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Hierarchical Barycentric Multimodal Representation Learning for Medical Image Analysis.

Peijie Qiu, Zhaoqi An, Sungmin Ha

Medrxiv : the Preprint Server for Health Sciences

|April 20, 2026

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This study introduces a geometric approach for multimodal medical image analysis, using Wasserstein barycenters to improve data representation. The new method enhances diagnostic accuracy for tasks like brain tumor segmentation, even with missing data.

Area of Science:

Medical image analysis
Machine learning
Geometric deep learning

Background:

Multimodal medical image analysis uses diverse data (e.g., MRI, DTI, PET) to improve diagnostics.
Learning robust representations is crucial but challenging with missing data and varied distributions.
Existing methods lack theoretical grounding in the geometric behavior of multimodal data.

Purpose of the Study:

Introduce a generalized geometric framework for multimodal representation learning.
Unify existing methods using a barycentric perspective.
Propose a novel approach using Wasserstein barycenters with hierarchical priors.

Main Methods:

Developed a generalized geometric perspective based on barycenters.
Implemented generalized Wasserstein barycenters with hierarchical modality-specific priors.

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Evaluated the framework on brain tumor MRI segmentation and normative modeling tasks.

Main Results:

Demonstrated consistent improvements over existing multimodal approaches.
Showcased enhanced representation quality by preserving unimodal distribution geometry.
Validated the framework's effectiveness on key clinical applications.

Conclusions:

The proposed barycentric formulation offers a unified theoretical understanding.
The novel approach effectively handles missing modalities and heterogeneous data.
Scalable, theoretically grounded methods advance robust representation learning in medical imaging.