Projective Alpha Colour

Abstract

Alpha colours were introduced for image compositing, using a pixel coverage model. Algebraically they resemble homogeneous coordinates, widely used in projective geometry calculations. We show why this is the case. This allows us to extend alpha beyond compositing, to all colour calculations regardless of whether pixels are involved and without the need for a coverage model. Our approach includes multi-channel spectral calculations and removes the need for 7 channel and 6 channel alpha colour operations. It provides a unified explanation of pre-multiplied and non pre-multiplied colours, including negative coordinates and infinite points in colour space. It permits filter and illumination operations. It unifies the three existing significant compositing models in a single framework. It achieves this with a physically-plausible energy basis.Keywords: projective geometry, homogeneous coordinates, image compositing, alpha blending, alpha compositing, colour representation, filtering, spectral colour, projective alpha colour