# An Evaluation Framework for the Accuracy of Camera Transfer Functions Estimated from Differently Exposed Images

## Summary (2 min read)

### 1. Estimating and Measuring the Camera Transfer Function

- Many algorithms in computer vision assume that the radiance of the scene is known.
- Changes in scene radiance between images can be used to determine scene structure and illumination [12].
- Alternatively a polynomial [11] or a constrained piecewise linear model has been used [1, 2].
- The authors use these images to estimate the CTF by one of the above methods, thus enabling a quantitative comparison of estimated and measured CTF.

### 2. Experimental Setup

- The authors CTF measurements are based essentially on a homogeneous light source realized by an integrating sphere .
- The authors illuminate the camera sensor directly by this light source, with all optics removed to ensure homogeneous illumination over the entire sensor area, and to avoid distortions introduced by the optics.
- The image acquisition process integrates this irradiance E (measured in Wm2 ) over exposure time t and area A of a sensor element, yielding the energy.

### Q = AEt

- Additionally, in case of a color camera, the irradiance incident on the sensor will be filtered by colorfilters (e.g., Bayer color-filter-array) beforehand.
- The quantity of light q undergoes further mostly nonlinear transformations described by the CTF f such as, e.g., dynamic range compression and quantization.
- To measure the CTF in their experimental setup, the authors record the camera response f(q) for different known distances x.
- Samples of the CTF are then straightfowardly obtained from (2) and (3).
- The image pairs of exposure ratio k = 2 recorded this way are used to estimate the CTF like in [10, 8].

### 3. Estimating the Camera Transfer Function

- Based on such an image pair the joint histogram between these two images [10, 8] can be computed.
- Afterwards the function g(f), defined by g(f(q)) = f(kq) has to be estimated from this joint histogram.
- The line has been fitted into the datapoints between the toe and shoulder region using a linear regression χ2-fitting.

### 4. Results

- Range limits are not accounted for in this model.
- Therefore α corresponds to the dark current for positive values only.
- The mean absolute difference between these data points and the fitted model of the measured CTF is µred = 0.4973, µgreen = 0.1870, and µblue = 0.4705 intensity values for the red, green, and blue channel respectively, which proves that the model assumption is valid for this camera.
- As can be seen in figure 3, the camera model (1) does not fit as good as for the 3-chip camera.
- Table 2 shows the measured and estimated parameters for each color channel of the AVT Dolphin F145C single chip Bayer colorfilter-array camera.

### 5. Discussion

- The authors have shown that it is possible to directly measure the CTF and, under the same environmental circumstances, to acquire image pairs with known exposure ratio.
- The directly measured CTF can be used to verify the accuracy of the assumed camera model or to find a camera model for a specific camera.
- From the simultaneously acquired image pairs of known exposure ratio one can estimate the CTF using the same algorithms which are available for nonlaboratory conditions.
- Additionally this method can give insight into the limitations of an estimation algorithm for the CTF, which can be used to improve the algorithm.

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##### Citations

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### Cites background from "An Evaluation Framework for the Acc..."

...Also the camera may have a nonlinear camera transfer function [35] relating the incident radiation to gray levels....

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### Cites background from "An Evaluation Framework for the Acc..."

...The exposure times are set as EV (exposure value)....

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##### References

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### "An Evaluation Framework for the Acc..." refers methods in this paper

...Also, the orientation of visible surfaces of the scene can be obtained from the radiance by shape from shading algorithms [2]....

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1,204 citations

### "An Evaluation Framework for the Acc..." refers methods in this paper

...Radiance maps were moreover used to render synthetic objects more realistically into the scene [3]....

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837 citations

### "An Evaluation Framework for the Acc..." refers methods in this paper

...An alternative to chart-based measurements of the CTF is to use differently exposed images of the same scene [4, 5, 6, 7, 8, 9, 10, 11, 12]....

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...Alternatively a polynomial [8] or a constrained piecewise linear model has been used [11, 12]....

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303 citations

### "An Evaluation Framework for the Acc..." refers background or methods in this paper

...It has been shown that one needs to either know the exposure ratios or make an assumption about the CTF [9, 10]....

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...An alternative to chart-based measurements of the CTF is to use differently exposed images of the same scene [4, 5, 6, 7, 8, 9, 10, 11, 12]....

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##### Frequently Asked Questions (2)

###### Q2. What have the authors stated for future works in "An evaluation framework for the accuracy of camera transfer functions estimated from differently exposed images" ?

The authors intend to evaluate further estimation algorithms and a larger variety of cameras, in the near future.