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→Interpretation: Adding hats to the eigenvectors to express that they are unitary vectors. |
Adding a reference with relevant information about measurements that can be computed in order to infer the shape of the tensors. Those techniques are commonly used in medical imaging to analyze DTI MRI's. |
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===Interpretation===
As in the three-dimensional case, the eigenvalues <math>\lambda_1,\lambda_2,\lambda_3</math> of <math>S_w[p]</math>, and the corresponding eigenvectors <math>\hat{e}_1,\hat{e}_2,\hat{e}_3</math>, summarize the distribution of gradient directions within the neighborhood of ''p'' defined by the window <math>w</math>. This information can be visualized as an [[ellipsoid]] whose semi-axes are equal to the eigenvalues and directed along their corresponding eigenvectors.<ref name="Medioni"/><ref>{{Cite journal|last=Westin|first=C.-F.|last2=Maier|first2=S.E.|last3=Mamata|first3=H.|last4=Nabavi|first4=A.|last5=Jolesz|first5=F.A.|last6=Kikinis|first6=R.|date=2002-06|title=Processing and visualization for diffusion tensor MRI|url=https://linkinghub.elsevier.com/retrieve/pii/S1361841502000531|journal=Medical Image Analysis|language=en|volume=6|issue=2|pages=93–108|doi=10.1016/S1361-8415(02)00053-1}}</ref>
[[File:STgeneric.png|thumb|center|240px|Ellipsoidal representation of the 3D structure tensor.]]
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