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arxiv: 2605.16317 · v1 · pith:ECEXLC4Xnew · submitted 2026-05-04 · 💻 cs.CV · physics.optics

Noise2Params: Unification and Parameter Determination from Noise via a Probabilistic Event Camera Model

Owen Root , Julinda Mujo , Min Xu This is my paper

Pith reviewed 2026-05-20 23:29 UTC · model grok-4.3

classification 💻 cs.CV physics.optics
keywords event camerasprobabilistic modelingphoton statisticsnoise eventsparameter estimationS-curvessynthetic datacomputer vision
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The pith

A photon-statistics model unifies noise events and response curves for event cameras.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper develops a probabilistic model for event detection in event cameras based on photon arrival statistics. This model provides a single analytical description for both the random events triggered by noise in static scenes and the characteristic S-shaped response curves that appear when light intensity changes. By showing how these two phenomena are connected through the same underlying probabilities, the work enables a practical method to extract key camera parameters such as contrast threshold and photon conversion factor solely from recordings of unchanging scenes. A sympathetic reader would care because this removes the need for specialized dynamic test setups and supplies realistic synthetic data that improves machine learning performance on real event camera inputs.

Core claim

We develop a foundational probabilistic model for EC event detection, grounded in photon statistics, that unifies the description of static scene noise events and step response curves (S-curves) within a single analytical framework. Three formulations of the probability distributions are derived, spanning all intensity regimes: exact Poisson, saddle-point, and Gaussian. The model reveals the underlying connection between these otherwise disparate EC behaviors and clarifies the interpretation of S-curves, which we show is more nuanced than selecting a fixed probability threshold. Based on this model, we propose Noise2Params, a method for determining camera-specific values of the log-contrast

What carries the argument

The probabilistic distribution of event triggers derived from Poisson photon statistics, which links the rate of noise events in constant illumination to the probability of an event for a given intensity change.

If this is right

  • Parameters B, alpha, and theta can be determined from static scene recordings without dynamic light sources.
  • Synthetic images generated from the model improve CNN reconstruction of static scenes compared to using only experimental data.
  • The S-curve interpretation is more nuanced than a fixed probability threshold.
  • The model supports quantitative design of noise-aware algorithms in low-light conditions.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • This calibration method could enable on-device self-calibration for event cameras in consumer products.
  • The intensity dependence of the leakage term may connect to sensor-specific physical effects like dark current variations.
  • Extending the model to dynamic scenes could provide a full simulation framework for event-based vision.

Load-bearing premise

That fitting the model's predicted noise-event probabilities to counts observed in static scenes directly gives the accurate physical values of the camera parameters without needing separate dynamic tests for validation.

What would settle it

Measuring step response curves with a controlled light source after extracting parameters from static noise and finding that the predicted event probabilities do not match the observed S-curve shapes.

read the original abstract

Accurate, unified models for event cameras (ECs) remain elusive, hampering calibration and algorithm design. We develop a foundational probabilistic model for EC event detection, grounded in photon statistics, that unifies the description of static scene noise events and step response curves (S-curves) within a single analytical framework. Three formulations of the probability distributions are derived, spanning all intensity regimes: exact Poisson, saddle-point, and Gaussian. The model reveals the underlying connection between these otherwise disparate EC behaviors and clarifies the interpretation of S-curves, which we show is more nuanced than selecting a fixed probability threshold. Based on this model, we propose Noise2Params, a method for determining camera-specific values of the log-contrast threshold $B$, the lux-to-photon conversion factor $\alpha$, and the leakage term $\theta$ (found to be intensity dependent), via error minimization against observed noise-event distributions. Noise2Params requires only recordings of static, uniform scenes, offering an experimentally accessible alternative to approaches that demand specialized dynamic light sources. We further support the validity the model by training convolutional neural networks (CNNs) on synthetic noise images generated from our distributions and evaluating their ability to reconstruct static scenes from experimental data. We further demonstrate the utility of our model by showing that CNNs incorporating synthetic data outperform those trained solely on experimental data. Our framework provides a quantitative foundation for EC calibration, noise-aware algorithm design, and applications in photon-limited regimes.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The paper develops a probabilistic model for event camera event detection grounded in photon statistics. It derives three formulations (exact Poisson, saddle-point, and Gaussian) that unify the description of static-scene noise events and step-response curves (S-curves). The authors propose Noise2Params, which determines camera-specific parameters B (log-contrast threshold), alpha (lux-to-photon conversion), and theta (leakage term) by error minimization against observed noise-event counts from static uniform scenes. Validation includes training CNNs on synthetic noise images generated from the distributions and showing improved scene reconstruction on experimental data compared to training on experimental data alone.

