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Updated: Jun 2, 2026
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Extracting Metrics for Three-dimensional Root Systems: Volume and Surface Analysis from In-soil X-ray Computed Tomography Data
Published on: April 26, 2016
Efficient computation of enclosed volume and surface area from the same triangulated surface representation
Ingela Nyström1, George J Grevera, Bruce E Hirsch
1Centre for Image Analysis, Uppsala University, Uppsala, Sweden. ingela@cb.uu.se
Summary
This study introduces a t-shell data structure for efficient and accurate volume and surface area computation of digital objects. It combines the strengths of digital and triangulated surfaces, improving measurements for real-world applications.
Area of Science:
- Computational geometry
- Medical imaging
- Computer graphics
Background:
- Digital surfaces offer efficient visualization and volume measurement but lack surface area accuracy.
- Triangulated surfaces provide accurate surface area but are less efficient for volume computation and visualization.
- A need exists for a method combining the advantages of both digital and triangulated surface representations.
Purpose of the Study:
- To develop an efficient method for computing the volume enclosed by triangulated surfaces.
- To introduce a novel data structure, the t-shell, for representing triangulated digital surfaces.
- To overcome the limitations of existing digital and triangulated surface representations.
Main Methods:
- Developed a t-shell data structure for triangulated digital surfaces.
- Created a lookup table for area and volume contributions based on Marching Cubes configurations.
- Implemented incremental computation of surface area and volume during shell scanning using the lookup table and triangle normal orientation.
Main Results:
- The t-shell data structure efficiently computes volume for triangulated surfaces, comparable to digital surface integration.
- Surface area measurements using the t-shell are more accurate than those from digital surfaces.
- Volume measurements using the t-shell closely approximate digital volume measurements and improve with decreasing voxel size.
Conclusions:
- The t-shell data structure effectively integrates the benefits of digital and triangulated surfaces for accurate surface area and efficient volume computation.
- This method offers a superior approach for volume and surface area measurement in applications involving digitized objects.
- Accuracy of measurements improves with higher resolution (smaller voxel size).
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