# hw1 - R =" 0.65 D G =" 0.575 D B =" 0.45...

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Due Friday, 9/16/05 at 5 PM ECE 638 Homework No. 1 Fall 2003 1. Prove that Grassman laws are satisfied for a trichromatic sensor that obeys the model developed in class. 2. In class we defined the chromaticity diagram or Maxwell’s triangle, as the plane that intersects a 3-D coordinate system, say RGB at the points (1,0.0), (0,1,0), and (0,0,1). The coordinate axes need not be perpendicular. The triangle formed by three lines connecting these points is what we plot as the chromaticity diagram. Find the angle that the coordinate axes must make with respect to each other in order for the chromaticity diagram to be an equilateral triangle with unit altitude. 3. For the sensors shown in parts a – c below, do the following: i. Plot the spectral locus and chromaticity gamut in the rgb sensor chromaticity plane. ii. Find the response of the sensor to the stimulus iii. Determine the amounts of each of three monochromatic primaries D

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Unformatted text preview: R ( ! ) = " ( ! # 0.65) , D G ( ! ) = " ( # 0.575) , D B ( ! ) = " ( ! # 0.45) required to match this stimulus. Is a direct match possible? You should work parts a and b by hand, except for matrix inversions. You should use Matlab for part c. a. Sensor 1 b. Sensor 2- 2 -ECE 638 Homework No. 1 c. Sensor 3 (HVS cone responses downloadable from the course website) 4. Prove the necessary and sufficient condition stated in class for prediction of the response of one sensor to an arbitrary stimulus based on the response of another sensor to that same stimulus. 5. For the three sensors in Problem 3 and for the primaries D R ( ! ) = " ( ! # 0.65) , D G ( ! ) = " ( # 0.575) , D B ( ! ) = " ( ! # 0.45) , a. Plot the color matching function. b. Plot the spectral locus in the primary chromaticity plane (Cartesian coordinates). You will probably want to use Matlab for this entire problem....
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hw1 - R =" 0.65 D G =" 0.575 D B =" 0.45...

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