A Fast Method to Calculate the Volumetric Divergence Metric for Evaluating the Accuracy of the Extracted Isosurface
Author: 
Cuilan WangAuthors Info & Claims
Cuilan WangAuthors Info & ClaimsArticle No.: 27, Pages 1 - 19
Abstract
In this paper, a new method is introduced to calculate the volumetric divergence (VD) metric, which is defined as the volume between the extracted isosurface mesh and the isosurface given by trilinear interpolation. This metric can be used to evaluate the accuracy of the extracted isosurface mesh against the trilinear interpolation isosurface. In the new method, each cube in a scalar volumetric dataset is sliced, the cross-sectional area of the VD region on each slice is calculated analytically, and then all the cross-sectional areas are integrated numerically to generate the volume of the VD region (i.e., the VD metric). The more the cube is sliced, the more accurate the metric becomes. The existing method that calculates the VD metric is a pure numerical method. Its execution time is long when the metric accuracy is high. The new method is 15-70 times faster than the existing method when both methods achieve the same level of accuracy.
References
[1]
M. Bailey. 2000. Volume Graphics. Springer, London, Chapter Manufacturing Isovolumes, 79--93.
[2]
K. Brodlie and J. Wood. 2001. Recent Advances in Volume Visualization. Computer Graphics Forum 20, 2 (2001), 125--148.
[3]
E. Chernyaev. 1995. Marching Cubes 33: Construction of Topologically Correct Isosurfaces. Technical Report Technical Report CERN CN 95-17. CERN.
[4]
P. Cignoni, F. Ganovelli, C. Montani, and R. Scopigno. 2000. Reconstruction of Topologically Correct and Adaptive Trilinear Isosurfaces. Computers 8 Graphics 24, 3 (2000), 399--418.
[5]
P. Cignoni, C. Rocchini, and R. Scopigno. 1998. Metro: Measuring Error on Simplified Surfaces. Comp. Graphics Forum 17, 2 (1998), 167--174.
[6]
H. Cline, W. Lorensen, and S. Ludke. 1988. Two algorithms for the three-dimensional reconstruction of tomograms. Medical Physics 15, 3 (1988), 320--327.
[7]
B. Duffy, H. Carr, and T. Möller. 2013. Integrating isosurface statistics and histograms. IEEE Trans. on Visualization and Comp. Graphics 19, 2 (2013), 263--277.
[8]
M. Garland and P. Heckbert. 1997. Surface Simplification using Quadric Error Metrics. In Comp. Graphics (Proc., SIGGRAPH 97), Vol. 31. 209--216.
[9]
B. Hamann, I. Trotts, and G. Farin. 1997. On Approximating Contours of the Piecewise Trilinear Interpolant using Triangular Rational-quadratic Bezier Patches. IEEE Trans. on Visualization and Comp. Graphics 3, 3 (1997), 215--227.
[10]
M. Khoury and R. Wenger. 2010. On the fractal dimension of isosurfaces. IEEE Trans. on Visualization and Comp. Graphics 16, 6 (2010), 1198--1205.
[11]
R. Klein, G. Liebich, and W. Straßer. 1996. Mesh Reduction with Error Control. In Visualization '96. San Francisco, 311--318.
[12]
A. Lopes and K. Brodlie. 2003. Improving the Robustness and Accuracy of the Marching Cubes Algorithm for Isosurfacing. IEEE Trans. on Visualization and Comp. Graphics 9, 1 (2003), 16--29.
[13]
B. Natarajan. 1994. On Generating Topologically Consistent Isosurfaces from Uniform Samples. The Visual Computer 11 (1994), 52--62.
[14]
T. Newman and H. Yi. 2006. A Survey of the Marching Cubes Algorithm. Computers 8 Graphics 30, 5 (2006), 854--879.
[15]
G. Nielson. 2003. On Marching Cubes. IEEE Trans. on Visualization and Comp. Graphics 9, 3 (2003), 283--297.
[16]
G. Treece, R. Prager, and A. Gee. 1999. Regularised Marching Tetrahedra: Improved Isosurface Extraction. Computers 8 Graphics 23, 4 (1999), 583--598.
[17]
C. Wang and S. Lai. 2016. Adaptive Isosurface Reconstruction Using a Volumetric-Divergence-Based Metric. In Proceedings of 12th International Symposium on Visual Computing (ISVC '16). Las Vegas, NV, USA, 367--378.
[18]
C. Wang and T. Newman. 2014. New Metric for Evaluating the Accuracy of Marching Isosurfacing Algorithms. In Proceedings of the 2014 ACM Southeast Regional Conference. New York, 22:1--22:6.
[19]
C. Wang, T. Newman, and J. Lee. 2008. On Accuracy of Marching Isosurfacing Methods. In Proceedings of the Eurographics/IEEE VGTC Workshop on Volume Graphics '08. Los Angeles, 49--56.
[20]
R. Wenger. 2013. Isosurfaces: geometry, topology, and algorithms. CRC Press.
Index Terms
- A Fast Method to Calculate the Volumetric Divergence Metric for Evaluating the Accuracy of the Extracted Isosurface
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Published: 24 August 2018
Published in PACMCGIT Volume 1, Issue 2
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