Von Kries Coefficients and Sensor Sharpening

In Chapter 3 we have seen that sensors that have very narrow band-response functions simplify the functions which relate the energy measured by the sensor to the geometry of the object, the reflectance of the object patch, and the irradiance falling onto the patch. If the response function is very narrow, it can be approximated by a delta function. In this case, the energy measured by a sensor I at sensor position X/ is given by 

If the illuminant is assumed to be uniform over the entire image, we obtain an even simpler equation. 

In order to obtain an output image that is corrected for the color of the illuminant we only need to divide each channel by L,. The output image will then appear to have been taken under a white light. This can be done by applying a diagonal transform. Let S be a diagonal 

An image corrected for the color of the illuminant can be computed by applying the linear transform S(, j-- j ) to each image pixel. The output color o = [or, og, ob T is given by 

The second illuminant L can be considered to be an illuminant to which the eye has adapted itself. Necessary and sufficient conditions for von Kries chromatic adaptation to provide color constancy were derived by West and Brill (1982). 

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