Learning Adaptive Regularization for Image Labeling Using Geometric Assignment

TL;DR

This paper introduces a novel method for learning adaptive regularization parameters in image labeling tasks by leveraging a Riemannian gradient flow on the parameter manifold, enabling exact inference-based learning.

Contribution

It proposes a new geometric approach to parameter learning in image labeling that ensures the learning process commutes with numerical integration, enhancing model expressiveness and performance.

Findings

Demonstrates improved labeling accuracy on benchmark datasets.

Shows the mathematical model's expressiveness and limitations.

Validates the approach through carefully designed experiments.

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 determine 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.