  We propose and study a method called FLOT that estimates scene flow on point
clouds. We start the design of FLOT by noticing that scene flow estimation on
point clouds reduces to estimating a permutation matrix in a perfect world.
Inspired by recent works on graph matching, we build a method to find these
correspondences by borrowing tools from optimal transport. Then, we relax the
transport constraints to take into account real-world imperfections. The
transport cost between two points is given by the pairwise similarity between
deep features extracted by a neural network trained under full supervision
using synthetic datasets. Our main finding is that FLOT can perform as well as
the best existing methods on synthetic and real-world datasets while requiring
much less parameters and without using multiscale analysis. Our second finding
is that, on the training datasets considered, most of the performance can be
explained by the learned transport cost. This yields a simpler method,
FLOT$_0$, which is obtained using a particular choice of optimal transport
parameters and performs nearly as well as FLOT.
