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 was 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 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 , , and are the color balanced red, green, and blue components of a pixel in the image; , , and are the red, green, and blue components of the image before color balancing, and , , and 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 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. 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. 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 , , and are the color-balanced tristimulus values; , , and are the tristimulus values of the viewing illuminant (the white point to which the image is being transformed to conform to); , , and are the tristimulus values of an object believed to be white in the