Could anyone explain to me why the last derivative formula correspond to the filter at the bottom right?
f(x+1) is the pixel that is at the right of x and f(x-1) is the pixel at the left of x, therefore the filter should be [-1 0 1] and not the other way around.
motoole2
The correct answer here is [1 0 -1], under the assumption that this derivative filter is being applied through a convolution operation. If it were a correlation operation, then you'd be correct in saying the filter should be [-1 0 1]. See this slide for the definitions of both, and try plugging in the definition of this derivative filter.
Could anyone explain to me why the last derivative formula correspond to the filter at the bottom right? f(x+1) is the pixel that is at the right of x and f(x-1) is the pixel at the left of x, therefore the filter should be [-1 0 1] and not the other way around.
The correct answer here is [1 0 -1], under the assumption that this derivative filter is being applied through a convolution operation. If it were a correlation operation, then you'd be correct in saying the filter should be [-1 0 1]. See this slide for the definitions of both, and try plugging in the definition of this derivative filter.