# Question 5, August 2012, Part 1

Part 1 , 2

## Solution:

a) $\gamma=1$

b)

$(x_r,y_r)=(\frac{a}{a+d+g},\frac{d}{a+d+g})$
$(x_g,y_g)=(\frac{b}{b+e+h},\frac{e}{b+e+h})$
$(x_b,y_b)=(\frac{c}{c+f+i},\frac{f}{c+f+i})$

c)

$(x_w,y_w)=(\frac{a+b+c}{a+b+c+d+e+f+g+h+i},\frac{d+e+f}{a+b+c+d+e+f+g+h+i})$

d) If $(X,Y,Z)=(0,1/2,1/2)$, then $(x,y)=(0,1/2)$.
In the chromaticity diagram, this point is outside the horse shoe shape, so its RGB values are not all larger than 0 ($R<0,G>0,B>0$).

e) We are likely to see quantization artifact in dark region.

### Related Problem

Consider a color imaging device that takes input values of $(r,g,b)$ and produces ouput $(X,Y,Z)$ values given by

$\left[ {\begin{array}{*{20}{c}} X\\ Y\\ Z \end{array}} \right] = \left[ {\begin{array}{*{20}{c}} a&b&c\\ d&e&f\\ g&h&i \end{array}} \right]\left[ {\begin{array}{*{20}{c}} r^\alpha\\ g^\alpha\\ b^\alpha \end{array}} \right]$

a) Calculate the white point of the device in chromaticity coordinates.

b) What are the primaries associated with the r,g, and b components respectively?

c) What is the gamma of the device?

d) Draw the region on the chromaticity diagram corresponding to $r < 0, g > 0, b > 0$.

## Alumni Liaison

Ph.D. 2007, working on developing cool imaging technologies for digital cameras, camera phones, and video surveillance cameras.