Question

The hue, intensity and saturation values for a pixel are \( H = 0.5 \, {rad} \), \( S = 0.5 \), and \( I = 0.3 \), respectively. If the pixel is converted to RGB color model, then the value of the green pixel would be __________ (rounded off to 2 decimal places).

Hint:

When converting HSI to RGB, determine the sector of the hue first (based on degrees or radians), then apply the respective formulas. Always keep track of units and rounding.

Answer 1

We are given HSV (H, S, I) and need to convert to RGB. Since the HSV here is defined in radians, and Hue is in the range \([0, 2\pi]\), first convert H to degrees:
\[ H = 0.5 \, \text{rad} \times \frac{180}{\pi} \approx 28.65^\circ \]
So, \(H\) lies in the Red-Green sector (i.e., sector 1 where \(0^\circ \leq H < 120^\circ\)).

The formula to convert from HSI to RGB when \(0 \leq H < \frac{2\pi}{3}\) is:

\[ R = I \left(1 + \frac{S \cos H}{\cos\left(\frac{\pi}{3} - H\right)} \right) \] \[ B = I (1 - S) \] \[ G = 3I - (R + B) \]

Using:
\[ I = 0.3,\quad S = 0.5,\quad H = 0.5 \]

Calculate:
\[ R = 0.3 \left(1 + \frac{0.5 \cos(0.5)}{\cos\left(\frac{\pi}{3} - 0.5\right)} \right) \approx 0.3 \left(1 + \frac{0.5 \times 0.8776}{0.854} \right) \] \[ \Rightarrow R \approx 0.3 \left(1 + 0.5138\right) = 0.3 \times 1.5138 = 0.4541 \]
\[ B = 0.3(1 - 0.5) = 0.15 \] \[ G = 3 \times 0.3 - (0.4541 + 0.15) = 0.9 - 0.6041 = 0.2959 \]

Final Answer: \(\fbox{0.30}\)