Colour Correction using Root-Polynomial Regression

Cameras record three colour responses (RGB) which are device dependent. Camera coordinates are mapped to a standard colour space such as XYZ useful for colour measurement by a mapping function e.g. the simple 3 × 3 linear transform (usually derived through regression). This mapping, which we will refer to as LCC (linear colour correction), has been demonstrated to work well in the number of studies. However, it can map RGBs to XYZs with high error. The advantage of the LCC is that it is independent of camera exposure. An alternative and potentially more powerful method for colour correction is polynomial colour correction (PCC). Here, the R,G and B values at a pixel are extended by the polynomial terms. For a given calibration training set PCC can significantly reduce the colorimetric error. However, the PCC fit depends on exposure i.e. as exposure changes the vector of polynomial components is altered in a non-linear way which results in hue and saturation shifts. This paper proposes a new polynomial-type regression loosely related to the idea of fractional polynomials which we call ‘Root-Polynomial Colour Correction’ (RPCC). Our idea is to take each term in a polynomial expansion and take its k root of each k-degree term. It is easy to show terms defined in this way scale with exposure. RPCC is a simple (low complexity) extension of LCC. The experiments presented in the paper demonstrate that RPCC enhances colour correction performance on real and synthetic data.