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.

翻译：在蓬勃发展的医学影像领域，三维体积的精确计算对于后续三维重建对象的定性分析具有重要意义。结合多元微积分、行进立方体算法和二进制索引树数据结构，我们开发了一种高效计算从计算机断层扫描或磁共振成像恢复的任何体数据固有体积的算法。我们基于多边形网格生成方法提出了体积值的30种配置方案。该算法以扫描线顺序处理数据，并与重建算法同步构建Fenwick树，从而确保查询时间显著加快，并辅助用户进行切片或模型变换的编辑操作。我们在简单三维对象（如球体、圆柱体）到复杂结构（如肺部、心腔）上测试了算法的准确性。结果偏差在±0.004 cm³范围内，且仍存在进一步优化的空间。