Technical Details
As a consequence of its definition, the Sobel operator can be implemented by simple means in both hardware and software: only eight image points around a point are needed to compute the corresponding result and only integer arithmetic is needed to compute the gradient vector approximation. Furthermore, the two discrete filters described above are both separable:
and the two derivatives Gx and Gy can therefore be computed as
In certain implementations, this separable computation may be advantageous since it implies fewer arithmetic computations for each image point.
Applying convolution K to pixel group P can be represented in pseudocode as:
N(x,y) = Sum of { K(i,j).P(x-i,y-j)}, for i,j running from -1 to 1. N(x,y) represents the new matrix resulted after applying the Convolution K to P. where P is pixel matrix.Read more about this topic: Sobel Operator
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