An 8-bit remote sensing image has brightness values ranging from 24 to 120. While applying the minimum-maximum contrast stretch, which of the following statements is/are CORRECT?
Show Hint
Apply DN_out = (DN_in - min)/(max - min) x 255 using min = 24 and max = 120.
The original brightness values between 24 and 120 would be linearly distributed between 0 and 255
An original brightness value of 48 would become approximately 64
The original brightness values between 24 and 120 would be linearly distributed between 24 and 255
An original brightness value of 36 would become approximately 46
Show Solution
The Correct Option isA, B
Solution and Explanation
Step 1: State the stretch as a straight-line mapping through two known points. The input minimum maps to output 0, i.e. the point $(24,0)$, and the input maximum maps to output 255, i.e. the point $(120,255)$. The slope is $m=\dfrac{255-0}{120-24}=\dfrac{255}{96}=2.65625$, giving $DN_{out}=2.65625\,(DN_{in}-24)$. Step 2: Confirm the endpoints, which settles options (A) and (C). At $DN_{in}=24$: $DN_{out}=0$. At $DN_{in}=120$: $DN_{out}=255$. The mapped range is exactly 0 to 255, confirming (A) and ruling out (C), which wrongly keeps the lower end at 24 instead of stretching it to 0. Step 3: Evaluate at $DN_{in}=48$ for option (B). \[ DN_{out}=2.65625\times24=63.75\approx64 \] matching option (B) exactly, so (B) is correct. Step 4: Evaluate at $DN_{in}=36$ for option (D). \[ DN_{out}=2.65625\times12=31.875\approx32 \] not 46, so option (D) is wrong. Step 5: Final answer. The correct statements are that the stretch spans 0 to 255 and that 48 maps to about 64.\[ \boxed{\text{Options (A) and (B)}} \]
