Question

If f(x,y) is an image function of two variables, then the first order derivative of a one dimensional function, f(x) is:

(a) f(x+1)-f(x)

(b) f(x)-f(x+1)

(c) f(x-1)-f(x+1)

(d) f(x)+f(x-1)

The question was posed to me in an internship interview.

I'd like to ask this question from Sharpening Spatial Filters in division Intensity Transformations and Spatial Filtering of Digital Image Processing

Answer 1

Correct option is (a) f(x+1)-f(x)

Easy explanation: The first order derivative of a single dimensional function f(x) is the difference between f(x) and f(x+1).

That is, ∂f/∂x=f(x+1)-f(x).