Negative images are formed by a non-linear transformation of digital images
A thresholding function is used to produce a two-level binary digital image
Logarithmic transformation of an image is used to expand the values of dark pixels in a digital image
Power law transformation with fractional exponent is used to map dark input values of an image into a wider range of output values
Show Solution
The Correct Option isA
Solution and Explanation
Step 1: Classify each transformation as linear or non-linear from its mathematical form. A function of $r$ is linear only if it can be written as $s=a\,r+b$ for constants $a,b$. Step 2: Apply this test to the negative transformation. $s=(L-1)-r=(-1)r+(L-1)$ fits the form $a\,r+b$ exactly with $a=-1$, $b=L-1$, so it is linear. Calling it non-linear, as option (A) does, is a false statement, and since the question asks for the INCORRECT option, (A) is the answer. Step 3: Confirm thresholding is a valid, correct statement. Thresholding is a piecewise-constant step function of $r$ whose defined purpose (producing a two-level binary image) exactly matches option (B), so (B) is true. Step 4: Confirm log and power-law statements are both correct using their derivatives. For the log transform, $\dfrac{ds}{dr}=\dfrac{c}{1+r}$ is large for small $r$ (dark pixels) and small for large $r$: dark values spread over a wide output range, exactly as (C) states. For power law with $\gamma<1$, $\dfrac{ds}{dr}=c\gamma\,r^{\gamma-1}$, and since $\gamma-1<0$, this is also large near $r=0$ and small near $r=L-1$, again expanding dark values, exactly as (D) states. Step 5: Final answer. Every option except (A) is true; (A) alone is incorrect because the negative transform is linear.\[ \boxed{\text{Option (A)}} \]
