Question

Which of the following derivatives produce a double response at step changes in gray level?

(a) First order derivative

(b) Third order derivative

(c) Second order derivative

(d) First and second order derivatives

I had been asked this question in a national level competition.

My question is from Sharpening Spatial Filters topic in division Intensity Transformations and Spatial Filtering of Digital Image Processing

Answer 1

Correct answer is (c) Second order derivative

Easy explanation: Second order derivatives produce a double line response for the step changes in the gray level. We also note of second-order derivatives that, for similar changes in gray-level values in an image, their response is stronger to a line than to a step, and to a point than to a line.