Barnes-Hut Approximation for Point SetGeodesic Shooting
This incremental improvement enables faster clinical research and practical applications in medical imaging by addressing a known bottleneck in point set registration.
The paper tackles the computational inefficiency of exact geodesic shooting for point set registration, which requires O(N^2) calculations, by proposing a Barnes-Hut approximation that reduces complexity to O(N b + N log N) and achieves up to 3-fold speedup with comparable accuracy in simulated and medical image analyses.
Geodesic shooting has been successfully applied to diffeo-morphic registration of point sets. Exact computation of the geodesicshooting between point sets, however, requiresO(N2) calculations each time step on the number of points in the point set. We proposean approximation approach based on the Barnes-Hut algorithm to speedup point set geodesic shooting. This approximation can reduce the al-gorithm complexity toO(N b+N logN). The evaluation of the proposedmethod in both simulated images and the medial temporal lobe thick-ness analysis demonstrates a comparable accuracy to the exact point set geodesic shooting while offering up to 3-fold speed up. This improvementopens up a range of clinical research studies and practical problems towhich the method can be effectively applied.