Matrix Calculations for Digital Photography

Different digital cameras have different spectral sensitivities and opto-electronic conversion functions (OECF’s), 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 most rigorous way to do this is to provide the raw data along with the camera color channel OECF’s and spectral sensitivities. Another option is to transform the data itself into some sort of standard form with assumed OECF and spectral characteristics, or to specify a transformation. There are a number of paths to take in determining such transformations. The results obtained are variable, and depend on the scene and capture device spectral characteristics, and how the transformation to the standard data form was determined. Since the spectral spaces spanned by different cameras are different, and the intended use of the data in digital photography is to produce a reproduction for viewing, the obvious choice for a standard spectral space is a spectral space spanned by a set of color matching functions, e.g. a color space. This paper outlines several methods for determining 3x3 matrix transformations from camera spectral spaces to a standard color space based on the ITU-R BT.709 red, green, and blue (RGB) primaries. Since these transformations are intended for digital cameras, they are based on either of two assumptions about the scene spectral correlation statistics: standard surface reflection statistics as represented by a Macbeth Color Checker (MBCC), or the assumption of no spectral correlation (maximum ignorance). This paper only deals with 3x3 matrix transformations 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. If the illumination source, colorants, and corresponding spectral correlation statistics of the scene or original are known, as is typically the case with film scans, the actual correlation statistics should be applied by using the appropriate spectral correlation matrix, or