Communication, Networking, Signal and Image Processing (CS)
Question 5: Image Processing
August 2013
Question
Problem 1. (50 pts)
Problem 2. (50 pts)
Let r0(λ), g0(λ) , and b0(λ) be the CIE color matching functions for red, green, and blue primaries at 700 nm, 546.1 nm, and 435.8 nm, respectively, and let [r,g,b] be the corresponding CIE tristimulus values.
Furthermore, let f1(λ), f2(λ), and f3(λ) be the spectral response functions for the three color outputs of a color camera. So for each pixel of the camera sensor, there is a 3-dimensional output vector given by F = [F1,F2,F3]t, where
$ F_1 = \int_{-\infty}^{\infty}f_1(\lambda)I(\lambda)d\lambda $,
$ F_2 = \int_{-\infty}^{\infty}f_2(\lambda)I(\lambda)d\lambda $,
$ F_3 = \int_{-\infty}^{\infty}f_3(\lambda)I(\lambda)d\lambda $
where $ I(\lambda) $ is the energy spectrum of the incoming light and $ f_k(\lambda)\geq 0 $ for $ k = 0, 1, 2. $.
Furthermore, assume there exists a matrix, $ M $, so that
a) Why is it necessary that $ f_k(\lambda) \geq 0 $ for $ k = 0, 1, 2 $?<span style="line-height: 1.5em;" />
b) Are the functions,
