Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment
This work addresses the problem of unsupervised label learning for image labeling, offering a flexible approach that eliminates the need for pre-existing labels, though it builds incrementally on existing clustering and assignment flow methods.
The paper tackles unsupervised learning of compact label dictionaries by coupling assignment flow for supervised labeling with Riemannian gradient flows for label evolution on feature manifolds, demonstrating improved image labeling and proper label generation in experiments with manifold-valued features.
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.