Question

Which of the following is not a valid response when we apply a second derivative?

(a) Zero response at onset of gray level step

(b) Nonzero response at onset of gray level step

(c) Zero response at flat segments

(d) Nonzero response along the ramps

I have been asked this question in examination.

The origin of the question is Sharpening Spatial Filters in section Intensity Transformations and Spatial Filtering of Digital Image Processing

Answer 1

Correct option is (b) Nonzero response at onset of gray level step

The explanation is: The derivations of digital functions are defined in terms of differences. The definition we use for second derivative should be zero in flat segments, zero at the onset of a gray level step or ramp and nonzero along the ramps.