(Cont.) 3D Lung CT Registration via Iterative Optimal Transport on Pulmonary Vessel Point Clouds

Overview

Accurate intra-patient lung CT registration is critical for radiation therapy planning, longitudinal disease tracking, and 4D CT motion modelling. Large non-rigid deformations between expiratory (EXP) and inspiratory (INSP) breathing phases make this task particularly challenging, and conventional intensity-based approaches (e.g. ANTs) can lead to mismatch. This work adapts the Iterative Optimal Transport (IOT) framework (originally proposed for 2D multimodal image registration) to the 3D setting using pulmonary vessel point clouds derived from paired EXP/INSP CT scans.

Presentation Recording

Key Contributions

• Adapted the IOT framework from 2D multimodal images to 3D pulmonary vessel point clouds, introducing a 3D Förstner corner detector (foerstner_3d()) for structure-aware point sampling and per-axis unit-variance normalization.
• Demonstrated that point sampler choice is the dominant factor in registration quality: Förstner-scalar sampling with UOT-KL achieves a ~60% reduction in mean nearest-neighbor distance versus at most 7% for farthest-point sampling (all comparisons p < 0.001).
• Showed that KL marginal penalties are necessary even in same-modality 3D registration: phase-dependent vascular visibility creates mass imbalance between fixed and moving point clouds, and removing KL significantly degrades performance.
• Established that increasing polynomial degree from 2 to 3 yields only marginal, largely non-significant improvements, suggesting geometric quality of sampled points matters far more than model expressivity.

Methods

We evaluated three registration paths on the DIR-LAB COPDgene dataset (10 subjects, L = 300 landmarks each):

• Path A (Supervised): IOT fit directly on DIR-LAB landmark pairs
• Path B (Unsupervised, sparse): IOT fit on sampled vessel point clouds (N = 1,000), applied directly at landmark locations
• Path C (Unsupervised, TPS): IOT fit on vessel point clouds, with a Thin-Plate Spline interpolant fit to vessel displacement vectors and evaluated at landmarks

Path C is the clinically motivated setting: it does not require vessel segmentation at inference time and is applicable to downstream tasks such as lung nodule tracking.

Results

Path A achieves a mean landmark error (ME) of 3.9 mm across subjects, while Paths B and C achieve ~15.6 mm ME — a ~12 mm gap reflecting the difficulty of the fully unsupervised setting. The gap between Path B and Path C is negligible (~0.14 mm), confirming that TPS interpolation does not degrade performance relative to direct polynomial evaluation while enabling denser displacement fields.

Future Directions

• Motion-weighted sampling: extend foerstner_3d() to bias point selection toward regions of both high geometric structure and high expected motion (e.g. the lung periphery)
• Image information integration: incorporate voxel-intensity features alongside geometric point clouds
• Evaluation on clinical targets: extend benchmarking to lung nodule/lesion tracking

Acknowledgments

Work conducted under the instruction of Dr. William Hsu and the guidance of Yunzheng Zhu at the UCLA Medical & Imaging Informatics (Hsu Lab).