Learning Adaptive Regularization for Image Labeling Using Geometric Assignment

Ruben Hühnerbein, Fabrizio Savarino, Stefania Petra, Christoph Schnörr

Abstract: 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 parameter prediction map based on kernel regression and optimal parameter values, enables the assignment flow to perform adaptive regularization that can be directly applied to novel data.