A Laplacian for an image f(x, y) is defined as:is given by ________(a) [f(x + 1, y) + f(x – 1, y) – 2f(x, y)] and [f(x, y + 1) + f(x, y – 1) – 2f(x, y)] respectively(b) [f(x + 1, y + 1) + f(x, y – 1) – 2f(x, y)] and [f(x , y + 1) + f(x – 1, y) – 2f(x, y)] respectively(c) [f(x, y + 1) + f(x, y – 1) – 2f(x, y)] and [f(x + 1, y) + f(x – 1, y) – 2f(x, y)] respectively(d) None of the mentionedI had been asked this question in homework.I'd like to ask this question from Use of Second Order Derivative for Enhancement in section Image Enhancement of Digital Image Processing

A Laplacian for an image f(x, y) is defined as:is given by ________(a)

1.	A Laplacian for an image f(x, y) is defined as:is given by ________(a) [f(x + 1, y) + f(x – 1, y) – 2f(x, y)] and [f(x, y + 1) + f(x, y – 1) – 2f(x, y)] respectively(b) [f(x + 1, y + 1) + f(x, y – 1) – 2f(x, y)] and [f(x , y + 1) + f(x – 1, y) – 2f(x, y)] respectively(c) [f(x, y + 1) + f(x, y – 1) – 2f(x, y)] and [f(x + 1, y) + f(x – 1, y) – 2f(x, y)] respectively(d) None of the mentionedI had been asked this question in homework.I'd like to ask this question from Use of Second Order Derivative for Enhancement in section Image Enhancement of Digital Image Processing
Answer» The correct answer is (a) [f(x + 1, y) + f(x – 1, y) – 2F(x, y)] and [f(x, y + 1) + f(x, y – 1) – 2f(x, y)] respectively The explanation is: For a LAPLACIAN given by:∇^2 f= Applying second order DERIVATIVE in x DIRECTION (∂^2 f)/∂x^2= [f(x + 1, y) + f(x – 1, y) – 2f(x, y)], and Applying second order derivative in y direction (∂^2 f)/∂y^2 = [f(x, y + 1) + f(x, y – 1) – 2f(x, y)].

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