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Projective Alpha Colour
Author(s) -
Willis Philip
Publication year - 2006
Publication title -
computer graphics forum
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.578
H-Index - 120
eISSN - 1467-8659
pISSN - 0167-7055
DOI - 10.1111/j.1467-8659.2006.00975.x
Subject(s) - compositing , homogeneous coordinates , alpha (finance) , channel (broadcasting) , homogeneous , image (mathematics) , pixel , projective test , representation (politics) , computer science , mathematics , geometry , computer vision , pure mathematics , combinatorics , construct validity , statistics , psychometrics , computer network , politics , political science , law
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