WikiSysop: Created page with "== Citation == J. M. Almira, H. Phelippeau, and A. Martinez-Sanchez, “Fast normalized cross-correlation for template matching with rotations,” Journal of Applied Mathematics and Computing, vol. 70, no. 5, pp. 4937–4969, 2024. == Abstract == Normalized cross-correlation is the reference approach to carry out template matching on images. When it is computed in Fourier space, it can handle efficiently template translations but it cannot do so with template rotation..."

2025-02-04T06:33:43Z

Created page with "== Citation == J. M. Almira, H. Phelippeau, and A. Martinez-Sanchez, “Fast normalized cross-correlation for template matching with rotations,” Journal of Applied Mathematics and Computing, vol. 70, no. 5, pp. 4937–4969, 2024. == Abstract == Normalized cross-correlation is the reference approach to carry out template matching on images. When it is computed in Fourier space, it can handle efficiently template translations but it cannot do so with template rotation..."

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== Citation ==

J. M. Almira, H. Phelippeau, and A. Martinez-Sanchez, “Fast normalized cross-correlation for template matching with rotations,” Journal of Applied Mathematics and Computing, vol. 70, no. 5, pp. 4937–4969, 2024.

== Abstract ==

Normalized cross-correlation is the reference approach to carry out template matching
on images. When it is computed in Fourier space, it can handle efficiently template
translations but it cannot do so with template rotations. Including rotations requires
sampling the whole space of rotations, repeating the computation of the correlation
each time. This article develops an alternative mathematical theory to handle efficiently,
at the same time, rotations and translations. Our proposal has a reduced computational
complexity because it does not require to repeatedly sample the space of rotations.
To do so, we integrate the information relative to all rotated versions of the template
into a unique symmetric tensor template -which is computed only once per template-.
Afterward, we demonstrate that the correlation between the image to be processed
with the independent tensor components of the tensorial template contains enough
information to recover template instance positions and rotations.Our proposed method
has the potential to speed up conventional template matching computations by a factor
of several magnitude orders for the case of 3D images.

== Keywords ==

== Links ==

https://link.springer.com/article/10.1007/s12190-024-02157-6

== Related software ==

== Related methods ==

== Comments ==

2024Almira TTM - Revision history