HP Labs Technical Reports

Inner Products and Orthogonality in Colour Recording Filter Design

Vora, Poorvi

HPL-98-189

Keyword(s): noise; sensitivity; digital cameras; scanners; color; colour

Abstract: We formalize ideas of orthogonality and inner products implicit in the development of a number of figures of merit (FOM, [1]) of colour recording filters. We show that, in negligible measurement noise, the data dependence of each FOM based on linear colour correction is equivalent to a choice of inner product (and hence of orthogonality). Further, we show that optimal sensors with respect to noise sensitivity are simply defined as orthogonal with respect to this inner product. We also develop the idea of a generalized Q-factor by generalizing the euclidean inner product to include all inner products. Simulations demonstrate the utility of our analytical results.

31 Pages

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