Question

Which of the facts(s) is/are true for the second order derivative of a digital function?

(a) Must be zero in the flat areas

(b) Must be nonzero at the onset and end of a gray-level step or ramp discontinuities

(c) Must be zero along the ramps of constant slope

(d) All of the mentioned

This question was posed to me by my college director while I was bunking the class.

My enquiry is from Sharpening Spatial Filters-2 in division Intensity Transformations and Spatial Filtering of Digital Image Processing

Answer 1

Right option is (c) Must be zero along the ramps of constant slope

Explanation: The second order derivative of a digital function is defined as:

 Must be zero in the flat areas i.e. areas of constant grey values.

 Must be nonzero at the onset of a gray-level step or ramp discontinuities.

 Must be zero along the gray-level ramps of constant slope.