Generalized structure tensor: Difference between revisions

Revision as of 23:27, 25 October 2019

Revision as of 21:36, 10 September 2020

Line 69:

[\frac{\partial f}{\partial \xi}, \frac{\partial f}{\partial \eta}] d\xi d\eta +\lambda_{min} I </math>

where <math> 0\le \lambda_{min}\le \lambda_{max}</math> are errors of (infinitesimal) translation in the best direction (designated by the angle <math> \theta </math>) and the worst direction (designated by <math> \theta+\pi/2</math>). The function <math> w(\omegaxi,\eta) </math> is the window function defining the "outer scale" wherein the detection of <math>\theta</math> will be carried out, which can be omitted if it is already included in <math>f</math> or if <math>f</math> is the full image (rather than local). The matrix <math> I </math> is the identity matrix. Using the chain rule, it can be shown that the integration above can be implemented as convolutions in Cartesian coordinates applied to the ordinary structure tensor when <math>\xi,\eta</math> pair the real and imaginary parts of an analytic function <math>g(z)</math>,

:<math>

\begin{array}{c}