Image Registration: Difference between revisions
| (5 intermediate revisions by the same user not shown) | |||
| Line 1: | Line 1: | ||
Image registration is recovering an affine transformation (rotation | Image registration is recovering an affine transformation (scale, rotation, translation) between two images. | ||
Image registration can be performed in the frequency domain with the Fourier transform or in the spatial domain with a log-polar transformation. | Image registration can be performed in the frequency domain with the Fourier transform or in the spatial domain with a log-polar transformation. | ||
| Line 30: | Line 30: | ||
\end{pmatrix} | \end{pmatrix} | ||
</math> | </math> | ||
==Phase correlation== | |||
{{main | Wikipedia: Phase correlation}} | |||
By the [https://en.wikipedia.org/wiki/Discrete_Fourier_transform#Shift_theorem Fourier shift theorem], a translation in the spatial domain is a linear phase shift in the Fourier domain.<br> | |||
Hence, if you have two images with only a translation, you can identify the translation by estimating the phase shift. | |||
==Log-Polar Transformation== | ==Log-Polar Transformation== | ||
This is copied from Wolberg and Zokai<ref name="wolberg2000robust"> | This is copied from Wolberg and Zokai<ref name="wolberg2000robust"/>. See also Reddy (1996)<ref name="reddy1996fft"/>. | ||
The log-polar transformation is defined as follows:<br> | The log-polar transformation is defined as follows:<br> | ||
| Line 48: | Line 53: | ||
\( \lambda r \mapsto \log(\lambda r) = \log(\lambda) + \log(r) \)<br> | \( \lambda r \mapsto \log(\lambda r) = \log(\lambda) + \log(r) \)<br> | ||
These translations can be found using [[Wikipedia: Cross-correlation]]. | These translations can be found using [[Wikipedia: Cross-correlation]] or [[Wikipedia: Phase correlation]]. | ||
;Algorithm | ;Algorithm | ||
| Line 64: | Line 69: | ||
===Adaptive Log-Polar Transformation=== | ===Adaptive Log-Polar Transformation=== | ||
The goal of Adaptive Polar Transform by Matungka ''et al.''<ref name="matungka2009adaptive" | The goal of Adaptive Polar Transform by Matungka ''et al.''<ref name="matungka2009adaptive"/> 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 fig4.png | 500px | Adaptive Polar Transform]] | ||
| Line 130: | Line 135: | ||
==References== | ==References== | ||
{{reflist|refs= | |||
<ref name="wolberg2000robust">George Wolberg, and Siavash Zokai (2000). ''Robust Image Registration Using Log-Polar Transform'' DOI: [https://doi.org/10.1109/ICIP.2000.901003 10.1109/ICIP.2000.901003] URL: [https://home.cis.rit.edu/~cnspci/references/wolberg2000.pdf https://home.cis.rit.edu/~cnspci/references/wolberg2000.pdf]</ref> | |||
<ref name="reddy1996fft">B. S. Reddy and B. N. Chatterji, "An FFT-based technique for translation, rotation, and scale-invariant image registration," in IEEE Transactions on Image Processing, vol. 5, no. 8, pp. 1266-1271, Aug. 1996, doi: 10.1109/83.506761. https://ieeexplore.ieee.org/document/506761</ref> | |||
<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> | |||
}} | |||