Thursday, April 21, 2011

Matrix Calculations for Digital Photography

Different digital cameras have different spectral sensitivities and opto-electronic conversion functions (OECF), and therefore produce different data about the same scene. Correct interpretation of the data requires that it be presented in some sort of standard form. The obvious choice for a standard spectral space is a spectral space spanned by a set of color matching functions, a color space.
3x3 matrices are used for transformations from camera spectral spaces to a standard color space based on the ITU-R BT.709 red, green, and blue (RGB) primaries.

3x3 matrix transformations are used most because such transformations are most appropriate when the relationship between the scene radiance and the radiance incident on the sensor is variable, different illumination sources are used, and the colorants found in the scene are unknown or highly variable.


The first step in determining the desired transformations is to linearize the data obtained from the camera with respect to the source or scene radiance.

For this experiment, the camera data was linearized by measuring the camera and focal plane OECF’s of the
camera for a variety of scene dynamic ranges and mean reflectances, and constructing a flare model which predicts the camera flare based on focal plane image statistics.

Accurate OECF measurements for camera data linearization are extremely important, particularly with the LS methods, since the regression tries to transform the chart image data to aim linear values.


The numerical results of the experiments conducted are presented in the following table:



(WPPLS): white point preserving LS regressions.
(WTWPPLS):  weighted white point preserving LS regressions.

By Saria J. Beainy


Resource: "The Fifth Color Imaging Conference: Color Science, Systems, and Applications" by Paul M. Hubel and Jack Holm, Graham D. Finlayson, Mark S. Drew.

4 comments:

  1. I never thought that matrices had a wide application in digital cameras. There can be little doubt that people now have a better understanding of the effects of these matrices on digital photography. Really liked your post..............

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  2. Congrats Saria! wonderful!
    Zeina

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  3. I really liked your post Saria! People by now should be able to gain a better understanding concerning the efects of matrices on digital photography. Its very interesting to know that matrix calculations are used in serval fields including the field of photography!
    Thankyou!!

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  4. Nice and interesting post!! Good to know that matrices can be also applied in photography.

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