Flow-based Generative Models for Learning Manifold to Manifold Mappings.

Area of Science:

• Computer Vision
• Machine Learning
• Medical Imaging
• Generative Models

Background:

• Non-Euclidean data is common in computer vision and machine learning.
• Existing generative models and modality transfer methods are limited to natural images, not manifold-valued data.
• A gap exists in generative models for manifold-valued data, particularly for applications like brain imaging.

Purpose of the Study:

• To address the scarcity of generative models for manifold-valued data.
• To develop modality transfer models for manifold-valued data, specifically for brain imaging.
• To expand the application of generative models from natural images to manifold-valued measurements.

Main Methods:

• Designed a two-stream version of GLOW (generative, flow-based invertible models).
• Introduced three new types of invertible layers for manifold-valued data.
• Ensured that the Jacobian determinants are easily calculable for the new layers.

Main Results:

• Successfully synthesized manifold-valued measurement fields from one type to another.
• Demonstrated reliable and accurate reconstruction of orientation distribution functions (ODF) from diffusion tensor images (DTI) using Human Connectome Project (HCP) data.
• Showcased the potential of using faster, lower-resolution DTI to reconstruct higher-resolution ODF data.

Conclusions:

• The developed generative models effectively handle manifold-valued data for cross-modality translation.
• The new invertible layers provide a robust theoretical and practical foundation for generative modeling on manifolds.
• This work opens new avenues for efficient and accurate brain imaging analysis by leveraging faster acquisition techniques.