5,337
edits
Image Registration: Difference between revisions
→Adaptive Log-Polar Transformation
| Line 73: | Line 73: | ||
* \(n_\rho\) be the number of samples (i.e. resolution) along the \(\rho\) axis | * \(n_\rho\) be the number of samples (i.e. resolution) along the \(\rho\) axis | ||
* \(n_\theta\) be the number of samples along the \(\theta\) axis | * \(n_\theta\) be the number of samples along the \(\theta\) axis | ||
* \(r_i\) the radius size for pixel | * \(r_i\) the radius size for pixel <math display="inline">i=1,...,n_\rho</math> | ||
* | * <math display="inline">\theta = 0,...,n_\theta - 1</math> | ||
To prevent undersampling along \(\rho\), we must have \(R_{n_\rho} - R_{n_\rho-1} \leq 1\). | To prevent undersampling along \(\rho\), we must have \(R_{n_\rho} - R_{n_\rho-1} \leq 1\). | ||
| Line 81: | Line 81: | ||
This leads to the following equations:<br> | This leads to the following equations:<br> | ||
<math> | <math display="block"> | ||
\begin{align} | \begin{align} | ||
R_i &= \exp(i \times \frac{\log R_{max}}{n_\rho}), \qquad R_{max} = R_{n_\rho}\\ | R_i &= \exp(i \times \frac{\log R_{max}}{n_\rho}), \qquad R_{max} = R_{n_\rho}\\ | ||
| Line 88: | Line 88: | ||
\end{align} | \end{align} | ||
</math> | </math> | ||
However, using these would lead to oversampling of the fovea region wasting computation resources. | However, using these would lead to oversampling of the fovea region wasting computation resources. | ||
}} | }} | ||