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Image Registration: Difference between revisions
→Adaptive Log-Polar Transformation
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for j=1 to n_{theta_i} | for j=1 to n_{theta_i} | ||
IP(i,j)=I(R_max + R_i*cos(2*pi*j/n_theta_i), | IP(i,j)=I(R_max + R_i*cos(2*pi*j/n_theta_i), | ||
R_max + R_i*sin(2*pi*j/n_theta_i) | R_max + R_i*sin(2*pi*j/n_theta_i)) | ||
</pre> | </pre> | ||
The paper continues to define a projection \(\mathfrak{R}, \Theta\) to a 1-d image: | |||
\[ | |||
\Theta(j) = \sum_{i=1}^{n_4}\left[ \eta_{ij}^1 IP\left(i, \left\lceil\frac{j-1}{\Omega_i}\right\rceil\right) + \eta^2_{ij}IP\left(i, \left\lceil\frac{j}{\Omega_i}\right\rceil\right) \right] | |||
\] | |||
where: | |||
* \(i \in [1,...,n_r]\) | |||
* \(j \in [1,...,\hat{n}_\theta\) | |||
* \(\Omega_i = \frac{\hat{n}_0}{n_{\theta_i}}\) | |||
* \(\eta_{ij}^1=\Omega_i(j-1) - \lfloor \Omega_i(j-1)\rfloor\) | |||
* \(\eta_{ij}^2=1-\eta_{ij}^1\) | |||
* \(IP(i, 0) = 0 \quad \forall i\) | |||
Then: | |||
* A scale change appears as ''variable-scale'' i.e. \(\mathbfrak{R_1(\lambda r)\) while \(\Theta\) is slightly altered. | |||
* A rotation in the cartesian image appears as a phase-shift in \(\Theta\).<br> | |||
==References== | ==References== | ||