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：在医学影像这一新兴领域中，精确计算三维体积对于后续三维重建物体的定性分析具有重要意义。结合多元微积分、移动立方体算法和树状数组数据结构，我们开发了一种高效计算任何从计算机断层扫描（CT）或磁共振（MR）恢复的体素数据内在体积的算法。我们基于多边形网格生成方法提出了30种体积值构型。该算法以扫描线顺序处理数据，并同时与重建算法协同构建芬威克树（Fenwick树），从而显著加快查询速度，并方便用户对模型进行切片或变换编辑。我们在简单三维物体（例如球体、圆柱体）到复杂结构（例如肺、心腔）上测试了该算法的精度。结果偏差在$\pm 0.004 \text{cm}^3$范围内，且仍有进一步改进的空间。