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Image Registration: Difference between revisions
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(Created page with "Image registration is recovering an affine transformation (rotation + translation) between two images.") |
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Image registration is recovering an affine transformation (rotation + translation) between two images. | Image registration is recovering an affine transformation (rotation + translation) between two images. | ||
==Problem Statement== | |||
We are given two images <math>I_1</math> and <math>I_2</math>.<br> | |||
Let <math>(x,y)</math> be uv coordinates within the image.<br> | |||
We want to find a rotation and translation from <math>(x,y)</math> to <math>(x',y')</math> such that <math>I_1(x,y) = I_2(x', y')</math>.<br> | |||
This is represented as:<br> | |||
<math> x' = a_1 x + a_2 y + a_3</math><br> | |||
<math> y' = a_4 x + a_5 y + a_6</math><br> | |||
This can also be written as:<br> | |||
<math> | |||
\begin{pmatrix} | |||
x' \\ y' \\ 1 | |||
\end{pmatrix} | |||
= | |||
\begin{pmatrix} | |||
a_1 & a_2 & a_3\\ | |||
a_4 & a_5 & a_6\\ | |||
0 & 0 & 1 | |||
\end{pmatrix} | |||
\begin{pmatrix} | |||
x \\ y \\ 1 | |||
\end{pmatrix} | |||
</math> | |||
==Log-Polar Transformation== | |||
==References== | |||