DARK: dynamic graphs based angle-aware registration of knee ultrasound point clouds

Real world medical imaging tasks often deviate sharply from the clean, controlled conditions assumed in standard computer vision benchmarks. This gap is particularly evident when registering point clouds of bony anatomy derived via 3D freehand ultrasound. Noise from the transducer tracking methods used, along with image segmentation errors, leads to spatially irregular data, resulting in minimal or no pointwise correspondence between scans. Consequently, many registration methods that perform well on open datasets, such as ModelNet40, struggle to generalise effectively in this medical domain. In this work, we introduce DARK (Dynamic Graphs based Angle-aware Registration of Knee Ultrasound Point Clouds), a registration framework purpose-built for this highly challenging setting. DARK integrates dynamic graph-based denoising with a quaternion-based Multi-Layer Perceptron (MLP) head, trained using a geodesic loss defined on the SO(3) rotation group. This design enables robust alignment of sparse, noisy and clinically acquired 3D ultrasound point clouds. Critically, unlike many prior methods that rely on simulated data or strong anatomical priors, DARK is trained and evaluated entirely on 3D freehand ultrasound data. Tested on 32 difficult cases involving knee flexion at varying angles with no pointwise overlap, DARK achieves a mean geodesic loss of 33.8°, substantially outperforming both classical and learning-based baselines. This research highlights the value of applying geometric ideas to medical registration tasks, particularly for challenging modalities like ultrasound.