Root-Polynomial Colour Correction

摘要

Cameras record three colour responses (RGB) which are devicerndependent i.e. different cameras will produce different RGBrnresponses for the same scene. Moreover, the RGB responses dornnot correspond to the device-independent tristimulus values as definedrnby the CIE. The most common method for mapping RGBs tornXYZs is the simple 3×3 linear transform (usually derived throughrnregression). While this mapping can work well it does sometimesrnmap RGBs to XYZs with high error. On the plus side the linearrntransform is independent of camera exposure. An alternativernand on the face of it more powerful, method for colour correctionrnis polynomial regression. Here, the RGB at a pixel is augmentedrnby polynomial terms e.g up to second order RGB mapsrnto the 9-vector (R,G,B,R~2,G~2,B~2,RG,RB,GB). With respect to thisrnpolynomial expansion colour correction is a 9×3 linear transform.rnFor a given calibration set-up polynomial regression canrnwork very well indeed and can reduce colorimetric error by morernthan 50%. However, unlike linear maps the polynomial fit dependsrnon exposure: as exposure changes the vector of polynomialrncomponents alters in a non linear way. In this paper we propose arnnew polynomial-type regression which we call ‘Root-PolynomialrnColour Correction’. Our idea is to take each term in a polynomialrnexpansion and take its kth root of each k-order term. For the 2ndrnorder polynomial expansion the corresponding independent rootrnterms are R,G,B,√RG,√RB and√GB (6 independent terms insteadrnof 9: the first roots of R, G and B equal the 2~(nd) roots of R~2,rnG~2 and B~2). It is easy to show terms defined in this way scale withrnexposure and so a 6×3 regression mapping can be used for colourrncorrection. Encouragingly, our initial experiments demonstraternthat root-polynomial colour correction enhances colour correctionrnperformance on real and synthetic data.