The derivative of digital function is defined in terms of difference. Then, which of the following defines the second order derivative ∂^2 f/∂x^2 = ___________ 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 mentionedI had been asked this question by my school teacher while I was bunking the class.My question comes from Sharpening Spatial Filters-2 topic in section Intensity Transformations and Spatial Filtering of Digital Image Processing

The derivative of digital function is defined in terms of difference.

1.	The derivative of digital function is defined in terms of difference. Then, which of the following defines the second order derivative ∂^2 f/∂x^2 = ___________ 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 mentionedI had been asked this question by my school teacher while I was bunking the class.My question comes from Sharpening Spatial Filters-2 topic in section Intensity Transformations and Spatial Filtering of Digital Image Processing
Answer» Right answer is (B) f(x+1)+ f(x-1)-2f(x) Best explanation: The definition of a second ORDER DERIVATIVE of a one dimensional image f(x) is: (∂^2 f)/∂x^2 =f(x+1)+ f(x-1)-2f(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.

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