3D Transport-based Morphometry (3D-TBM) for medical image analysis

TL;DR

The paper tackles the lack of accessible tools for 3D transport-based morphometry in clinical imaging by introducing 3D-TBM, a Python-based pipeline that integrates preprocessing, Linear Optimal Transport embeddings, and downstream statistical analyses (PCA, PLDA, CCA) with inverse visualization to interpret results in the original image space. The LOT embedding linearizes morphological variations while preserving invertibility, enabling reconstruction and intuitive visualization of model directions in anatomy. Key contributions include a complete end-to-end workflow, data handling conventions, and illustrative experiments on the IXI dataset showing the benefits of using an intrinsic mean (Wasserstein barycenter) as the reference for improved predictive accuracy. The public release via PyTransKit and accompanying tutorials aim to lower barriers for adopting TBM in clinical research, facilitating interpretable, transport-domain analyses of 3D medical images.

Abstract

Transport-Based Morphometry (TBM) has emerged as a new framework for 3D medical image analysis. By embedding images into a transport domain via invertible transformations, TBM facilitates effective classification, regression, and other tasks using transport-domain features. Crucially, the inverse mapping enables the projection of analytic results back into the original image space, allowing researchers to directly interpret clinical features associated with model outputs in a spatially meaningful way. To facilitate broader adoption of TBM in clinical imaging research, we present 3D-TBM, a tool designed for morphological analysis of 3D medical images. The framework includes data preprocessing, computation of optimal transport embeddings, and analytical methods such as visualization of main transport directions, together with techniques for discerning discriminating directions and related analysis methods. We also provide comprehensive documentation and practical tutorials to support researchers interested in applying 3D-TBM in their own medical imaging studies. The source code is publicly available through PyTransKit.

Figures (8)

• Figure 1: The workflow of Transport-Based Morphometry (TBM). It includes 4 steps: step 1: preparing data for 3D-TBM; step 2: embedding 3D images into the transport domain; step 3: using the model for variable analysis, classification, and regression; and step 4: visualizing the analysis results.
• Figure 2: Intrinsic mean
• Figure 3: An example, through the transport map, the mass in the image is transported and aligned with the reference.
• Figure 4: Visualize the geodesic from from $I_1$ to $I_0$
• Figure 5: Image variations along the first three principal component directions derived from PCA.