  Motion coherence is an important clue for distinguishing true correspondences
from false ones. Modeling motion coherence on sparse putative correspondences
is challenging due to their sparsity and uneven distributions. Existing works
on motion coherence are sensitive to parameter settings and have difficulty in
dealing with complex motion patterns. In this paper, we introduce a network
called Laplacian Motion Coherence Network (LMCNet) to learn motion coherence
property for correspondence pruning. We propose a novel formulation of fitting
coherent motions with a smooth function on a graph of correspondences and show
that this formulation allows a closed-form solution by graph Laplacian. This
closed-form solution enables us to design a differentiable layer in a learning
framework to capture global motion coherence from putative correspondences. The
global motion coherence is further combined with local coherence extracted by
another local layer to robustly detect inlier correspondences. Experiments
demonstrate that LMCNet has superior performances to the state of the art in
relative camera pose estimation and correspondences pruning of dynamic scenes.
