	'''Spatial Statistics:''' The AI successfully learned the global blur characteristic of a lens, matching the <math>1/f^\alpha</math> power law slope of the camera simulation (-2.82 vs -2.93) rather than the sharper physical scene (-2.30).		'''Spatial Statistics:''' The AI successfully learned the global blur characteristic of a lens, matching the <math>1/f^\alpha</math> power law slope of the camera simulation (-2.82 vs -2.93) rather than the sharper physical scene (-2.30).
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	'''Spectral Statistics:''' The AI exhibited high color channel correlation (<math>R^2 = 0.969</math>), suggesting it has learned the demosaicing artifacts present in its training data of internet photographs.		'''Spectral Statistics:''' The AI exhibited high color channel correlation (<math>R^2 = 0.969</math>), suggesting it has learned the demosaicing artifacts present in its training data of internet photographs.

	'''Optical Statistics:''' The most significant discriminator was the Point Spread Function. The AI rendered bright light sources as generic Gaussian blobs, completely missing the wave-optics diffraction patterns (starbursts) mandated by the physical aperture.		'''Optical Statistics:''' The most significant visual discriminator was the Point Spread Function. The AI rendered bright light sources as generic Gaussian blobs, completely missing the wave-optics diffraction patterns (starbursts) mandated by the physical aperture.

	[[File:radiometricsummary.png\|thumb\|center\|800px\|Figure 12: Summary of Radiometric Forensics. This study successfully identified statistical fingerprints across four physical domains. While AI models have learned to mimic the global blur (Spatial) and color coupling (Spectral) of digital cameras, they fail to replicate the signal-dependent nature of photon shot noise (Photometric) and the wave-optics diffraction of point sources (Optical).]]		[[File:radiometricsummary.png\|thumb\|center\|800px\|Figure 12: Summary of Radiometric Forensics. This study successfully identified statistical fingerprints across four physical domains. While AI models have learned to mimic the global blur (Spatial) and color coupling (Spectral) of digital cameras, they fail to replicate the signal-dependent nature of photon shot noise (Photometric) and the wave-optics diffraction of point sources (Optical).]]

Mikesomm: Moved figures down.

2025-12-14T05:25:16Z

Moved figures down.

← Older revision		Revision as of 05:25, 14 December 2025
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	=== Local Spatial Statistics: Gradient Magnitude ===		=== Local Spatial Statistics: Gradient Magnitude ===

	[[File:Localnoiseresponse.png\|thumb\|right\|600px\|Figure 9: Photometric Statistics. Left: The Camera simulation (Set B) shows a strong correlation between signal intensity and local variance (slope = 1.94), consistent with photon shot noise processed through a non-linear gamma curve. Right: The GenAI (Set C) shows a much weaker relationship (slope = 0.80), indicating that the noise is a uniform texture rather than a physical signal-dependent phenomenon.]]

	While the Power Spectral Density provides a global view of frequency content, it can be dominated by large-scale structures. To investigate spatial statistics at a finer granularity, the gradient magnitude was analyzed as a complementary metric. This feature measures the strength of local contrast transitions at every pixel <math>(x,y)</math>, defined as the magnitude of the gradient vector:		While the Power Spectral Density provides a global view of frequency content, it can be dominated by large-scale structures. To investigate spatial statistics at a finer granularity, the gradient magnitude was analyzed as a complementary metric. This feature measures the strength of local contrast transitions at every pixel <math>(x,y)</math>, defined as the magnitude of the gradient vector:
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	=== Photometric Statistics: Signal-Dependent Noise ===		=== Photometric Statistics: Signal-Dependent Noise ===

	[[File:~~Colorcorr~~.png\|thumb\|right\|~~800px~~\|Figure 10: ~~Spectral~~ Statistics. ~~Heatmaps showing the correlation between Red and Green channels.~~ Set ~~A (Physics, left~~) shows ~~lower~~ correlation (~~<math>R^2~~=0.~~958</math>~~) ~~due to spectral independence~~. ~~Set B~~ (~~Camera, <math>R^2=0.965</math>, center) and~~ Set C (~~GenAI, <math>R^2~~=0.~~969</math>, right~~) ~~show higher coupling~~, ~~likely due to the AI learning the color interpolation artifacts of~~ the ~~Bayer filter demosaicing process~~.]]		[[File:Localnoiseresponse.png\|thumb\|right\|600px\|Figure 9: Photometric Statistics. Left: The Camera simulation (Set B) shows a strong correlation between signal intensity and local variance (slope = 1.94), consistent with photon shot noise processed through a non-linear gamma curve. Right: The GenAI (Set C) shows a much weaker relationship (slope = 0.80), indicating that the noise is a uniform texture rather than a physical signal-dependent phenomenon.]]

