Question

What kind of relation can be obtained between the response of first order derivative and second order derivative of an image having a transition into gray-level step from zero?

(a) First order derivative has a stronger response than a second order

(b) Second order derivative has a stronger response than a first order

(c) Both first and second order derivative has the same response

(d) None of the mentioned

I had been asked this question in examination.

This intriguing question comes from Sharpening Spatial Filters-2 topic in chapter Intensity Transformations and Spatial Filtering of Digital Image Processing

Answer 1

Correct choice is (c) Both first and second order derivative has the same response

The explanation: This is because a first order derivative has stronger response to a gray-level step than a second order, but, the response becomes same if transition into gray-level step is from zero.