Fast and Scalable Optimal Transport for Brain Tractograms

TL;DR

This paper introduces a fast, scalable GPU-based multiscale algorithm for regularized Optimal Transport, enabling efficient analysis of brain tractograms and facilitating applications like label transfer and probabilistic atlas estimation.

Contribution

The authors develop a novel multiscale GPU algorithm for regularized Optimal Transport with linear memory, specifically tailored for brain tractogram analysis, and provide a user-friendly implementation.

Findings

Transport plans computed in minutes for millions of points

Effective label transfer for brain tractogram segmentation

Probabilistic atlas estimation using Wasserstein barycenter

Abstract

We present a new multiscale algorithm for solving regularized Optimal Transport problems on the GPU, with a linear memory footprint. Relying on Sinkhorn divergences which are convex, smooth and positive definite loss functions, this method enables the computation of transport plans between millions of points in a matter of minutes. We show the effectiveness of this approach on brain tractograms modeled either as bundles of fibers or as track density maps. We use the resulting smooth assignments to perform label transfer for atlas-based segmentation of fiber tractograms. The parameters -- blur and reach -- of our method are meaningful, defining the minimum and maximum distance at which two fibers are compared with each other. They can be set according to anatomical knowledge. Furthermore, we also propose to estimate a probabilistic atlas of a population of track density maps as a Wasserstein barycenter. Our CUDA implementation is endowed with a user-friendly PyTorch interface, freely available on the PyPi repository (pip install geomloss) and at www.kernel-operations.io/geomloss.