用新型3D二叉索引树加速医学影像体积计算，提升重建效率。
Novel 3D Binary Indexed Tree for Volume Computation of 3D Reconstructed Models from Volumetric Data
- 结合扫描线处理与二叉索引树，实时计算三维体积。
- 在球体、肺部等结构上误差小于±0.004cm³。
- 适合需要快速切片或变形的医学建模场景。
在医学影像领域，精确计算三维体积对后续定性分析至关重要。本文结合多元微积分、等值面提取算法（marching cubes）与二叉索引树数据结构，提出一种高效算法，用于从CT或MR volumetric data中恢复的任意三维体数据的固有体积计算。基于多边形网格生成方法，我们设计了30种体积值配置方案。算法在扫描线顺序中同步处理数据并构建Fenwick树，实现极快查询响应，支持用户对模型进行切片或变换操作。我们在简单物体（如球体、圆柱体）和复杂结构（如肺部、心室）上测试了准确性，结果误差控制在±0.004 cm³以内，仍有优化空间。
原文摘要 · Abstract (English)
In the burgeoning field of medical imaging, precise computation of 3D volume holds a significant importance for subsequent qualitative analysis of 3D reconstructed objects. Combining multivariate calculus, marching cube algorithm, and binary indexed tree data structure, we developed an algorithm for efficient computation of intrinsic volume of any volumetric data recovered from computed tomography (CT) or magnetic resonance (MR). We proposed the 30 configurations of volume values based on the polygonal mesh generation method. Our algorithm processes the data in scan-line order simultaneously with reconstruction algorithm to create a Fenwick tree, ensuring query time much faster and assisting users' edition of slicing or transforming model. We tested the algorithm's accuracy on simple 3D objects (e.g., sphere, cylinder) to complicated structures (e.g., lungs, cardiac chambers). The result deviated within $\pm 0.004 \text{cm}^3$ and there is still room for further improvement.
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