Question

What kind of relation can be obtained between first order derivative and second order derivative of an image having a on the basis of edge productions that shows a transition like a ramp of constant slope?

(a) First order derivative produces thick edge while second order produces a very fine edge

(b) Second order derivative produces thick edge while first order produces a very fine edge

(c) Both first and second order produces thick edge

(d) Both first and second order produces a very fine edge

This question was addressed to me in examination.

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

Answer 1

Correct choice is (a) First order derivative produces thick edge while second order produces a very fine edge

Easy explanation: the first order derivative remains nonzero along the entire ramp of constant slope, while the second order derivative remain nonzero only at onset and end of such ramps.

If an edge in an image shows transition like the ramp of constant slope, the first order and second order derivative values shows the production of thick and finer edge respectively.