Marching cubes: A high resolution 3D surface construction algorithm
SIGGRAPH '87 Proceedings of the 14th annual conference on Computer graphics and interactive techniques
Length estimators for digitized contours
Computer Vision, Graphics, and Image Processing
Design of Perimeter Estimators for Digitized Planar Shapes
IEEE Transactions on Pattern Analysis and Machine Intelligence
Random number generation and quasi-Monte Carlo methods
Random number generation and quasi-Monte Carlo methods
On generating topologically consistent isosurfaces from uniform samples
The Visual Computer: International Journal of Computer Graphics
The quickhull algorithm for convex hulls
ACM Transactions on Mathematical Software (TOMS)
Numerical Recipes in C: The Art of Scientific Computing
Numerical Recipes in C: The Art of Scientific Computing
Digital Planar Segment Based Polyhedrization for Surface Area Estimation
IWVF-4 Proceedings of the 4th International Workshop on Visual Form
Ray Tracing Point Sampled Geometry
Proceedings of the Eurographics Workshop on Rendering Techniques 2000
Fast and Robust Smallest Enclosing Balls
ESA '99 Proceedings of the 7th Annual European Symposium on Algorithms
Ray Tracing Point Set Surfaces
SMI '03 Proceedings of the Shape Modeling International 2003
Digital Geometry: Geometric Methods for Digital Picture Analysis
Digital Geometry: Geometric Methods for Digital Picture Analysis
Robust repair of polygonal models
ACM SIGGRAPH 2004 Papers
Computing a family of skeletons of volumetric models for shape description
Computer-Aided Design
A quasi-Monte Carlo method for computing areas of point-sampled surfaces
Computer-Aided Design
Estimation of surface area and surface area measure of three-dimensional sets from digitizations
Image and Vision Computing
Surface area estimation of digitized 3D objects using weighted local configurations
Image and Vision Computing
Measurements of digitized objects with fuzzy borders in 2D and 3D
Image and Vision Computing
Multigrid convergence and surface area estimation
Proceedings of the 11th international conference on Theoretical foundations of computer vision
A comparison of property estimators in stereology and digital geometry
IWCIA'04 Proceedings of the 10th international conference on Combinatorial Image Analysis
Measuring intrinsic volumes in digital 3d images
DGCI'06 Proceedings of the 13th international conference on Discrete Geometry for Computer Imagery
Surface volume estimation of digitized hyperplanes using weighted local configurations
DGCI'05 Proceedings of the 12th international conference on Discrete Geometry for Computer Imagery
IEEE Transactions on Image Processing
Robust shape normalization of 3D articulated volumetric models
Computer-Aided Design
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A novel and efficient quasi-Monte Carlo method for estimating the surface area of digitized 3D objects in the volumetric representation is presented. It operates directly on the original digitized objects without any surface reconstruction procedure. Based on the Cauchy-Crofton formula from integral geometry, the method estimates the surface area of a volumetric object by counting the number of intersection points between the object's boundary surface and a set of uniformly distributed lines generated with low-discrepancy sequences. Using a clustering technique, we also propose an effective algorithm for computing the intersection of a line with the boundary surface of volumetric objects. A number of digitized objects are used to evaluate the performance of the new method for surface area measurement.