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Furthermore, let <span class="texhtml">''f''<sub>1</sub>(λ)</span>, <span class="texhtml">''f''<sub>2</sub>(λ)</span>, and <span class="texhtml">''f''<sub>3</sub>(λ)</span> 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 <span class="texhtml">''F'' = [''F''<sub>1</sub>,''F''<sub>2</sub>,''F''<sub>3</sub>]<sup>''t''</sup></span>, where | Furthermore, let <span class="texhtml">''f''<sub>1</sub>(λ)</span>, <span class="texhtml">''f''<sub>2</sub>(λ)</span>, and <span class="texhtml">''f''<sub>3</sub>(λ)</span> 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 <span class="texhtml">''F'' = [''F''<sub>1</sub>,''F''<sub>2</sub>,''F''<sub>3</sub>]<sup>''t''</sup></span>, where | ||
| − | <math>F_1 = \int_{-\infty}^{\infty}f_1(\lambda)I(\lambda)d\lambda</math> | + | <math>F_1 = \int_{-\infty}^{\infty}f_1(\lambda)I(\lambda)d\lambda</math>, |
| + | <math>F_2 = \int_{-\infty}^{\infty}f_2(\lambda)I(\lambda)d\lambda</math>, | ||
| − | < | + | <math>F_3 = \int_{-\infty}^{\infty}f_3(\lambda)I(\lambda)d\lambda</math> |
| + | |||
| + | where <math>I(\lambda)</math> is the energy spectrum of the incoming light and <math>f_k(\lambda)\geq 0</math> for <math>k = 0, 1, 2.</math>. | ||
| + | |||
| + | Furthermore, assume there exists a matrix, <math>M</math>, so that | ||
| + | |||
| + | |||
| + | |||
| + | a) Why is it necessary that <math>f_k(\lambda) \geq 0</math> for <math>k = 0, 1, 2</math>?<span style="line-height: 1.5em;" /> | ||
| + | |||
| + | b) Are the functions, | ||
[[Category:ECE]] [[Category:QE]] [[Category:CNSIP]] [[Category:Problem_solving]] [[Category:Image_processing]] | [[Category:ECE]] [[Category:QE]] [[Category:CNSIP]] [[Category:Problem_solving]] [[Category:Image_processing]] | ||
Revision as of 19:25, 10 November 2014
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,