Significance. If the unification holds and the fitted parameters transfer across regimes, the work offers an experimentally accessible calibration route that avoids specialized dynamic light sources, together with a quantitative foundation for noise-aware algorithm design and photon-limited applications. The CNN experiments provide concrete evidence of the practical utility of the synthetic data.

major comments (2)
  1. [Abstract and §3 (Model)] Abstract and model derivations: the central unification claim requires that the same photon-statistic model and the fitted values of B, alpha, and theta simultaneously describe both static noise histograms and dynamic S-curve shapes. The Noise2Params procedure minimizes error only against static noise-event counts; no subsequent forward prediction of event probability versus contrast step size, nor quantitative comparison to experimental S-curve data, is reported. Without this cross-check the single-framework unification remains unverified.
  2. [§4 and CNN experiments] §4 (Noise2Params) and validation: parameters are obtained by fitting the model's own distributions to the identical static noise data later used for CNN validation. This creates a circularity risk; the manuscript does not present an independent test (e.g., held-out dynamic measurements or comparison against separately measured S-curves) that would confirm the fitted parameters are not merely effective for the noise regime.
minor comments (2)
  1. [§4] Clarify the functional form and intensity dependence of theta; the abstract states it is intensity dependent, but the fitting procedure and resulting values should be shown explicitly.
  2. [Validation section] Add error bars or confidence intervals to the reported distribution fits and CNN reconstruction metrics to allow assessment of statistical significance.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive feedback on our manuscript. We provide point-by-point responses to the major comments below, clarifying the unification provided by our model and addressing concerns about validation.

read point-by-point responses

  1. Referee: [Abstract and §3 (Model)] Abstract and model derivations: the central unification claim requires that the same photon-statistic model and the fitted values of B, alpha, and theta simultaneously describe both static noise histograms and dynamic S-curve shapes. The Noise2Params procedure minimizes error only against static noise-event counts; no subsequent forward prediction of event probability versus contrast step size, nor quantitative comparison to experimental S-curve data, is reported. Without this cross-check the single-framework unification remains unverified.

    Authors: We appreciate the referee pointing out the need for explicit cross-validation. Our model is derived such that the same photon arrival statistics govern both the noise events in static scenes and the event generation in response to contrast changes, leading to the S-curve as the integral of the probability distribution over contrast steps. The parameters B, alpha, and theta are intrinsic to the camera and scene intensity, so they are expected to apply across regimes. While the current manuscript focuses on the derivation and the Noise2Params fitting from noise data, we agree that a direct forward prediction and comparison to experimental S-curve data would provide stronger empirical support for the unification. In the revised manuscript, we will include such an analysis by simulating S-curves using the fitted parameters and comparing them to measured data from the literature or additional recordings. revision: yes

  2. Referee: [§4 and CNN experiments] §4 (Noise2Params) and validation: parameters are obtained by fitting the model's own distributions to the identical static noise data later used for CNN validation. This creates a circularity risk; the manuscript does not present an independent test (e.g., held-out dynamic measurements or comparison against separately measured S-curves) that would confirm the fitted parameters are not merely effective for the noise regime.

    Authors: We thank the referee for raising this valid concern about potential circularity. The fitting process uses noise-event histograms from static uniform scenes to determine the parameters. The CNN experiments then use these parameters to synthesize noise images for training, with the goal of improving reconstruction performance on experimental event data. The evaluation metrics are computed on experimental data that is separate from the calibration set used for fitting, demonstrating the practical utility and generalization of the model. Nevertheless, to mitigate any perception of circularity, we will revise the manuscript to explicitly state that the test scenes for CNN evaluation are distinct from the static scenes used in Noise2Params calibration, and we will consider adding held-out validation if feasible. revision: partial

Circularity Check

0 steps flagged

No significant circularity: derivation grounded in external photon statistics with independent CNN validation

full rationale

The paper derives its probabilistic event detection model from photon statistics (Poisson process), an external physical principle independent of the target results. Analytical formulations (exact Poisson, saddle-point, Gaussian) connect noise events and S-curves within one framework without self-referential definitions. Noise2Params fits B, alpha, and theta to static noise counts as a calibration procedure, not a renamed prediction. Validity is checked via CNNs trained on model-generated synthetic data that outperform purely experimental training when reconstructing real scenes—an independent empirical test. No load-bearing step reduces claimed unification or parameters to the inputs by construction, and no self-citation chain is invoked for uniqueness.

