Question

The derivative of digital function is defined in terms of difference. Then, which of the following defines the first order derivative ∂f/∂x= ___________ of a one-dimensional function f(x)?

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

(b) f(x+1)+ f(x-1)-2f(x)

(c) All of the mentioned depending upon the time when partial derivative will be dealt along two spatial axes

(d) None of the mentioned

The question was posed to me in an international level competition.

I'd like to ask this question from Sharpening Spatial Filters-2 in section Intensity Transformations and Spatial Filtering of Digital Image Processing

Answer 1

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

The best I can explain: The definition of a first order derivative of a one dimensional image f(x) is:

∂f/∂x= f(x+1)-f(x), where the partial derivative is used to keep notation same even for f(x, y) when partial derivative will be dealt along two spatial axes.