Noise calibration

Prerequisites

1. Rawpy

The calibration code the raspy package, which can be installed based on this instructions(https://pypi.org/project/rawpy/)

Note: If rawpy cannot be installed on Mac(m1/m2), you can refer to this issue(https://github.com/letmaik/rawpy/issues/171)

2. data

It is recommended that you organize the data to be calibrated into separate folders for each camera. Within each camera folder, you should further divide the data into several subfolders based on different ISO values.

Data Capture and Principles

We used five different models of cameras to separately capture color cards (24 color blocks) and black images. The color card is shown in the following image:

Dark images are as shown in the image below：

Both the color card and the black images were captured at nine different ISO values, with 15 identical images taken at each ISO value

$\text{Var}(D) = K(K I)+\text{Var}\left(N_o\right)$

Therefore, according to the formula mentioned in ELD¹, it is equivalent to obtaining 24 sets of different data points for each color card image under each ISO. Hence, we can fit a straight line and obtain the K and the signal-independent noise for the current camera at the current ISO：

Next, we obtain other parameters based on the captured dark images. Firstly, we can derive the distribution parameters of the sum of Read Noise (assuming it follows a TL distribution or a Gaussian distribution) and row noise by calculating the mean and variance of the entire image. Subsequently, we can obtain the parameters for the two assumptions where the Read Noise follows either a TL distribution or a Gaussian distribution.

Finally, according to the formula in ELD¹:

$\log (\sigma_{TL}) \mid \log (K) \sim \mathcal{N}(a_{TL} \log (K)+b_{TL}, \hat{\sigma}_{TL})$

$\log (\sigma_r) \mid \log (K) \sim \mathcal{N}(a_r \log (K)+b_r, \hat{\sigma}_r)$

We can use the K and distribution parameters obtained for each camera at different ISO levels as data points to fit a logarithmic linear relationship between them：

calibration process

For the calibration process, you can execute all steps at once by directly following the code given in the main function, or you can perform each step separately according to your needs. These steps include selecting the positions of color blocks, calibrating the color blocks to obtain K, calibrating dark images to obtain other parameters, and fitting log(K) and log(variance).

Acknowledgments

This code is based on the related works of ELD and PMN. We hereby express our gratitude to the authors and contributors of ELD¹ and PMN²!

Footnotes

1. 1https://arxiv.org/abs/2108.02158 ↩ ↩² ↩³

2. https://github.com/megvii-research/PMN/tree/TPAMI ↩