09. Discrete wavelength models projection operator - 2011

09. Discrete wavelength models projection operator - 2011 -...

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ECE 638: Principles of Digital Color Imaging Systems Lecture 9: Discrete Wavelength Models Projection Operator
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Synopsis Review of discrete wavelength model
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Discrete-wavelength trichomatic model Stimulus Sensor response Response of the i -th channel Define Span(S) defines HVS subspace Stack sensor outputs Set of visually independent primaries Color matching matrix for this set of visually independent primaries n – 31 × 1 s i – 31 × 1, i=1,2,3 q i = s i T n S = s 1 s 2 s 3 [ ] q = q 1 q 2 q 3 T = S T n A – 31 × 3 P
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Definition of projection operator Projection operator is a linear operator that extracts the fundamental component of the stimulus , i.e. Since , we can write that Following the earlier development of the fundamental component , we have that Substituting (3) into (2), we obtain Comparing (4) with (1), we get R n * n 31 × 31 n * = R n (1) span( A ) = span( S ) n * = A a * (2) a * = A T A ( ) 1 A T n (3) n * = A A T A ( ) 1 A T n (4) R = A A T A ( ) 1 A T (5 a ) n *
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09. Discrete wavelength models projection operator - 2011 -...

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