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This study investigates the limitations of leveraging euclidean distance-based metrics (i.e., Chamfer Distance (CD) and Hausdorff Distance (HD)) as evaluating registration accuracy in computer-assisted surgery (CAS), where the acquired data is subject to anisotropic noise and partially overlapped. We first conduct both theoretical analysis and exemplary visualizations, we confirm three major limitations of CD and HD including their sensitivity to non-overlapping regions, reliance on an isotropic noise assumption, and inability to accurately capture rotation errors. To address the limitation of partial overlap, we propose Single-directional Chamfer Distance (SCD) and Single-directional Hausdorff Distance (SHD) as enhanced metrics for CAS scenarios. Furthermore, we have validated the proposed metrics through a statistical analysis of registration results using 1,757 femur models from the MedShapeNet dataset, examining the correlation between euclidean distance-based metrics (i.e., CD, HD, SCD and SHD) and those metrics including Relative Rotation Error (RRE) and Relative Translation Error (RTE) that are computed based on ground-truth (GT) transformation, as well as target registration error (TRE) that necessitates the GT landmarks correspondences. The results show that SCD and SHD significantly outperform CD and HD in terms of correlation and consistency with TRE. For correlation analysis, the Pearson correlation coefficient (PCC) for SCD and SHD are 0.915 ( \(p < 0.0001\) ) and 0.652 ( \(p < 0.0001\) ), demonstrating stronger correlations with TRE against those of CD and HD being r = 0.225 with ( \(p < 0.0001\) ) and r = 0.159 ( \(p < 0.0001\) ). For consistency analysis, SCD achieves a best Cohen’s Kappa value of 0.788 ( \(p < 0.0001\) ) with TRE, significantly better than CD and HD being \(\kappa =\) 0.177 ( \(p < 0.0001\) ) and \(\kappa =0.158\) ( \(p < 0.0001\) ) respectively. In addition, experimental results using 25 sets of femur phantom data further confirm the feasibility of SCD and SHD for clinical applications. For example, PCC values between SCD and TRE, between SHD and TRE are 0.915 ( \(p < 0.0001\) ) and 0.652 ( \(p < 0.001\) ), which demonstrates the strong potential of SCD and SHD being adopted as more appropriate metrics that eliminate the landmark annotations for registration accuracy evaluation in CAS.

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Point Set Registration Metrics Reloaded for Computer-Assisted Surgery

  • 会议论文

  • 发表日期：

    2026年

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  • Xinzhe Du,
  • Shixing Ma,
  • Mingyang Liu,
  • Zhengyan Zhang,
  • Zhe Min

摘要

This study investigates the limitations of leveraging euclidean distance-based metrics (i.e., Chamfer Distance (CD) and Hausdorff Distance (HD)) as evaluating registration accuracy in computer-assisted surgery (CAS), where the acquired data is subject to anisotropic noise and partially overlapped. We first conduct both theoretical analysis and exemplary visualizations, we confirm three major limitations of CD and HD including their sensitivity to non-overlapping regions, reliance on an isotropic noise assumption, and inability to accurately capture rotation errors. To address the limitation of partial overlap, we propose Single-directional Chamfer Distance (SCD) and Single-directional Hausdorff Distance (SHD) as enhanced metrics for CAS scenarios. Furthermore, we have validated the proposed metrics through a statistical analysis of registration results using 1,757 femur models from the MedShapeNet dataset, examining the correlation between euclidean distance-based metrics (i.e., CD, HD, SCD and SHD) and those metrics including Relative Rotation Error (RRE) and Relative Translation Error (RTE) that are computed based on ground-truth (GT) transformation, as well as target registration error (TRE) that necessitates the GT landmarks correspondences. The results show that SCD and SHD significantly outperform CD and HD in terms of correlation and consistency with TRE. For correlation analysis, the Pearson correlation coefficient (PCC) for SCD and SHD are 0.915 ( \(p < 0.0001\) ) and 0.652 ( \(p < 0.0001\) ), demonstrating stronger correlations with TRE against those of CD and HD being r = 0.225 with ( \(p < 0.0001\) ) and r = 0.159 ( \(p < 0.0001\) ). For consistency analysis, SCD achieves a best Cohen’s Kappa value of 0.788 ( \(p < 0.0001\) ) with TRE, significantly better than CD and HD being \(\kappa =\) 0.177 ( \(p < 0.0001\) ) and \(\kappa =0.158\) ( \(p < 0.0001\) ) respectively. In addition, experimental results using 25 sets of femur phantom data further confirm the feasibility of SCD and SHD for clinical applications. For example, PCC values between SCD and TRE, between SHD and TRE are 0.915 ( \(p < 0.0001\) ) and 0.652 ( \(p < 0.001\) ), which demonstrates the strong potential of SCD and SHD being adopted as more appropriate metrics that eliminate the landmark annotations for registration accuracy evaluation in CAS.