HaomiaoJiang

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Background

Display Characterization

Display characterization is the process to build proper models for certain displays and estimate the underlying parameters. The display characteristics are usually measured in two categories, spatial properties and temporal properties. Spatial properties mainly include display gamma value, color bit depth, spectral power distribution, color spectral additivity, pixel independence and so on. Temporal properties include refresh rate, color breakup and so on. Among them, color bit-depth, refresh rate are given by the manufacture and these parameters will not vary a lot between displays. Also, shape of spectral power density is similar among LCD displays, which is shown in figure 1 below.

However, gamma values are different from display to display, even if they are from the same manufacture. So measuring or estimating the gamma for each display is essential in calibrating the display model.

Gamma Curve

Gamma curve characterize the relationship between the inputs value and the output luminance levels. Actually, this encodes and decodes luminance or tristimulus values in video or still image systems.

Gamma is also sometimes called gamma correction, gamma nonlinearity or gamma encoding. Mathematically, gamma correction is, in the simplest cases, defined by the power-law expression:

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle V_{out} = AV_{in} ^ \gamma}

Since black is not purely black and there always more or less exists ambient lighting, we can add a constant term as

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle V_{out} = AV_{in} ^ \gamma + c}

Usage in Vision Experiment

Measuring gamma value of display is essential in preparation of most of the vision experiments. With gamma value and spectral power distribution of the display, we can estimate the spectrum of light coming into the subjects eye. Then, we can transform the spectrum to XYZ or even other color space to do further processing. This process can be described by formular below

 Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle  XYZ = ieXYZfromEngery(SPD*(AV_{in}^\gamma + c_1)+c_2)) }

Here Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle c_1} stands for the luminance of black and Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle c_2} stands for the ambient lighting spectrum. These two terms can sometimes be ignored, assuming that we're working in dark room condition. Also, Spectral power distribution can somehow be estimated from the standard shape of LCD display. Thus, characterizing the gamma value is the critical point in output light estimation process.

Measuring Methods

Traditional Measuring Methods

Measuring Process

Traditionally, gamma values are measured by using spectrometer inside a dark room. Spectrometer is an instrument used to measure properties of light over a specific portion of the electromagnetic spectrum. With the spectrum in visible range, luminance values can also be calibrated by computing the XYZ.

Commonly used spectrometers include PR650 and PR715. An image for PR650 is shown in figure 2 below.

The calibration process is described as below:

1. Stabilize spectrometer on a tripod and focus it on screen
2. Display a flat patch on screen
3. Take measurement of XYZ value (Save Y only)
4. Change brightness levels and redo step 3

To calibrate display with PR650, you can use code from PsychToolbox or from dmToolbox.

Detailed instructions about steps and calling APIs can be found at Vista Lab Wiki Page and pdc wiki correspondingly.

Deficiencies

Although it's very accurate to measure the gamma curve with spectrometer in most cases, it still has some imperfectness.

Its main drawbacks are listed as below

1. High cost - The spectrometer is not affordable to most of the users. It can be only used in labs and some other research institutions.
2. Time consuming - The measuring speed of spectrometer can be extremely slow in low light conditions. When calibration is done with 256 input levels, the measuring process can take up to eight hours.
3. Poor Performance with low light - PR650 is not sensitive enough to measure the luminance when light is below 10 Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle cd/m^2 }

Thus, we need a simple method to make quick estimation about display gamma.

Dithering Methods

In this section, we will introduce a method to estimate the display gamma by matching the luminance of a gray patch and a dithered patch.

The dithering pattern is a kind of chessboard pattern with intervened black-gray (or gray-white). An illusion image about the chessboard pattern is shown in figure 3 below.

Chess box size is equal to the pixel size of the screen. When screen resolution is high enough, the blurring effects in human vision system can make the dithered patch look exactly the same as a gray patch. The brightness can be calculated as an average of the black and gray (or gray and white).

The subjects are asked to match the brightness of the gray patch and dithered patch by adjusting the brightness of gray in dithered patch. When subjects find the match point, we have equation

 Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle I_{gray} = \frac{I_{d\_black}+I_{d\_gray}}{2}+e }

 Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle I = AV_{in}^\gamma + c}

Here Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle e} stands for the error term.

If we have only one data point, display gamma can be solved by minimizing absolute error and we have

 Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle  \gamma = \log (2) / \log(V_{d\_gray}/V_{gray})}

If we have multiple measurements, display gamma can be solved by least mean square algorithm. That is

 Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \gamma = argmin \|e\|_2 = argmin \|2V_{gray}^\gamma-V_{d\_gray}^\gamma-1\|_2}

Online Dithering Test

Online dithering test is a web based application to make a short gamma test online. Its algorithm is almost the same as dithering test.

However, due to the computing complexity limits of online dithering method, we made the following two modifications

1. Subjects are asked to change the intensity of gray patch to make a match instead of adjusting the dithered patch. This is much easier to be handled in web applications but it sacrifices a little the minimun adjustment step size as tradeoffs.
2. Gamma value are calculated through a stochastic manner and the final estimation is made by taking average of gammas from each gray level. This method is much simpler in computation and it doesn't require any space to store the past experiment data. The equation of this stochastic estimation is as below

 Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle  \gamma = \frac{1}{N}\sum\limits_{i=1}^N  \log (2) / \log(V_{d\_gray}^{(i)} /  V_{gray}^{(i)})}

Test Results

Experiment Settings and Test Environment

The experiments are run by two healthy subjects for 15 different levels on two different displays.

Tests are done in normal indoor conditions with up to 150 lux ambient lighting.

Partial tests are done in dark room condition to see the influence of ambient lighting.

No tests have been done in outdoor conditions (up to 400 lux) since most LCD displays are not supposed to be used in that kind of environment.

Dithering Method Test Results

Some text. Some analysis. Some figures.

Online Dithering Test Results

Some text. Some analysis. Some figures. Maybe some equations.

Conclusions

Here is where you say what your results mean.

References - Resources and related work

References

Software

Appendix I - Code and Data

Code

File:CodeFile.zip

Data

zip file with my data