Manifold topological deep learning for biomedical data

Area of Science:

• Data Science
• Computer Vision
• Computational Topology

Background:

• Topological deep learning (TDL) excels at processing point-cloud data by integrating algebraic topology and deep neural networks.
• Current TDL methods are limited and cannot be applied to differentiable-manifold data, such as images, due to challenges in differential topology.

Purpose of the Study:

• To extend topological deep learning to differentiable-manifold data, including images.
• To introduce a novel manifold topological deep learning (MTDL) framework capable of processing complex manifold data.

Main Methods:

• The MTDL framework integrates Hodge theory with a streamlined convolutional neural network.
• Images are represented as smooth manifolds, and their vector fields are decomposed into three orthogonal components using Hodge theory.
• These components are concatenated to serve as input for the convolutional neural network.

Main Results:

• MTDL was evaluated on the MedMNIST v2 benchmark, a large database of 717,287 biomedical images.
• The MTDL framework demonstrated significantly superior performance compared to existing competing methods.
• This validates the framework's effectiveness in handling diverse 2D and 3D biomedical image datasets.

Conclusions:

• The MTDL framework successfully extends topological deep learning to a broad range of smooth manifold data, notably images.
• This research opens new avenues for applying TDL in fields dealing with manifold-structured data, such as medical imaging and computer vision.