Manifold-Guided Multi-Reference Registration for Left-Ventricular Motion Tracking in 3D Echocardiography
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Abstract
Purpose: To develop and evaluate a data-driven multi-reference registration strategy for left-ventricular motion tracking in three-dimensional echocardiography, using an intrinsic low-dimensional cardiac trajectory to determine the temporal placement of local registration references.
Materials and Methods: Twelve healthy-volunteer three-dimensional echocardiographic sequences from a publicly available myocardial-tracking benchmark were analyzed. We evaluated six low-dimensional representation methods (PCA, t-SNE, Diffusion Maps, LLE, UMAP, and Isomap) in standard and time-embedded forms using geometric and physiologically relevant criteria. Four reference frames were automatically extracted from the resulting two-dimensional trajectories. Time-embedded PCA and Diffusion Maps produced identical four-reference sets for all analyzed cases and therefore resulted in the same proposed registration configuration. We compared five primary registration configurations—single-reference, sequential frame-to-frame, the proposed manifold-guided multi-reference strategy, a partial B-Spline–Fourier (BSF) implementation, and a Fixed Four-Reference Control—using landmark-based Target Registration Error (TRE) in millimeters. We also evaluated an additional Two-Reference Control (K=2) that retained only the initial ED and principal internal references as a reference-number sensitivity analysis.
Results: For both time-embedded PCA and Diffusion Maps, the automatically selected principal internal reference coincided with the expert-defined end-systolic (ES) frame in 10 of 12 cases and differed by one frame in the remaining two cases. The proposed strategy achieved mean-cycle, ES-frame, and final-frame TRE values of 6.8 ± 1.6 mm, 11.5 ± 2.7 mm, and 4.0 ± 1.2 mm, respectively. For mean-cycle TRE, Strategy 3 showed a median paired reduction of 0.99 mm relative to the Fixed Four-Reference Control [95% CI: 0.94–1.08; |r_rb|=0.91; p_Holm=0.033]. At ES, the corresponding reduction relative to the Fixed Four-Reference Control was 2.000 mm [1.945–2.055; |r_rb|=1.000; p_Holm=0.021]. The K=2 control showed no significant mean-cycle difference from the other configurations, but Strategy 3 reduced ES-frame TRE relative to K=2 by 1.265 mm [0.304–2.445; |r_rb|=0.909; p_Holm=0.029] and final-frame TRE by 1.156 mm [0.483–2.142; |r_rb|=1.000; p_Holm=0.029]. No statistically significant final-frame difference was detected between Strategy 3 and the Fixed Four-Reference Control.
Conclusion: Within this benchmark of 12 healthy-volunteer sequences, the findings support the internal technical feasibility of using the intrinsic low-dimensional organization of a cardiac image sequence for data-driven reference-frame placement within a multi-reference registration architecture. Time-embedded PCA and Diffusion Maps produced identical reference configurations, indicating no additional reference-selection benefit from the more computationally demanding Diffusion Maps representation in the present benchmark. The K=2 sensitivity analysis showed phase-specific effects of removing the intermediate references, while the absence of a significant mean-cycle difference prevents interpretation of K=4 as uniformly superior or empirically optimal. Independent validation in larger and clinically heterogeneous datasets is required before broader generalization.
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