Novel 3D Binary Indexed Tree for Volume Computation of 3D Reconstructed Models from Volumetric Data
This addresses the need for efficient volume computation in medical imaging for analysis of 3D reconstructed models, but it appears incremental as it builds on existing techniques like marching cubes and binary indexed trees.
The paper tackled the problem of precise 3D volume computation for medical imaging by developing an algorithm that combines a binary indexed tree with reconstruction methods, achieving accuracy within ±0.004 cm³ for structures like lungs and cardiac chambers.
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.