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Application of Deep Learning-Based Medical Image Segmentation via Orbital Computed Tomography

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Manifold Topological Deep Learning for Biomedical Data.

Xiang Liu¹, Zhe Su¹, Yongyi Shi²

¹Department of Mathematics, Michigan State University, MI, 48824, USA.

Research Square

|April 29, 2025

Summary

This summary is machine-generated.

Manifold topological deep learning (MTDL) extends topological deep learning to image data on smooth manifolds. This novel approach significantly improves performance on biomedical image datasets.

Keywords:

Biomedical Data Analysis Differentiable Manifold Hodge Decomposition Topological Deep Learning

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Area of Science:

Computer Science
Mathematics
Data Science

Background:

Topological deep learning (TDL) excels with point-cloud data but has limitations with images on differentiable manifolds.
Challenges in differential topology have hindered TDL's application to image data.

Purpose of the Study:

Introduce manifold topological deep learning (MTDL) to process data on differentiable manifolds, specifically images.
Extend the capabilities of TDL to a broader range of data types.

Main Methods:

Represent images as smooth manifolds with vector fields.
Decompose vector fields into three orthogonal components using Hodge theory.
Concatenate these components as input for a convolutional neural network (CNN).

Main Results:

MTDL was evaluated on the MedMNIST v2 benchmark, a large collection of biomedical images.
The proposed MTDL framework demonstrated significantly superior performance compared to existing methods.
This validates the effectiveness of integrating Hodge theory and differential topology into deep learning for image analysis.

Conclusions:

MTDL successfully extends topological deep learning to data residing on smooth manifolds.
The framework offers a powerful new paradigm for analyzing complex image data, particularly in the biomedical domain.
This research opens new avenues for applying topological methods in deep learning for image recognition and analysis.