# Learning Adaptive Regularization for Image Labeling Using Geometric Assignment

arXiv: https://arxiv.org/abs/1910.09976 · HTML: https://mlsanity.com/paper/1910.09976/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Oct 2019.

## Built on by (most cited first, 3 of 3)

- [Sigma Flows for Image and Data Labeling and Learning Structured Prediction](https://mlsanity.com/paper/2408.15946/) (2024)
- [A Nonlocal Graph-PDE and Higher-Order Geometric Integration for Image Labeling](https://mlsanity.com/paper/2205.03991/) (2022)
- [Riemannian Patch Assignment Gradient Flows](https://mlsanity.com/paper/2504.13024/) (2025)

## Abstract (arXiv)

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.