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Check out Szeliski's book: http://szeliski.org/Book/drafts/SzeliskiBook_20100903_draft.pdf There is also an old book on feature detection: http://www.amazon.com/Feature-Extraction-Processing-Computer-Edition/dp/0123965497 You can read the sections that you care about. Also, I think it is always a good idea to read about scale space theory if you are to ...

I think the first smoothing, by $\sigma_D$, is only done to get more stable derivatives whereas in the second step the convolution by a Gaussian with $\sigma_I$ is done to establish the 'scale-space' in which the operator is applied. Ignoring $\sigma_D$, this looks like this in Matlab: dx = [-1 0 1; -1 0 1; -1 0 1]; % Simple mask for derivative Ix = ...