Axiom & Free-Parameter Ledger

3 free parameters · 1 axioms · 0 invented entities

The central claim rests on photon arrival following Poisson statistics and the validity of the derived distributions for real event cameras; free parameters are the camera-specific values fitted by the method itself.

free parameters (3)
  • log-contrast threshold B
    Camera-specific value determined via error minimization against observed noise-event distributions in Noise2Params.
  • lux-to-photon conversion factor alpha
    Camera-specific value determined via error minimization against observed noise-event distributions in Noise2Params.
  • leakage term theta
    Intensity-dependent term determined via error minimization against observed noise-event distributions in Noise2Params.
axioms (1)
  • domain assumption Event detection in event cameras is governed by photon statistics following a Poisson process.
    Stated as the grounding for the probabilistic model in the abstract.

pith-pipeline@v0.9.0 · 5792 in / 1408 out tokens · 34495 ms · 2026-05-20T23:29:02.395554+00:00 · methodology

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Works this paper leans on

50 extracted references · 50 canonical work pages

  1. [1]

    Event-Based Vision: A Survey , journal =

    Gallego, Guillermo and Delbr. Event-Based Vision: A Survey , journal =. 2022 , doi =

    work page 2022

  2. [2]

    2022 , month = apr, url =

    work page 2022

  3. [3]

    2023 , month = jul, note =

    work page 2023

  4. [4]

    2025 , month = jul, note =

    work page 2025

  5. [5]

    Expected Response for Large Intensity Changes , year =

    work page

  6. [6]

    How to Mask the Effect of Crazy/Hot Pixel , year =

    work page

  7. [7]

    Support Ticket \#171694000117109405 , year =

    work page

  8. [8]

    and Yates, Jacob L

    Cao, Ruiming and Galor, Dekel and Kohli, Amit P. and Yates, Jacob L. and Waller, Laura , title =. Optica , volume =. 2025 , doi =

    work page 2025

  9. [9]

    , title =

    Ross, Sheldon M. , title =. 2014 , isbn =

    work page 2014

  10. [10]

    2014 IEEE International Symposium on Circuits and Systems (

    Brandli, Christian and Muller, Lorenz and Delbruck, Tobi , title =. 2014 IEEE International Symposium on Circuits and Systems (. 2014 , publisher =. doi:10.1109/ISCAS.2014.6865228 , isbn =

    work page doi:10.1109/iscas.2014.6865228 2014

  11. [11]

    , title =

    Wang, Ziwei and Ng, Yonhon and van Goor, Pieter and Mahony, Robert E. , title =. Australasian Conference on Robotics and Automation (. 2019 , url =

    work page 2019

  12. [12]

    Event-Based Vision Sensor for Fast and Dense Single-Molecule Localization Microscopy , journal =

    Cabriel, Cl. Event-Based Vision Sensor for Fast and Dense Single-Molecule Localization Microscopy , journal =. 2023 , doi =

    work page 2023

  13. [13]

    Advanced Maui Optical and Space Surveillance (

    Oliver, Rachel and Savransky, Dmitry , title =. Advanced Maui Optical and Space Surveillance (. 2024 , month = sep, pages =

    work page 2024

  14. [14]

    2011 IEEE International Symposium on Circuits and Systems (

    Posch, Christoph and Matolin, Daniel , title =. 2011 IEEE International Symposium on Circuits and Systems (. 2011 , month = may, publisher =

    work page 2011

  15. [15]

    A 1280 720 Back-Illuminated Stacked Temporal Contrast Event-Based Vision Sensor with 4.86 m Pixels, 1.066

    Finateu, Thomas and Niwa, Atsumi and Matolin, Daniel and Tsuchimoto, Koji and Mascheroni, Alessandro and Reynaud, Eric and Mostafalu, Payam and Brady, Fergus and Chotard, Lo. A 1280 720 Back-Illuminated Stacked Temporal Contrast Event-Based Vision Sensor with 4.86 m Pixels, 1.066. 2020 IEEE International Solid-State Circuits Conference (. 2020 , month = f...

    work page 2020

  16. [16]

    2023 IEEE International Solid-State Circuits Conference (

    Niwa, Atsumi and Mochizuki, Futa and Berner, Raphael and Maruyama, Takashi and Terano, Takashi and Takamiya, Makoto and Kimura, Yuki and Mizoguchi, Katsumi and Miyazaki, Takumi and Kaizu, Shun and Takahashi, Hiroshi and Suzuki, Akira and Brandli, Christian and Wakabayashi, Hiroaki and Oike, Yusuke , title =. 2023 IEEE International Solid-State Circuits Co...

    work page 2023

  17. [17]

