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

This preprint is currently undergoing revisions for submission to a conference. It focuses on algorithms and data structures within the realm of computer graphics, and does not involve AI or deep learning. This paper was presented at ISEF 2024, accompanied by a software demonstration showcasing its functionality and practical applications… Read more

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 ±0.004cm^3 and there is still room for further improvement.

Information

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Citation

@misc{nguyenle2024novel3dbinaryindexed,
      title={Novel 3D Binary Indexed Tree for Volume Computation of 3D Reconstructed Models from Volumetric Data}, 
      author={Quoc-Bao Nguyen-Le and Tuan-Hy Le and Anh-Triet Do},
      year={2024},
      eprint={2412.10441},
      archivePrefix={arXiv},
      primaryClass={cs.GR},
      url={https://arxiv.org/abs/2412.10441}, 
}