# Efficient optimization for Hierarchically-structured Interacting Segments (HINTS)

## TL;DR

This paper introduces a novel optimization algorithm called Path-Moves for hierarchical segmentation models with geometric interactions, enabling effective use of complex tree-structured label hierarchies in biomedical image segmentation.

## Contribution

The paper presents the Path-Moves algorithm, a new optimization method capable of handling arbitrary tree-structured hierarchies with interactions, overcoming limitations of existing methods.

## Key findings

- Achieves state-of-the-art biomedical segmentation results.
- Handles complex tree hierarchies with geometric segment interactions.
- Outperforms previous optimization approaches in accuracy and applicability.

## Abstract

We propose an effective optimization algorithm for a general hierarchical segmentation model with geometric interactions between segments. Any given tree can specify a partial order over object labels defining a hierarchy. It is well-established that segment interactions, such as inclusion/exclusion and margin constraints, make the model significantly more discriminant. However, existing optimization methods do not allow full use of such models. Generic -expansion results in weak local minima, while common binary multi-layered formulations lead to non-submodularity, complex high-order potentials, or polar domain unwrapping and shape biases. In practice, applying these methods to arbitrary trees does not work except for simple cases. Our main contribution is an optimization method for the Hierarchically-structured Interacting Segments (HINTS) model with arbitrary trees. Our Path-Moves algorithm is based on multi-label MRF formulation and can be seen as a combination of well-known a-expansion and Ishikawa techniques. We show state-of-the-art biomedical segmentation for many diverse examples of complex trees.