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It represents the distribution of the gradient not just its “predominant” direction (for instance the mineigenvector is the direction with least gadient). The introduction may confuse the reader. I tried to make it more comprehensible and added a note in case someone has a better idea on how to expand the explanation. |
Adding an example of a “window function” commonly used. |
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\end{bmatrix}
</math>
where <math>I_x</math> and <math>I_y</math> are the [[partial derivative]]s of <math>I</math> with respect to ''x'' and ''y''; the integrals range over the plane <math>\mathbb{R}^2</math>; and ''w'' is some fixed "window function" (such as a [[Gaussian blur]]), a [[distribution (mathematics)|distribution]] on two variables. Note that the matrix <math>S_w</math> is itself a function of {{nowrap|1=''p'' = (''x'', ''y'')}}.
The formula above can be written also as <math>S_w(p)=\int w(r) S_0(p-r)\,d r</math>, where <math>S_0</math> is the matrix-valued function defined by
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