Structure tensor: Difference between revisions

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Revision as of 20:46, 15 October 2022

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The three-dimensional structure tensor has been used to analyze three-dimensional video data (viewed as a function of ''x'', ''y'', and time ''t'').<ref name="Jahne1993" />

If one in this context aims at image descriptors that are ''invariant'' under [[Galilean transformationstransformation]]s, to make it possible to compare image measurements that have been obtained under variations of a priori unknown image velocities <math>v = (v_x, v_y)^\text{T}</math>

:<math> \begin{bmatrix} x' \\ y' \\ t' \end{bmatrix} = G \begin{bmatrix} x \\ y \\ t \end{bmatrix} = \begin{bmatrix} x - v_x \, t \\ y - v_y \, t \\ t \end{bmatrix} </math>,

it is, however, from a computational viewpoint preferable to parameterize the components in the structure tensor/second-moment matrix <math>S</math> using the notion of ''Galilean diagonalization''<ref name=lin04icpr>