OFD - Decomposition of Optical Flow on the Sphere
Version 1.0, 2013

Clemens Kirisits (clemens.kirisits@univie.ac.at)
Lukas Lang (lukas.lang@univie.ac.at)
Computational Science Center, University of Vienna, Austria. http://www.csc.univie.ac.at/

1. Introduction

This is a MATLAB implementation of Decomposition of Optical Flow on the 
Sphere (OFD) as described in:

C. Kirisits, L. F. Lang and O. Scherzer. Decomposition of optical flow on 
the sphere, GEM. Int. J. Geomath., 5(1):117-141, April, 2014

Available at http://dx.doi.org/10.1007/s13137-013-0055-8
Preprint available at https://arxiv.org/abs/1312.4354

If you use this software in your work you must cite the abovementioned paper in any resulting publication!

BibTeX:

@article{KirLanSch14,
  author     = {Kirisits, C. and Lang, L.~F. and Scherzer, O.},
  title      = {Decomposition of optical flow on the sphere},
  doi        = {10.1007/s13137-013-0055-8},
  issn       = {1869-2672},
  journal    = {GEM. Int. J. Geomath.},
  fjournal   = {GEM - International Journal on Geomathematics},
  keywords   = {Optical flow; Vector spherical harmonics; Biomedical imaging; Computer vision; Variational methods; Vector field decomposition; 92C55; 92C37; 92C17; 35A15; 68U10; 33C55},
  language   = {English},
  month      = apr,
  number     = {1},
  pages      = {117--141},
  publisher  = {Springer Berlin Heidelberg},
  url        = {http://dx.doi.org/10.1007/s13137-013-0055-8},
  volume     = {5},
  year       = {2014}
}

2. License & Disclaimer

Copyright 2013 Clemens Kirisits and Lukas Lang.

This file is part of OFD. OFD is free software: you can redistribute it 
and/or modify it under the terms of the GNU General Public License as 
published by the Free Software Foundation, either version 3 of the License,
 or (at your option) any later version.

OFD is distributed in the hope that it will be useful, but WITHOUT ANY 
WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS 
FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.

You should have received a copy of the GNU General Public License along 
with OFD.  If not, see <http://www.gnu.org/licenses/>.

For the full license statement see the file COPYING.

Moreover, this work incorporates source code from the color wheel by 
Deqing Sun, Department of Computer Science, Brown University. The license 
statement can be found in the respective files.

3. Requirements

This software was originally written for and tested with Matlab R2012b.
It has been recently modified to also run with R2015a.

Note that this software uses the TriRep class which since R2013a is marked 
as 'will be removed in a future release'. It also used flipdim, which will 
be removed at some point in the future.

See http://www.mathworks.de/de/help/matlab/release-notes.html

The following libraries are required for parts of this sofware:

export_fig: used for producing high quality figures from the results.
URL: http://www.mathworks.com/matlabcentral/fileexchange/23629-exportfig

4. Usage

For easier use we provide a startup script (startup.m), which sets up the 
Matlab search path. It includes required libraries and adds required 
subdirectories. Make sure to download the required packages and to set the 
library paths properly. Then simply run the startup script.

To run the test cases execute

>> runtests('./test')

The following run scripts are included:

- runof.m (computes optical flow on sphere)
- runofd.m (computes a u+v decomposition)
- runodb.m (used different bases for u and v)
- runofhd.m (computes a hierarchical decomposition)
- runhelmholtz.m (computes a Helmholtz decomposition)

The following scripts also exist but were not included in the paper:

- runsurffit.m (fitting a sphere-like surface)
- runofs.m (optical flow on sphere-like surfaces)
- runofc.m (continuity equation-based velocity estimation)

If you want to reproduce the experiments from the paper run

- experiments/prepare.m (creates and stores linear system)
- experiments/runofexperiments.m (computes optical flow and Helmholtz decompositions)
- experiments/runofdexperiments.m (computes u+v decompositions)
- experiments/runofhdexperiments.m (computes hierarchical decompositions)

and the appropriate experiments/render{of, ofd, ofhd}experiments.m script 
to create and store all the figures.

5. Acknowledgements

This package includes the color wheel from http://vision.middlebury.edu/flow/
By courtesy of Deqing Sun, Department of Computer Science, Brown University.

We thank Pia Aanstad from the University of Innsbruck for kindly providing 
the microscopy data.