Two Dimensional Detection

$$(I * g) * h_x = I * (g * h_x)$$

where $g$ is the Gaussian Filter, $h_x$ is the x-version of our gradient operator which could be Sobel Operator, $I$ is the image function.

We prefer the the version on the right because it creates reusable function that we can apply to any image, and it operates on a smaller kernel, saving computational power.

Tweaking $\sigma$

Smaller value of $\sigma$ detect finer features and edges, because less noise is removed and hence the gradient is more volatile.

Larger value will only leave larger edges detected.