Image Registration: Difference between revisions
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===Adaptive Log-Polar Transformation=== | ===Adaptive Log-Polar Transformation=== | ||
The goal of Adaptive Polar Transform by Matungka ''et al.''<ref name="matungka2009adaptive"><cite class="journal">Rittavee Matungka, Yuan F. Zheng, and Robert L. Ewing (2009). ''Image Registration Using Adaptive Polar Transform'' DOI: [https://doi.org/10.1109/TIP.2009.2025010 10.1109/TIP.2009.2025010] URL: [https://home.cis.rit.edu/~cnspci/references/wolberg2000.pdf https://home.cis.rit.edu/~cnspci/references/wolberg2000.pdf]</cite></ref> is to address the non-uniform sampling of the log-polar transformation. | The goal of Adaptive Polar Transform by Matungka ''et al.''<ref name="matungka2009adaptive"><cite class="journal">Rittavee Matungka, Yuan F. Zheng, and Robert L. Ewing (2009). ''Image Registration Using Adaptive Polar Transform'' DOI: [https://doi.org/10.1109/TIP.2009.2025010 10.1109/TIP.2009.2025010] URL: [https://home.cis.rit.edu/~cnspci/references/wolberg2000.pdf https://home.cis.rit.edu/~cnspci/references/wolberg2000.pdf]</cite></ref> is to address the non-uniform sampling of the log-polar transformation. | ||
Let the following | |||
* \(n_\rho\) be the number of samples (i.e. resolution) along the \(\rho\) axis | |||
* \(n_\theta\) be the number of samples along the \(\theta\) axis | |||
* \(r_i\) the radius size for pixel \(i=1,...,n_p\) | |||
* \(\theta = 0,...,n_\theta - 1\) | |||
To prevent undersampling along \(\rho\), we must have \(R_{n_\rho} - R_{n_\rho-1} \leq 1\). | |||
I.e. the outermost two circles must have \(\leq 1\) pixel difference. | |||
To prevent undersampling along \(\theta\), we must have at least \(2\pi R_{max}\) pixels along the \(\theta\) axis. | |||
This leads to the following equations:<br> | |||
\[ | |||
\begin{align} | |||
R_i &= \exp(i \times \frac{\log R_{max}}{n_\rho}), \qquad R_{max} = R_{n_\rho}\\ | |||
n_\rho &\geq \frac{\log R_{max}}{\log R_{max} - \log(R_{max}-1)}\\ | |||
n_\theta &\geq 2\pi R_{max} | |||
\end{align} | |||
\] | |||
==References== | ==References== |