a projective transform, stored as a homography
What a tilted specimen does to a map: the plane is seen obliquely, so straight lines stay straight but parallel ones need not, and the scale varies across the frame. Eight parameters, fitted by the direct linear transform and solved robustly.
Unlike a polynomial this is a genuine geometric map, so its inverse is another homography rather than an iteration.
Syntax
T = spatialTransformProjective(H)
T = spatialTransformProjective.fit(posA,posB)
T = spatialTransformProjective.fit(posA,posB,'weights',w)Input
| H | 3x3 homography, scaled so H(3,3) = 1 |
| posA, posB | vector3d, the same points in the two frames |
| w | double, one weight per point |
Output
| T | spatialTransformProjective |
Class Properties
| H | 3x3 homography acting on [x; y; 1], divided through by the third row |
See also
Citing this page.
This page is part of the documentation of
MTEX, a free and open
source MATLAB toolbox for analyzing and modeling crystallographic textures.
It was written by The MTEX Developers and is published at
https://mtex-toolbox.github.io/spatialTransformProjective.html.
If you use MTEX, or reuse text or figures from this page, in your research,
please cite
F. Bachmann, R. Hielscher, H. Schaeben: Texture Analysis with MTEX - Free and Open Source Software Toolbox, Solid State Phenomena 160 (2010), 63-68. 10.4028/www.scientific.net/SSP.160.63
BibTeX
@article{bachmann2010mtex,
author = {F. Bachmann and R. Hielscher and H. Schaeben},
title = {Texture Analysis with MTEX - Free and Open Source Software Toolbox},
journal = {Solid State Phenomena},
volume = {160},
pages = {63-68},
year = {2010},
doi = {10.4028/www.scientific.net/SSP.160.63},
url = {https://doi.org/10.4028/www.scientific.net/SSP.160.63}
}Other papers describing specific MTEX methods are listed under Publications — please cite the one that best fits your application. The MTEX source code is licensed under the GNU General Public License v2.0; the text and figures of this documentation are licensed under CC BY 4.0, which permits reuse — including by automated systems — provided The MTEX Developers and this page are credited.