minimal_surface

This code implements the basic algorithm from this paper, which only computes optimal silhouette-consistent minimal surfaces of given volume with gradient descent on GPU:

Fast and Globally Optimal Single View Reconstruction of Curved Objects M. R. Oswald, E. Toeppe and D. Cremers; In IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2012.

Based on a minimal user input, this algorithm interactively determines the objects' silhouette and subsequently computes a silhouette-consistent 3D model which is precisely the globally minimal surface with user-specified volume. In above paper, the authors also proposed the weighted minimal surface which is NOT included in this repository.

1. Requirements

This code has three party dependencies:

0. MATLAB (mandatory)

1. CUDA (mandatory)

2. CMake (mandatory)

2. Getting started

This code is tested under:

• Ubuntu 16.04
• CMake 3.5.1
• CUDA 8.0
• MATLAB R2019a

Download the demo dataset:

• cd pathto/code/data

• ./download.sh

Build Mex file:

• Set MATLAB_ROOT environment variable in to your installed matlab path, such as

  export MATLAB_ROOT='/usr/local/MATLAB/R2019a' in ~/.bashrc

• In Terminal do cd pathto/code

  mkdir build

  cd build

  cmake ..

  make

• In build/lib is the mex file and in build/bin is the binary

• cd ..

• execute the matlab script example.m

3. Input

• mask: a boolean binary describing the silhouette.
• volume: the desired volume of result.

4. Parameters

• max_iter: the max number of iteration for gradient descent.
• tol: the stopping criterion by residual.
• tau: the step size for gradient descent.

5. License

minimal_surface is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License, see here, with an additional request:

If you make use of the library in any form in a scientific publication, please refer to https://github.com/zhenzhangye/minimal_surface and cite following papers

@INPROCEEDINGS{6247718,
  author={M. R. {Oswald} and E. {Töppe} and D. {Cremers}},
  booktitle={2012 IEEE Conference on Computer Vision and Pattern Recognition},
  title={Fast and globally optimal single view reconstruction of curved objects},
  year={2012},
  pages={534-541},
  doi={10.1109/CVPR.2012.6247718},
  month={June},
}

@article{haefner2019variational,
  title={Variational Uncalibrated Photometric Stereo under General Lighting},
  author={Haefner, Bjoern and Ye, Zhenzhang and Gao, Maolin and Wu, Tao and Qu{\'e}au, Yvain and Cremers, Daniel},
  journal={arXiv preprint arXiv:1904.03942},
  year={2019}
}