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

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.

💡 Research Summary

The paper introduces 3D‑TBM (3‑dimensional Transport‑Based Morphometry), a comprehensive framework that leverages optimal mass transport (OMT) theory to embed 3‑D medical images into a linear optimal transport (LOT) space and then perform a full suite of analyses—including classification, regression, dimensionality reduction, and visual interpretation—within a single, user‑friendly Python package called PyTransKit.
Key contributions are:

1. End‑to‑end pipeline – The authors delineate four stages: (i) preprocessing (registration, segmentation, cropping, centering) where users supply NumPy‑formatted volumes; (ii) LOT embedding, which normalizes each image, selects or computes a reference (mean image or Wasserstein barycenter), and solves the mass‑preserving mapping f_i from the reference to each subject using a multiscale accelerated gradient descent. Parallel execution is supported to handle large 3‑D datasets.
2. Linearized feature representation – The transport maps are transformed into vectors via (f_i – Id)·√I₀, yielding an N × D matrix amenable to standard statistical and machine‑learning tools. Because the OMT map is invertible, any learned direction (e.g., a principal component or discriminant vector) can be projected back to image space using the inverse deformation field and its Jacobian determinant, providing anatomically meaningful visualizations.
3. Statistical and predictive modeling – The framework integrates PCA, LDA/PLDA, CCA, and regression methods directly on LOT features. The authors demonstrate that these transport‑based features outperform raw intensity features on the publicly available IXI brain MRI dataset. Specifically, they classify subjects as “young adult” (< 35 y) versus “older adult” (> 60 y) using white‑matter masks and predict chronological age as a continuous outcome. The transport‑based models achieve higher accuracy and R², and the back‑projected components highlight age‑related structural changes in frontal and temporal regions.
4. Visualization tools – PyTransKit includes functions to display transport maps, geodesic interpolations between a subject and the reference (α‑weighted blends of the identity and transport map), and reconstructed images from inverse maps. These visualizations make the otherwise abstract transport domain interpretable for clinicians and researchers.
5. Comparison with existing tools – While packages such as ANTs, MONAI, FreeSurfer, and SPM excel at registration, segmentation, and deep‑learning pipelines, none provide native support for transport‑based morphometry. General OMT libraries (e.g., POT) lack TBM‑specific utilities, forcing users to write custom code. 3D‑TBM fills this gap by offering a dedicated, well‑documented, and extensible toolbox that streamlines the entire workflow from raw data to interpretable results.
   The paper also discusses future extensions: multimodal transport embeddings (combining T1, T2, diffusion), deep‑learning approximations of transport maps to accelerate computation, large‑scale cohort pipelines (e.g., ADNI, UK Biobank), and integration of transport‑based features into clinical decision‑support systems. By providing both powerful analytical capabilities and transparent visual explanations, 3D‑TBM positions itself as a valuable addition to the medical imaging AI toolbox, especially for studies where morphological interpretation is critical.