# Image Gradient - Flipping Effect of the Convolution Matrix (Kernel) for Edge Detection

Prewitt operator is a common operator to compute image gradient in edge detection, and I knew that to apply this Prewitt operator to an image is just to convolve them together, say, the image is represent as $A$, and as the wikipedia page lays out, the Prewitt operator for *x-gradient is $$G_x=\pmatrix{ -1 & 0 & 1\\\ -1 & 0 & 1\\\ -1 & 0 & 1}$$, for y-gradient is $$G_y=\pmatrix{1 & 1 & 1\\\ 0 & 0 & 0\\\ -1 & -1 & -1}$$

So if I want to compute the x-gradient of image $A$, convolve them like this,$$A_x=A*G_x$$, but here comes my problem. $G_x$ is the kernel, when convolve it with $A$, $G_x$ should be flipped which turn it into this, $$G_x=\pmatrix{1 &0 &-1\\\ 1 &0 &-1\\\ 1 &0 &-1}$$ right? If so, the x-gradient will be something like this, $$\nabla A_x=A(x-1,y)-A(x+1,y)$$ , BUT I think it should be $$\nabla A_x=A(x+1,y) - A(x-1,y)$$.

So I presume that either $G_x$ and $G_y$ should not be flipped when convolve them with $A$, or $G_x$ doesn't look like the above, and it should be this,$$G_x=\pmatrix{1& 0& -1\\\ 1& 0& -1\\\ 1& 0& -1}$$

Anyone can help me with this?