# Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment

## TL;DR

This paper presents an unsupervised method that combines assignment flow with Riemannian gradient flows to learn labels on feature manifolds, enabling adaptive and spatially regularized image labeling without prior labels.

## Contribution

It introduces a novel coupling of assignment flow with label evolution on manifolds, allowing unsupervised label learning and adaptation in image labeling tasks.

## Key findings

- Improves image labeling accuracy through label adaptivity.
- Enables learning of compact label dictionaries without supervision.
- Demonstrates effectiveness on manifold-valued features across multiple scenarios.

## Abstract

This paper introduces the unsupervised assignment flow that couples the assignment flow for supervised image labeling with Riemannian gradient flows for label evolution on feature manifolds. The latter component of the approach encompasses extensions of state-of-the-art clustering approaches to manifold-valued data. Coupling label evolution with the spatially regularized assignment flow induces a sparsifying effect that enables to learn compact label dictionaries in an unsupervised manner. Our approach alleviates the requirement for supervised labeling to have proper labels at hand, because an initial set of labels can evolve and adapt to better values while being assigned to given data. The separation between feature and assignment manifolds enables the flexible application which is demonstrated for three scenarios with manifold-valued features. Experiments demonstrate a beneficial effect in both directions: adaptivity of labels improves image labeling, and steering label evolution by spatially regularized assignments leads to proper labels, because the assignment flow for supervised labeling is exactly used without any approximation for label learning.