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Image Registration: Difference between revisions
→Adaptive Log-Polar Transformation
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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. | ||
[[File: Adaptive polar transform fig4.png | 500px | Adaptive Polar Transform]] | |||
[[File: Adaptive polar transform fig5.png | 500px | Adaptive Polar Transform Lena]] | |||
{{ hidden | Motivation | | {{ hidden | Motivation | | ||
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This leads to the following equations:<br> | This leads to the following equations:<br> | ||
<math> | |||
\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}\\ | ||
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n_\theta &\geq 2\pi R_{max} | n_\theta &\geq 2\pi R_{max} | ||
\end{align} | \end{align} | ||
</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. | ||
}} | }} | ||
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Given an image of size \(2 R_{max} \times 2 R_{max}\), let (R_i\) the radius size for pixel \(i=1,...,n_\rho\). | Given an image of size \(2 R_{max} \times 2 R_{max}\), let (R_i\) the radius size for pixel \(i=1,...,n_\rho\). | ||
The main idea is that the number of pixels \(n_\theta\) should be adaptive to the radius | The main idea is that the number of pixels \(n_\theta\) should be adaptive to the radius: | ||
\[ | \[ | ||
\begin{align} | \begin{align} | ||