Adaptive Block Coordinate Descent for Distortion Optimization

Adaptive block coordinate descent (ABCD) is a new algorithm for optimizing geometric distortions and computing inversion-free maps in 2D and 3D. This code has a Matlab I/O interface and C++ implementation of ABCD algorithm with gradient descent (GD) and projected Newton (PN) solvers.

DOI Paper Video

Dependencies

• Eigen (default solver)
• Pardiso (optional)
• libigl (mesh loading)
• boost (graph coloring)

Build

We provide windows binaries (mexw64) that support Eigen library. For running ABCD solver on other platforms, all C++ Mex code has to be compiled first. This can be done in Matlab by running the following script:

cd mexed_solver/mex
compile_all_mex

Follow instructions of compile_all_mex.m for building ABCD code with Pardiso

• We recommend to compile Pardiso version directly from Visual Studio on Windows (read instructions or contact authors for project files).

Running the demo

Run in Matlab command window:

ABCD_PN_demo

Data formats

Examples of different input formats are shown in the demo script

2D input

We support obj files (with or without texture) or mat files that contain triangles, vertices and initialization (T, V, fV)

• Specify in options.is_uv_mesh if it is a surface parametrization or a planar deformation problem

3D input

We support mat files that contain tetrahedrons, vertices and initialization (T, V, fV)

Solver specifications

We set all ABCD parameters at the beginning of the demo script (optimzier_spec and fixer_spec structs). Note that ABCD is a highly customizable solver and you can reconfigure it by changing the following fields in a solver spec struct:

    energy_num           : distortion energies for optimizer (0,2) and fixer (3)
                         : 0 - ARAP
                         : 2 - symmetric Dirichlet (modified)
                         : 3 - invalid simplex penalty
    invalid_penalty      : cost of flipped and collapsed simplices
    is_flip_barrier      : enable/disable energy barriers
    
    is_parallel          : enable/disable openmp parallelization
    use_pardiso          : enable/disable Pardiso 
    
    ls_interval          : line search interval (fixer interval > 1.0)
    ls_alpha             : backtracking  search parameter
    ls_beta              : backtracking  search parameter
    ls_max_iter          : backtracking  search parameter
    
    block_iteration_range: controls the number of block iterations for inexact BCD
    cycle_num            : number of sucessive iterations in alternating optimization
    tolerance            : termination criteria
                
    K_hat_list           : partitioning thresholds (if not set, then 
    K_hat_size           : local-global blending is disabled)

• Additional parameters in options struct:

  free_bnd             : set boundary vertices to be free or fixed  
  fixed_vertices       : indices of anchor vertices 
  iter_num             : the maximal number of all iterations 
  

Visualization

A simple Matlab code is provided for data visualization.

License

This project is licensed under Mozilla Public License, version 2.0 - see the LICENSE.md file for details