OFCM - Brightness and Mass Conservation Laws on Evolving Sphere-Like Surfaces

Lukas Lang (ll542@cam.ac.uk)
Department of Applied Mathematics and Theoretical Physics
University of Cambridge, UK.
http://www.damtp.cam.ac.uk/people/ll542/

1. Introduction

This is a Matlab implementation as described in:

L. F. Lang. A Numerical Framework for Efficient Motion Estimation on Evolving Sphere-Like Surfaces based on Brightness and Mass Conservation Laws, 2018.

If you use this software in your work please cite the abovementioned paper in any resulting publication.

BibTeX:

@techreport{Lan18_report,
  author     = {Lang, L.~F.},
  title      = {A Numerical Framework for Efficient Motion Estimation on Evolving Sphere-Like Surfaces based on Brightness and Mass Conservation Laws},
  institution= {DAMTP, University of Cambridge, United Kingdom},
  number     = {arXiv:1805.01006},
  numpages   = {12},
  type       = {Preprint on ArXiv},
  url        = {https://arxiv.org/abs/1805.01006},
  year       = {2018}
}

This software package requires parts of

L. F. Lang and O. Scherzer. Optical Flow on Evolving Sphere-Like Surfaces,
Inverse Probl. Imaging, 11(2):305-338, 2017.

Available at https://dx.doi.org/10.3934/ipi.2017015
Preprint available at https://arxiv.org/abs/1506.03358

which iteself requires parts of

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

The computed results are based on the data:

Aanstad, Pia. (2018). Time-lapse (4D) volumetric fluorescence microscopy image sequence of a living zebrafish embryo [Data set]. Zenodo. 
URL: https://doi.org/10.5281/zenodo.1211598

2. License & Disclaimer

Copyright 2017 Lukas Lang.

This file is part of OFCM. OFCM 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.

OFCM 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 OFCM.  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.

Furthermore, this work includes source code of imgaussian, lgwt, and vol3d.
The license statement can be found in the respective folders.

tiffread.m is licensed under GNU GPL v3.

3. Requirements

This software was originally written for and tested with Matlab R2017b.

The following libraries are required for parts of this sofware:

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

The following libraries are already included in the folder 'external':

imgaussian: used for fast Gaussian filtering of 3D data.
URL: http://de.mathworks.com/matlabcentral/fileexchange/25397-imgaussian

tiffread.m: used for reading LSM microscopy data files.
URL: http://www.cytosim.org/misc/index.html

lgwt: used for computing Legendre-Gauss quadrature weights and nodes.
URL: https://de.mathworks.com/matlabcentral/fileexchange/4540-legendre-gauss-quadrature-weights-and-nodes

vol3dv2: used for plotting of volumetric microscopy data.
https://de.mathworks.com/matlabcentral/fileexchange/22940-vol3d-v2

Moreover, it requires the code of OFD (Decomposition of Optical Flow on the Sphere).
The version used is: https://doi.org/10.5281/zenodo.1238901
Download/check it out from https://github.com/lukaslang/ofd

Moreover, it requires the code of OFISH (Optical Flow on Evolving Sphere-Like Surfaces).
The version used is: https://doi.org/10.5281/zenodo.1238904
Download/check it out from https://github.com/lukaslang/ofish

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')

Note that test/readlsmTest.m requires a certain LSM file to be available 
(set via datapath.m)!

In order to run the software with real data set the path to your LSM files
in the script:

- datapath.m.

The following run scripts are included:

- runof.m (computes the optical flow on evolving sphere-like surfaces)
- runcm.m (computes the mass conservation-based velocity on evolving sphere-like surfaces)

The figures in the paper were created with the script:

- runpaperresults.m

For faster processing we recommend compiling the imgaussian.c script:

>> cd external
>> cd imgaussian
>> mex imgaussian.c

Make sure Matlab has rights to execute the imgaussian.mexw* file!

5. Acknowledgements

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