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Jorge Stolfi (talk | contribs) →Bogus theory?: The 3D case is bogus too. |
Jorge Stolfi (talk | contribs) →Bogus theory?: It seems that the definition was incorrect, that is all. |
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PS. The same holds for the three-dimensional case. The eigenvectors are the direction of the gradient and any two unit orthogonal vectors perpendicular to it. The eigenvalues are <math>\lambda_1 = I_x^2 + I_y^2 + I_z^2</math> and <math>\lambda_2 = \lambda_3 = 0</math>. <br/> If no one disagrees, I will try to fix the article.<br/>--[[User:Jorge Stolfi|Jorge Stolfi]] ([[User talk:Jorge Stolfi|talk]]) 15:55, 19 August 2010 (UTC)
Presumably what the author writes as <math>I_x^2</math> is not the square of something, but rather the integral of the derivative Ix^2 within a window; and ditto for the other three elements of ''S''. That seems to be the case in many applications. Yet the ''S'' matrix seems to be used in some cases as a surrogate of the Hessian of <math>I^2</math>, which includes ''S'' but second derivatives too. --[[User:Jorge Stolfi|Jorge Stolfi]] ([[User talk:Jorge Stolfi|talk]]) 17:41, 19 August 2010 (UTC)
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