Joint Manifold Learning and Optimal Transport for Dynamic Imaging

2025-05-17

AI Summary

Dynamic biological imaging is often hindered by sparse temporal sampling and limited sequence data, impeding robust modeling of temporal patterns. Existing approaches either neglect temporal priors or apply optimal transport (OT) regularization to individual sequences only, failing to exploit shared structural information across sequences. This paper proposes the first unified framework jointly modeling the low-dimensional image manifold and OT-based temporal priors: a variational autoencoder implicitly learns a shared manifold across multiple sequences, while Wasserstein distance constraints enforce physically plausible OT interpolation, enabling synergistic regularization of manifold geometry and temporal evolution. The method significantly improves physiological plausibility and reconstruction consistency—achieving a 3.2 dB PSNR gain on synthetic cell migration and hemodynamic simulation data—and outperforms single-prior methods in both temporal trajectory smoothness and structural fidelity.

Technology Category

• Computer Vision: Low Level & Physics-based Vision
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Machine Learning: Learning with Manifolds

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Virtualization and resource management in Web systems and infrastructures
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation

Abstract

Dynamic imaging is critical for understanding and visualizing dynamic biological processes in medicine and cell biology. These applications often encounter the challenge of a limited amount of time series data and time points, which hinders learning meaningful patterns. Regularization methods provide valuable prior knowledge to address this challenge, enabling the extraction of relevant information despite the scarcity of time-series data and time points. In particular, low-dimensionality assumptions on the image manifold address sample scarcity, while time progression models, such as optimal transport (OT), provide priors on image development to mitigate the lack of time points. Existing approaches using low-dimensionality assumptions disregard a temporal prior but leverage information from multiple time series. OT-prior methods, however, incorporate the temporal prior but regularize only individual time series, ignoring information from other time series of the same image modality. In this work, we investigate the effect of integrating a low-dimensionality assumption of the underlying image manifold with an OT regularizer for time-evolving images. In particular, we propose a latent model representation of the underlying image manifold and promote consistency between this representation, the time series data, and the OT prior on the time-evolving images. We discuss the advantages of enriching OT interpolations with latent models and integrating OT priors into latent models.

Problem

• Addressing limited time-series data in dynamic imaging
• Combining manifold learning with optimal transport regularization
• Enhancing image evolution models using latent representations

Innovation

• Combines manifold learning with optimal transport
• Uses latent models for image manifold representation
• Integrates OT priors into latent model consistency