Novel 3D Binary Indexed Tree for Volume Computation of 3D Reconstructed Models from Volumetric Data

TL;DR

This paper introduces a novel 3D binary indexed tree algorithm that efficiently computes the volume of volumetric data from medical imaging, enhancing accuracy and processing speed.

Contribution

It combines multivariate calculus, marching cube, and binary indexed trees to improve volume computation from CT and MR data with faster query times.

Findings

Accurately computed volumes within ±0.004 cm³ for various models.

Created 30 configurations for volume values based on polygonal mesh.

Algorithm processes data in scan-line order for efficient reconstruction.

Abstract

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.