3.3. The RGB response of a camera
In theory, the output of a camera is characterized by three main factors: the spectral reflectance of the object at a point, the spectral power distribution of the prevailing illumination over the point and the spectral sensitivities (or responses) of the camera. The output is normalized against a selected white object. The general equation for the output of a camera channel at a pixel is
where Vi = the output signal of the ith camera channel,
i = blue, red or green channel,
x,y = pixel location in the image,
µ = scaling coefficients,
η = spectral sensitivity or spectral response,
Λ = the radiance of the incoming light,
λ = wavelength, and
Θ = imaging geometry like photometric angles.
If the light entering to the camera has impinged on some material surface, then the output can be written as
where I = spectral power distribution of the illumination, and
R = spectral reflectance of the material surface.
The scaling coefficient can be calculated using the following equation:
where the Rwhite = very often constant and its value is the maximum reflectance, and
Iref = the SPD of the illumination used in camera calibration.
Furthermore, according to the Dichromatic Reflection DR model (Shafer 1992), for many materials the reflectance can be divided into two components: interface (“specular”) and body (“diffuse”) parts. Both of these can be further divided into geometric terms K and the spectral part:
The DR model can be used as a good approximation model for light reflection of those materials which are optically inhomogeneous, opaque, covered by an optically inactive surface and are either on a curved or planar surface (Shafer 1992).
After quantization, Eq. is a discrete representation of a transform from a continuous, infinite but limited wavelength area to continuous, 3 dimensional value space. This causes data reduction and loss because the ability to discriminate two colour signals decreases. From a human vision point of view, the RGB space produced by an ordinary camera is nonuniform and cannot produce all visible colours.
When the SPD of the illumination is the same as it was in the calculation of the scaling coefficient, then the camera is said to be white balanced to this illumination. If it is not the same, the equations can be still used, but normalization of the illumination should be made. Even normalization cannot prevent the problem related to modelling the phenomena encountered in the limited dynamic range or nonuniform illumination.