Template for Edge detection

To find the edge image horizontally simple in Image processing. How it is to find the difference between one point on the address below (or above) the following point.

Ydiff(x,y) = I(x,,y) - I(x,y+1)------------ (1)

The Ydiff is the difference in axial location of image and I (x,, y) is the intensity of the pixel position (x,, y) in image results of using equation (1) is equivalent to. image convolution with template.
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Finding the vertical edge image can be the same.

Xdiff(x,,y) = I(x,,y) - I(x-,y) -------------(2)

The Xdiff is the difference in horizontal and equation (2) is equivalent to convolution with the template of image processing.