the homography best mapping the positions posA onto posB, by the direct linear transform

Syntax

T = spatialTransformProjective.fit(posA, posB)

Robust against outliers.

T = spatialTransformProjective.fit(posA, posB, weights=w)

The points weighted.

T = spatialTransformProjective.fit(posA, posB, robust=False) # plain least squares

Description

The equations x’ (h31 x + h32 y + 1) = h11 x + h12 y + h13, and likewise for y’, are solved by least squares, reweighted against outliers with Tukey’s bisquare unless robust=False. Both point sets are first centred and scaled, Hartley’s normalisation, so that points far from the origin do not dominate the fit.

A point with a missing position or no weight is dropped; at least four points are needed.

Input

`posA`	vector3d, the positions in the first frame
`posB`	vector3d, where they went in the second, one for each

Keywords

keyword	default	description
`weights`	`None`	array, the weight of every point pair
`robust`	`True`	reweight against outliers with Tukey’s bisquare
`maxIter`	`50`	the largest number of reweighting steps

Output

`T`	spatialTransformProjective, T * posA close to posB

References

R. Hartley, In defense of the eight-point algorithm, IEEE Transactions on Pattern Analysis and Machine Intelligence 19 (1997) 580-593

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.fit_py.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.

spatialTransformProjective.fit