Structure tensor: Difference between revisions

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Note that the average of the gradient <math>\nabla I</math> inside the window is '''not''' a good indicator of anisotropy. Aligned but oppositely oriented gradient vectors would cancel out in this average, whereas in the structure tensor they are properly added together.<ref>
{{cite journaltechreport|authorauthor1=T. Brox, |author2= J. Weickert, |author3=B. Burgeth and |author4=P. Mrazek |chaptername-list-style=amp |title=Nonlinear Structure Tensors|titleinstitution=Universität des Saarlandes, Tech. Report|issuenumber=113|pages=1–32|year=2004}}
</ref> This is a reason for why <math>(\nabla I)(\nabla I)^\text{T}</math> is used in the averaging of the structure tensor to optimize the direction instead of <math>\nabla I</math>.