Color_balance

In photography and image processing, color balance (sometimes gray balance, neutral balance, or white balance) refers to the adjustment of the relative amounts of red, green, and blue primary colors in an image such that neutral colors are reproduced correctly. Color balance changes the overall mixture of colors in an image and is used for generalized color correction.

Most electronic cameras have a means to select the type of illumination under which the photography is being done. Another option on some cameras is a button which one may press when the camera is looking at a gray card or other neutral object, to capture a "custom" color balance. A very common option is "automatic white balance" (AWB), which may be based on a scheme such as Retinex, an artificial neural networkBrian Funt, Vlad Cardei, and Kobus Barnard, "Learning color constancy." Proceedings of the Fourth IS&T/SID Color Imaging Conference, p 58-60 (1996). or a Bayesian method.Graham Finlayson, Paul M Hubel, and Steven Hordley, "Color by correlation." Proceedings of the fifth IS&T/SID Color Imaging Conference, p. 6-11 (1997).

Color balance and chromatic colors

Color balancing an image affects not only the neutrals, but other colors as well. An image that is not color balanced is said to have a color cast, as everything in the image appears to have been shifted towards one color or another.John A C Yule, Principles of Color Reproduction. New York: Wiley, 1967. Color balancing may be thought in terms of removing this color cast.

Color balance is also related to color constancy. Algorithms and techniques used to attain color constancy are frequently used for color balancing, as well. Color constancy is, in turn, related to chromatic adaptation. Conceptually, color balancing consists of two steps: first, determining the illuminant under which an image was captured; and second, scaling the components (e.g., R, G, and B) of the image or otherwise transforming the components so they conform to the viewing illuminant.

Viggiano found that white balancing in the camera\'s native RGB tended to produce less color inconstency (i.e., less distortion of the colors) than in monitor RGB for over 4000 hypothetical sets of camera sensitivities. This difference typically amounted to a factor of more than two in favor of camera RGB. This means that it is advantageous to get color balance right at the time an image is captured, rather than edit later on a monitor. If one must color balance later, balancing the raw image data will tend to produce less distortion of chromatic colors than balancing in monitor RGB.

Mathematics of color balance

Color balancing is sometimes performed on a three-component image (e.g., RGB) using a 3x3 matrix. This type of transformation is appropriate if the image were captured using the wrong white balance setting on a digital camera, or through a color filter.

Scaling monitor R, G, and B

In principle, one wants to scale all relative luminances in an image so that objects which are believed to be neutral appear so. If, say, a surface with R=240 was believed to be a white object, and if 255 is the count which corresponds to white, one could multiply all red values by 255/240. Doing analogously for green and blue would result, at least in theory, in a color balanced image. In this type of transformation the 3x3 matrix is a diagonal matrix.

where $R$, $G$, and $B$ are the color balanced red, green, and blue components of a pixel in the image; $R\backslash \text{'}$, $G\backslash \text{'}$, and $B\backslash \text{'}$ are the red, green, and blue components of the image before color balancing, and $R\backslash \text{'}\_w$, $G\backslash \text{'}\_w$, and $B\backslash \text{'}\_w$ are the red, green, and blue components of a pixel which is believed to be a white surface in the image before color balancing. This is a simple scaling of the red, green, and blue channels, and is why color balance tools in Photoshop and the GIMP have a white eyedropper tool. It has been demonstrated that performing the white balancing in the phosphor set assumed by sRGB tends to produce large errors in chromatic colors, even though it can render the neutral surfaces perfectly neutral.J A Stephen Viggiano, "Comparison of the accuracy of different white balancing options as quantified by their color constancy." Sensors and Camera Systems for Scientific, Industrial, and Digital Photography Applications V: Proceedings of the SPIE, volume 5301. Bellingham, WA: SPIE: the International Society for Optical Engineering, p 323-333 (2004), retrieved online 2007-05-15 from http://www.acolyte-color.com/papers/EI_2004.pdf.

Scaling X, Y, Z

If the image may be transformed into CIE XYZ tristimulus values, the color balancing may be performed there. This has been termed a “wrong von Kries” transformation.Mark D Fairchild, Color Appearance Models. Reading, MA: Addison-Wesley, 1998. Although it has been demonstrated to offer usually poorer results than balancing in monitor RGB, it is mentioned here as a bridge to other things. Mathematically, one computes:

where $X$, $Y$, and $Z$ are the color-balanced tristimulus values; $X\_w$, $Y\_w$, and $Z\_w$ are the tristimulus values of the viewing illuminant (the white point to which the image is being transformed to conform to); $X\backslash \text{'}\_w$, $Y\backslash \text{'}\_w$, and $Z\backslash \text{'}\_w$ are the tristimulus values of an object believed to be white in the un-color-balanced image, and $X\backslash \text{'}$, $Y\backslash \text{'}$, and $Z\backslash \text{'}$ are the tristimulus values of a pixel in the un-color-balanced image. If the tristimulus values of the monitor primaries are in a matrix $\backslash mathbf\{P\}$ so that:

$\backslash left[\backslash begin\{array\}\{c\}\; X\; \backslash \backslash \; Y\; \backslash \backslash \; Z\; \backslash end\{array\}\backslash right]=\backslash mathbf\{P\}\backslash left[\backslash begin\{array\}\{c\}L\_R\; \backslash \backslash \; L\_G\; \backslash \backslash \; L\_B\; \backslash end\{array\}\backslash right]$

where $L\_R$, $L\_G$, and $L\_B$ are the un-gamma corrected monitor RGB, one may use:

Von Kries\'s method

Johannes von Kries, whose theory of rods and three different color-sensitive cone types in the retina has survived as the dominant explanation of color sensation for over 100 years, motivated the method of converting color to the LMS color space, representing the effective stimuli for the Long-, Medium-, and Short-wavelength cone types that are modeled as adapting independently. A 3x3 matrix converts RGB or XYZ to LMS, and then the three LMS primary values are scaled to balance the neutral; the color can then be converted back to the desired final color space:Gaurav Sharma (2003). Digital Color Imaging Handbook. CRC Press. ISBN 084930900X. 

where $L$, $M$, and $S$ are the color-balanced LMS cone tristimulus values; $L\backslash \text{'}\_w$, $M\backslash \text{'}\_w$, and $S\backslash \text{'}\_w$ are the tristimulus values of an object believed to be white in the un-color-balanced image, and $L\backslash \text{'}$, $M\backslash \text{'}$, and $S\backslash \text{'}$ are the tristimulus values of a pixel in the un-color-balanced image.

Matrices to convert to LMS space were not specified by von Kries, but can be derived from CIE color matching functions and LMS color matching functions when the latter are specified; matrices can also be found in reference books.

Scaling camera RGB

By Viggiano\'s measure, and using his model of gaussian camera spectral sensitivities, most camera RGB spaces performed better than either monitor RGB or XYZ. If the camera\'s raw RGB values are known, one may use the 3x3 diagonal matrix:

and then convert to a working RGB space such as sRGB or Adobe RGB after balancing.

See also

• Chromatic adaptation
• Color temperature
• Gamma correction
• White point

References

External links

• Photoshop CS Tutorial listings, Color Balance, Color Selection, and more
• Correction of color balance in photography (GPL Gimp)
• Using Illumination Information in Color Balance Adjustments
• Television Production Color Balancing Cameras
• How do I adjust color balance in Photoshop Elements?
• PhotoNotes.org Dictionary - Colour/color balance

Film- and video-related

• White Balance - Intro at nikondigital.org
• Understanding White Balance - Tutorial
• White Balance - Understanding its use in digital photography

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