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Structure tensor of a function and the distribution of gradients

In computer vision, one often computes what's known as the structure tensor of an image. The structure tensor of a an image (i.e. a function) is a matrix that, I quote from Wikipedia. "summarizes ...
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Trouble deriving the Harris Corner Detection

I just started studying a small paper about the Harris Corner Detection. The problem is I don't understand how step 7 is derived from step 6. In step 7 the expression is expanded in a way that we get ...