Object-colour space revisited

Colorimetry can predict which lights will look alike. Such lights are called metameric. Two lights are known to be metameric if they have the same tri-stimulus values. Using the tri-stimulus values as the Cartesian coordinates one can represent light colours as points in a 3D space (referred to as the colorimetric space). All the light colours make a tri-dimensional manifold which can be represented as a circular cone in the colorimetric space. Furthermore, colorimetry can also predict which reflecting objects illuminated by the same light will look alike: those which reflect metameric lights. All the object colours can be represented as a closed solid inscribed in the light colour cone provided the illumination is fixed. However, when there are multiple illuminants the reflected light metamerism does not guarantee that the reflecting objects will look identical (referred to as the colour equivalence). In this paper three axioms are presented that allow the derivation of colour equivalence from metamerism. The colour of a reflecting object under various illuminations is shown to be specified by six numbers (referred to as its six-stimulus values). Using the six-stimulus values one can represent the colours of all the reflecting objects illuminated by various illuminants as a cone in the 6D space over the 5D ball.