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Efficient Hausdorff Distance Computation for Triangle Meshes with Error Bound

Paper: https://onlinelibrary.wiley.com/doi/full/10.1111/cgf.14395

What is it?

Giving two triangle meshes A.obj and B.obj, the following command gives the lower bound L and upper bound U of Hausdorff distance from A.obj to B.obj that U - L < 1e-6.

hausdorff -a A.obj -b B.obj -e 1e-6 -c abs -t point

The output will contain a line in the form of [distance] L - U and report many detailed information about the computational procedure.

Installation

This project can be built easily by:

git clone https://github.com/ZJUCADGeoSim/Hausdorff.git
cmake -S . -B build
cmake --build build

Then, you can find the binary hausdorff at ./build/bin.

Run our method for bound estimation:

./build/bin/hausdorff -a ./sample_data/hand-tri-smooth.obj -b ./sample_data/hand-tri.obj -t point

More complicated usages

  • Run Tang et al. [2009]'s method for bound estimation:
./build/bin/hausdorff -a ./sample_data/hand-tri-smooth.obj -b ./sample_data/hand-tri.obj -t triangle
  • Relative error can be applied via options -e 0.01 -c rel. It implies the stop condition U - L < 0.01 * L.
  • Diag-rel error can be applied via options -e 0.01 -c diag. It implies the stop condition U - L < 0.01 * diag length of bbox.

Motivation of this work

When working on the research about remeshing, we find that there is no code to compute the Hausdorff distance reliably and efficiently. So, we made it.