Tri-Directional Sub-Voxel Displacement and Ipsilateral Territory Decoupling for 3D Bilateral Coronary Artery Tree Reconstruction in Cardiac CT Angiography
Zeyu Jia, Xin Ming
Three-dimensional (3D) reconstruction of bilateral coronary trees (LCA and RCA) from cardiac computed tomography angiography (CCTA) is limited by $64^3$ quantization, territory ambiguity, and sinotubular junction (STJ) ostium drift. We present a canonical $SO(3)$ $(Z_{\text{IS}}, Y_{\text{PA}}, X_{\text{LR}})$ multi-scale representation and Riemannian arborescence framework. First, we map 3D CCTA volumes, centerlines, and thick-stem ostia into $(Z_{\text{IS}}, Y_{\text{PA}}, X_{\text{LR}})$ space, extending a 3D pyramid and tubular decoder with a $128^3 \to 64^3$ boundary skip, a stop-gradient $128^3$ residual branch, a sub-voxel displacement head $Δ\hat{\mathbf{u}}(\mathbf{x})$, a dual-channel ipsilateral head $(\mathbf{P}_{\text{LCA}}, \mathbf{P}_{\text{RCA}})$, and a $32^3$ ostium detector. Second, all $327,385$ active parameters ($398,843$ total) are trained in one 30-epoch AdamW loop ($ε= 10^{-8}$) under decoupled L2-SP and aortic-wall consistency. Third, our Riemannian solver couples cylindrical Valsalva-STJ calibration, $128^3$ orifice contact rooting, contralateral inhibition, centripetal pruning, and 4-stage curvature-adaptive normal-plane pullback. On 14 unseen ImageCAS development volumes (28 trees; cases 201--250 isolated), the framework achieves $2.1652 \pm 0.4686\text{ mm}$ $\text{CD}_{\text{CL}}$ ($\text{CD}_{\text{CL}}^{\text{arc1mm}} = 2.2697 \pm 0.4863\text{ mm}$, $p \le 0.00024$; $57.40\% / 78.20\%$ $\text{F1}@1/2\text{mm}$; $4.6880 / 4.9298\text{ mm}$ ostia). Zero-shot evaluation on 50 unseen volumes (Cases 251--300, 100 trees) yields $2.9389 \pm 1.2785\text{ mm}$ $\text{CD}_{\text{CL}}$ ($p \le 7.24 \times 10^{-7}$; ostia $5.1815 / 7.5442\text{ mm}$), with $2.7696 \pm 1.1919\text{ mm}$ pooled $N=64$ $\text{CD}_{\text{CL}}$ and $128/128$ trees ($β_0 = 1, β_1 = 0$, $0.0000\text{ mm}$ detachment).
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