We study the inverse problem of model parameter learning for pixelwise image labeling,
using the linear assignment flow and training data with ground truth. This is accomplished by
a Riemannian gradient flow on the manifold of parameters that determines the regularization
properties of the assignment flow. Using the symplectic partitioned Runge–Kutta method for
numerical integration, it is shown that deriving the sensitivity conditions of the parameter
learning problem and its discretization commute. A convenient property of our approach is …

We introduce and study the inverse problem of model parameter learning for image labeling,
based on the linear assignment flow. This flow parametrizes the assignment of labels to
feature data on the assignment manifold through a linear ODE on the tangent space. We
show that both common approaches are equivalent: either differentiating the continuous
system and numerical integration of the state and the adjoint system, or discretizing the
problem followed by constrained parameter optimization. Experiments demonstrate how a …