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Image Registration: Difference between revisions
→Log-Polar Transformation
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\( | \( | ||
\begin{align} | \begin{align} | ||
\rho &= \log(r) = \log\left(\sqrt{(x-x_c)^2 + (y-y_c)^2}\right)\\ | |||
\theta &= \operatorname{arctan2}(y-y_c, x-x_c) | |||
\end{align} | \end{align} | ||
\)<br> | \)<br> | ||
where <math>(x_c, y_c)</math> is the center of the image and <math>r</math> is the distance from the center of the image. | where <math>(x_c, y_c)</math> is the center of the image and <math>r</math> is the distance from the center of the image. | ||
Here a rotation in Cartesian coordinates <math>(x, y)</math> around the center \((x_c, y_c)\) corresponds to a shift in \( | Here a rotation in Cartesian coordinates <math>(x, y)</math> around the center \((x_c, y_c)\) corresponds to a shift in \(\theta\) in log-polar coordinates. | ||
A scale change (i.e. enlarge or stretch) is a shift in log-space:<br> | A scale change (i.e. enlarge or stretch) is a shift in log-space:<br> | ||