Question

The minimum and maximum Digital Number (DN) values of an image are 30 and 55, respectively. If the input DN value of a pixel is 35, the output DN value after linear contrast stretch of an 8-bit data is __________________ (in integer).

Hint:

For linear contrast stretching, the output DN value is calculated by normalizing the input DN value relative to the minimum and maximum values and then scaling it to the desired range.

Answer 1

Correct Answer: 51

For linear contrast stretching, we use the following formula: \[ \text{Output DN} = \frac{(X - \text{min})}{(\text{max} - \text{min})} \times (L_{\text{max}} - L_{\text{min}}) + L_{\text{min}} \] Where:
- \( X = 35 \) (the input DN value),
- \( \text{min} = 30 \) (the minimum DN value),
- \( \text{max} = 55 \) (the maximum DN value),
- \( L_{\text{max}} = 255 \) (the maximum possible value for 8-bit data),
- \( L_{\text{min}} = 0 \) (the minimum possible value for 8-bit data).
Substituting the values into the formula: \[ \text{Output DN} = \frac{(35 - 30)}{(55 - 30)} \times (255 - 0) = \frac{5}{25} \times 255 = 0.2 \times 255 = 51 \] Final Answer: \[ \boxed{51} \]