Learning Adaptive Regularization for Image Labeling Using Geometric Assignment

Ruben Hühnerbein,Fabrizio Savarino,Stefania Petra,Christoph Schnörr

doi:10.1007/s10851-020-00977-2

Ruben Hühnerbein, Fabrizio Savarino + Show 2 more

Open Access

https://doi.org/10.1007/s10851-020-00977-2

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Abstract

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 that learning is based on exact inference. Carefully designed experiments demonstrate the performance of our approach, the expressiveness of the mathematical model as well as its limitations, from the viewpoint of statistical learning and optimal control.

Highlights

1.1 Overview and ScopeThe image labeling problem, i.e., the problem to classify images pixelwise depending on the spatial context, has been thoroughly investigated during the last two decades using discrete graphical models
We focus on parameter learning for contextual pixelwise image labeling based on the assignment flow introduced by [2]
We introduced a parameter learning approach for image labeling based on the assignment flow

Summary

Introduction

The image labeling problem, i.e., the problem to classify images pixelwise depending on the spatial context, has been thoroughly investigated during the last two decades using discrete graphical models. While the evaluation (inference) of such models is well understood [15], learning the parameters of such models has remained elusive, in particular for models with higher connectivity of the underlying graph. We focus on parameter learning for contextual pixelwise image labeling based on the assignment flow introduced by [2]. We ignore the connection to discrete graphical models and focus on the parameter learning problem for the assignment flow directly. This problem is raised in [2, Section 5 and Fig. 14].

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