Question

Which of the following options is/are INCORRECT?

• A. Negative images are formed by a non-linear transformation of digital images
• B. A thresholding function is used to produce a two-level binary digital image
• C. Logarithmic transformation of an image is used to expand the values of dark pixels in a digital image
• D. Power law transformation with fractional exponent is used to map dark input values of an image into a wider range of output values

Hint:

Write out s = (L-1) - r for the negative transform and check whether it fits the form a.r + b.

Answer 1

The Correct Option is A

Step 1: Write the image negative transformation and check its linearity.
For an image with intensity levels in \([0,L-1]\), the negative transformation is \[ s = (L-1)-r \] where \(r\) is the input intensity and \(s\) the output intensity. This is a first-degree straight-line function of \(r\) with slope \(-1\) and intercept \(L-1\), which is, by definition, a LINEAR transformation, not a non-linear one. So the claim in option (A) that negative images are formed by a non-linear transformation is factually wrong, making (A) the INCORRECT statement asked for.
Step 2: Verify option (B), thresholding.
A thresholding function maps \(s=0\) for all \(r\) below a chosen threshold \(T\) and \(s=L-1\) for all \(r\ge T\). This is exactly how a grayscale image is converted into a two-level binary image, so option (B) is a correct statement.
Step 3: Verify option (C), logarithmic transformation.
The log transformation \(s=c\log(1+r)\) is a concave function that compresses high input values while expanding the low, dark input values over a wider output range, which is why log transforms are used to bring out detail in dark regions, so option (C) is a correct statement.
Step 4: Verify option (D), power law with fractional exponent.
The power law transformation \(s=c\,r^{\gamma}\), when \(\gamma<1\), behaves similarly to the log transform: it expands the range of dark input values into a wider band of output values while compressing bright values, so option (D) is also correct.
Step 5: Conclusion.
Only option (A) is incorrect because negative image formation is a linear, not non-linear, transformation.\[ \boxed{\text{Option (A) is incorrect}} \]