Question

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?

• A. The original brightness values between 24 and 120 would be linearly distributed between 0 and 255
• B. An original brightness value of 48 would become approximately 64
• C. The original brightness values between 24 and 120 would be linearly distributed between 24 and 255
• D. An original brightness value of 36 would become approximately 46

Hint:

Apply DN_out = (DN_in - min)/(max - min) x 255 using min = 24 and max = 120.

Answer 1

The Correct Option is A, B

Step 1: Write the min-max linear contrast stretch formula.
For an 8-bit image (output range 0 to 255), the min-max stretch maps an input digital number \(DN_{in}\) to \[ DN_{out} = \left(\dfrac{DN_{in}-DN_{min}}{DN_{max}-DN_{min}}\right)\times 255 \] with \(DN_{min}=24\), \(DN_{max}=120\). By construction this formula always maps \(DN_{min}\) to 0 and \(DN_{max}\) to 255, so the whole original range 24 to 120 stretches linearly to fill the full output range 0 to 255. This makes option (A) correct and option (C), which claims the output range stays 24 to 255, incorrect, since the stretch always resets the minimum to 0.
Step 2: Substitute \(DN_{in}=48\) to check option (B). \[ DN_{out} = \left(\dfrac{48-24}{120-24}\right)\times255 = \left(\dfrac{24}{96}\right)\times255 = 0.25\times255 = 63.75\approx64 \] This matches option (B), so (B) is correct.
Step 3: Substitute \(DN_{in}=36\) to check option (D). \[ DN_{out} = \left(\dfrac{36-24}{120-24}\right)\times255 = \left(\dfrac{12}{96}\right)\times255 = 0.125\times255 = 31.875\approx32 \] The computed value is approximately 32, not 46 as claimed in option (D), so (D) is incorrect.
Step 4: Conclusion.
Only the statements that the stretch spans 0 to 255 and that a value of 48 becomes approximately 64 are numerically correct.\[ \boxed{\text{(A) and (B) are correct}} \]