kisonecat/so3hd

Compute an SO(3)-invariant Hausdorff distance

so3hd

Compute the minimum of the Hausdorff distance between a 3-dimensional point cloud A and a point cloud rho(B), where rho is an element of SO(3).

To avoid the issue of building a nice cellular decomposition of SO(3), we pay the price of adding one additional dimension. That is, we use box in R^4 containing unit ball; then a point in that box is rescaled so that a point lies on the unit sphere S^3, which can then via the quaternions be regarded as an element of SO(3). Thus, the search space is a box.

Rather than trying to be opinionated as to what global search algorithm we ought to use to compute the minimum over rho in SO(3), we use NLopt, a nice optimization package with bindings for a variety of languages.

We rely on PCL to manage the point cloud data.

Building

mkdir build
cd build
cmake ..
make