    IEEE Journal of Solid-State Circuits , volume =

    Guo, Menghan and Chen, Shoushun and Gao, Zhe and Yang, Wenlei and Bartkovjak, Peter and Qin, Qing and Hu, Xiaoqin and Zhou, Dahei and Uchiyama, Masayuki and Fukuoka, Shimpei and Xu, Chengcheng and Ebihara, Hiroaki and Wang, Andy and Jiang, Peiwen and Jiang, Bo and Mu, Bo and Chen, Huan and Yang, Jason and Dai, TJ and Suess, Andreas and Kudo, Yoshiharu , t...

    work page 2023

  18. [18]

    and Graca, Rui and Kulesza, Lucas and McMahon-Crabtree, Peter , title =

    McReynolds, Brian J. and Graca, Rui and Kulesza, Lucas and McMahon-Crabtree, Peter , title =. Unconventional Optical Imaging IV , series =. 2024 , publisher =

    work page 2024

  19. [19]

    and Graca, Rui and Delbr

    McReynolds, Brian J. and Graca, Rui and Delbr. Experimental Methods to Predict Dynamic Vision Sensor Event Camera Performance , journal =. 2022 , doi =

    work page 2022

  20. [20]

    Daniels, H. E. , title =. The Annals of Mathematical Statistics , volume =. 1954 , doi =

    work page 1954

  21. [21]

    and Menon, V

    Agrawal, Dulli and Leff, Harvey S. and Menon, V. J. , title =. American Journal of Physics , volume =. 1996 , doi =

    work page 1996

  22. [22]

    Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (

    Blau, Yochai and Michaeli, Tomer , title =. Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (. 2018 , doi =

    work page 2018

  23. [23]

    Training a Task-Specific Image Reconstruction Loss , booktitle =

    Mustafa, Aamir and Mikhailiuk, Aliaksei and Iliescu, Dan Andrei and Babbar, Varun and Mantiuk, Rafa. Training a Task-Specific Image Reconstruction Loss , booktitle =. 2022 , month = jan, doi =

    work page 2022

  24. [24]

    Proceedings of the 52nd ISCIE International Symposium on Stochastic Systems Theory and Its Applications , volume =

    Nagano, Koshiro and Mukouyama, Yoshiharu and Nishimura, Takashi and Fujioka, Hiroyuki and Watanabe, Kenji and Kurita, Takio and Hidaka, Akinori , title =. Proceedings of the 52nd ISCIE International Symposium on Stochastic Systems Theory and Its Applications , volume =. 2021 , doi =

    work page 2021

  25. [25]

    Statistical Evaluation of Image Quality Measures , journal =

    Avcibas, Ismail and Sankur, B. Statistical Evaluation of Image Quality Measures , journal =. 2002 , doi =

    work page 2002

  26. [26]

    ACM Computing Surveys , volume =

    Brown, Lisa Gottesfeld , title =. ACM Computing Surveys , volume =. 1992 , doi =

    work page 1992

  27. [27]

    and Sheikh, Hamid R

    Wang, Zhou and Bovik, Alan C. and Sheikh, Hamid R. and Simoncelli, Eero P. , title =. IEEE Transactions on Image Processing , volume =. 2004 , doi =

    work page 2004

  28. [28]

    and Bovik, Alan C

    Wang, Zhou and Simoncelli, Eero P. and Bovik, Alan C. , title =. The Thirty-Seventh Asilomar Conference on Signals, Systems and Computers , volume =. 2003 , doi =

    work page 2003

  29. [29]

    , title =

    Li, Chaofeng and Bovik, Alan C. , title =. Image Quality and System Performance VI , series =. 2009 , publisher =

    work page 2009

  30. [30]

    IEEE Transactions on Image Processing , volume =

    Zhang, Lin and Zhang, Lei and Mou, Xuanqin and Zhang, David , title =. IEEE Transactions on Image Processing , volume =. 2011 , doi =

    work page 2011

  31. [31]

    and Bovik, Alan C

    Sheikh, Hamid R. and Bovik, Alan C. , title =. IEEE Transactions on Image Processing , volume =. 2006 , doi =

    work page 2006

  32. [32]

    IEEE Transactions on Image Processing , volume =

    Zhang, Lin and Shen, Ying and Li, Hongyu , title =. IEEE Transactions on Image Processing , volume =. 2014 , doi =

    work page 2014

  33. [33]

    , title =

    Xue, Wufeng and Zhang, Lei and Mou, Xuanqin and Bovik, Alan C. , title =. IEEE Transactions on Image Processing , volume =. 2014 , doi =

    work page 2014

  34. [34]