	In a physical imaging system, noise is signal-dependent. Photon shot noise follows a Poisson distribution where the variance <math>\sigma^2</math> increases linearly with the mean intensity <math>\mu</math>.[[#ref12\|<sup>[12]</sup>]] To test for this physical signature, local variance was analyzed against local mean intensity in non-overlapping <math>8 \times 8</math> pixel blocks. The relationship is modeled as:		In a physical imaging system, noise is signal-dependent. Photon shot noise follows a Poisson distribution where the variance <math>\sigma^2</math> increases linearly with the mean intensity <math>\mu</math>.[[#ref12\|<sup>[12]</sup>]] To test for this physical signature, local variance was analyzed against local mean intensity in non-overlapping <math>8 \times 8</math> pixel blocks. The relationship is modeled as:
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	=== Spectral Statistics: Color Correlation ===		=== Spectral Statistics: Color Correlation ===

	[[File:~~PSF~~.png\|thumb\|right\|~~600px~~\|Figure 11: ~~Optical~~ Statistics. ~~The Point Spread Function~~ (~~PSF~~) ~~extracted from the brightest pixel in the scene~~. ~~Left: The~~ Camera ~~simulation correctly displays~~ the ~~6-point starburst diffraction pattern caused by~~ the ~~triangular aperture. Right: The AI generation fails to replicate this wave-optics phenomenon, rendering a generic Gaussian blob instead~~.]]		[[File:Colorcorr.png\|thumb\|right\|800px\|Figure 10: Spectral Statistics. Heatmaps showing the correlation between Red and Green channels. Set A (Physics, left) shows lower correlation (<math>R^2=0.958</math>) due to spectral independence. Set B (Camera, <math>R^2=0.965</math>, center) and Set C (GenAI, <math>R^2=0.969</math>, right) show higher coupling, likely due to the AI learning the color interpolation artifacts of the Bayer filter demosaicing process.]]

	Physical light sources often have distinct spectral power distributions, meaning the energy in the Red and Green channels should vary somewhat independently (for example, a red taillight vs. a green signal). However, digital cameras introduce color coupling through the use of Color Filter Arrays (CFAs) and demosaicing algorithms, which interpolate missing color values from neighbors.[[#ref12\|<sup>[12]</sup>]] To quantify this coupling process, the Pearson correlation coefficient <math>r_{RG}</math> was computed for pixel pairs:		Physical light sources often have distinct spectral power distributions, meaning the energy in the Red and Green channels should vary somewhat independently (for example, a red taillight vs. a green signal). However, digital cameras introduce color coupling through the use of Color Filter Arrays (CFAs) and demosaicing algorithms, which interpolate missing color values from neighbors.[[#ref12\|<sup>[12]</sup>]] To quantify this coupling process, the Pearson correlation coefficient <math>r_{RG}</math> was computed for pixel pairs:
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	=== Optical Statistics: Point Spread Function (PSF) ===		=== Optical Statistics: Point Spread Function (PSF) ===

			[[File:PSF.png\|thumb\|right\|600px\|Figure 11: Optical Statistics. The Point Spread Function (PSF) extracted from the brightest pixel in the scene. Left: The Camera simulation correctly displays the 6-point starburst diffraction pattern caused by the triangular aperture. Right: The AI generation fails to replicate this wave-optics phenomenon, rendering a generic Gaussian blob instead.]]

	The most critical test of physical realism in night scenes is the Point Spread Function (PSF). High-intensity point sources should diffract according to the wave nature of light and the shape of the aperture.[[#ref12\|<sup>[12]</sup>]] The simulation used a triangular aperture, which physically mandates a 6-point starburst pattern. The effective PSF was extracted by cropping a <math>64 \times 64</math> region around the maximum intensity pixel <math>(x_0, y_0)</math> in each image:		The most critical test of physical realism in night scenes is the Point Spread Function (PSF). High-intensity point sources should diffract according to the wave nature of light and the shape of the aperture.[[#ref12\|<sup>[12]</sup>]] The simulation used a triangular aperture, which physically mandates a 6-point starburst pattern. The effective PSF was extracted by cropping a <math>64 \times 64</math> region around the maximum intensity pixel <math>(x_0, y_0)</math> in each image: