An expert-supervised numerical framework for 3D coronary artery reconstruction and blood flow velocity estimation from biplane angiography

This paper presents a computationally efficient, sequentially integrated, expert-supervised numerical framework for three-dimensional coronary artery reconstruction and blood flow velocity estimation from routine 2D biplane X-ray angiography frames. The processing pipeline begins with an iterative 2D segmentation scheme that couples the fast marching method, minimal path extraction, directional Sobel filtering, and an image linearisation technique to isolate vessel medial axes and boundaries. To eliminate misalignment and skew-line artefacts induced by asynchronous acquisitions and patient motion, we define a robust multipoint spatial offset correction scheme utilising an iteratively reweighted least squares procedure with a composite Huber M-estimator. For 3D reconstruction, a floating-boundary correspondence mapping optimisation stage explicitly integrates a local cross-sectional diameter discrepancy term into the objective function, resolving spatial degeneracies along epipolar directions. Functional haemodynamic evaluation is addressed through a multipoint kinematic tracing method utilising agglomerative time-based clustering. Validation was performed on a clinical dataset of 25 patient cases containing challenging imaging conditions, such as low frame rates (7.5–15 frames per second), significant vessel overlapping, and severely stenotic regions. Statistical geometric analysis demonstrates a mean error under 0.3 mm and a Dice similarity coefficient (DSC = 0.925 ± 0.038) for the 3D vessel reconstruction using automatically detected landmarks for motion correction. Furthermore, a comparative study reveals that a completely automated workflow remains statistically reliable only when multiple landmarks are identified, justifying the necessity of expert interaction. Finally, we compare two velocity computation approaches: one based on the inverse advection-diffusion transport problem, and the proposed method using kinematic transit-time estimation. The latter reduces average execution time from 135 seconds to 21 seconds and provides interpretable frame indices for contrast arrival, allowing the expert to directly verify or manually override them.