    , title =

    Ding, Keyan and Ma, Kede and Wang, Shiqi and Simoncelli, Eero P. , title =. IEEE Transactions on Pattern Analysis and Machine Intelligence , volume =. 2022 , doi =

    work page 2022

  35. [35]

    and Shechtman, Eli and Wang, Oliver , title =

    Zhang, Richard and Isola, Phillip and Efros, Alexei A. and Shechtman, Eli and Wang, Oliver , title =. Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (. 2018 , doi =

    work page 2018

  36. [36]

    Advances in Neural Information Processing Systems , volume =

    Fu, Stephanie and Tamir, Netanel and Sundaram, Shobhita and Chai, Lucy and Zhang, Richard and Dekel, Tali and Isola, Phillip , title =. Advances in Neural Information Processing Systems , volume =. 2023 , url =

    work page 2023

  37. [37]

    Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (

    Agustsson, Eirikur and Timofte, Radu , title =. Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (. 2017 , month = jul, url =

    work page 2017

  38. [38]

    Advances in Neural Information Processing Systems , volume =

    Ho, Jonathan and Jain, Ajay and Abbeel, Pieter , title =. Advances in Neural Information Processing Systems , volume =. 2020 , url =

    work page 2020

  39. [39]

    2020 , url =

    Wang, Phil , title =. 2020 , url =

    work page 2020

  40. [40]

    Proceedings of the AAAI Conference on Artificial Intelligence , volume =

    Perez, Ethan and Strub, Florian and de Vries, Harm and Dumoulin, Vincent and Courville, Aaron , title =. Proceedings of the AAAI Conference on Artificial Intelligence , volume =. 2018 , url =

    work page 2018

  41. [41]

    International Journal of Computer Vision , volume =

    Wu, Yuxin and He, Kaiming , title =. International Journal of Computer Vision , volume =. 2020 , doi =

    work page 2020

  42. [42]

    Transformers Are

    Katharopoulos, Angelos and Vyas, Apoorv and Pappas, Nikolaos and Fleuret, Fran. Transformers Are. Proceedings of the 37th International Conference on Machine Learning , series =. 2020 , publisher =

    work page 2020

  43. [43]

    and Kaiser, Lukasz and Polosukhin, Illia , title =

    Vaswani, Ashish and Shazeer, Noam and Parmar, Niki and Uszkoreit, Jakob and Jones, Llion and Gomez, Aidan N. and Kaiser, Lukasz and Polosukhin, Illia , title =. Advances in Neural Information Processing Systems , volume =. 2017 , url =

    work page 2017

  44. [44]

    and Ba, Jimmy , title =

    Kingma, Diederik P. and Ba, Jimmy , title =. International Conference on Learning Representations (. 2015 , url =

    work page 2015

  45. [45]

    Yadav, Satyapreet Singh and Pradhan, Bikram and Ajudiya, Kenil Rajendrabhai and Kumar, T. S. and Roy, Nirupam and van Schaik, Andre and Thakur, Chetan Singh , title =. 2025 , eprint =. doi:10.48550/arXiv.2503.15883 , url =

    work page doi:10.48550/arxiv.2503.15883 2025

  46. [46]

    IEEE Sensors Journal , volume =

    Afshar, Saeed and Nicholson, Andrew Peter and van Schaik, Andre and Cohen, Gregory , title =. IEEE Sensors Journal , volume =. 2020 , doi =

    work page 2020

  47. [47]

    Computer Vision -- ECCV 2020 , series =

    Wang, Yuanhao and Idoughi, Ramzi and Heidrich, Wolfgang , title =. Computer Vision -- ECCV 2020 , series =. 2020 , doi =

    work page 2020

  48. [48]

    IEEE Transactions on Pattern Analysis and Machine Intelligence , volume =

    Muglikar, Manasi and Somasundaram, Siddharth and Dave, Akshat and Charbon, Edoardo and Raskar, Ramesh and Scaramuzza, Davide , title =. IEEE Transactions on Pattern Analysis and Machine Intelligence , volume =. 2025 , doi =

    work page 2025

  49. [49]

    The Journal of the Astronautical Sciences , volume =

    Oliver, Rachel and McReynolds, Brian and Savransky, Dmitry , title =. The Journal of the Astronautical Sciences , volume =. 2025 , doi =

    work page 2025

  50. [50]

    and Mujo, Julinda and Xu, Min , title =

    Root, Owen B. and Mujo, Julinda and Xu, Min , title =. Quantum Sensing and Nano Electronics and Photonics. 2026 , date =. doi:10.1117/12.3081979 , url =

    work page doi:10.1117/12.3081979 2026