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
Fast surface tracking in three-dimensional binary images
Computer Vision, Graphics, and Image Processing
Design of Perimeter Estimators for Digitized Planar Shapes
IEEE Transactions on Pattern Analysis and Machine Intelligence
Multigrid Convergence of Geometric Features
Digital and Image Geometry, Advanced Lectures [based on a winter school held at Dagstuhl Castle, Germany in December 2000]
Weighted Distance Transforms for Images Using Elongated Voxel Grids
DGCI '02 Proceedings of the 10th International Conference on Discrete Geometry for Computer Imagery
A Comparative Evaluation of Length Estimators
ICPR '02 Proceedings of the 16 th International Conference on Pattern Recognition (ICPR'02) Volume 4 - Volume 4
Multigrid convergence and surface area estimation
Proceedings of the 11th international conference on Theoretical foundations of computer vision
Simplified patterns for extracting the isosurfaces of solid objects
Image and Vision Computing
Estimation of surface area and surface area measure of three-dimensional sets from digitizations
Image and Vision Computing
About the frequencies of some patterns in digital planes application to area estimators
DGCI'08 Proceedings of the 14th IAPR international conference on Discrete geometry for computer imagery
Surface area estimation of digitized 3D objects using quasi-Monte Carlo methods
Pattern Recognition
A graph-based framework for sub-pixel image segmentation
Theoretical Computer Science
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
On Multigrid Convergence of Local Algorithms for Intrinsic Volumes
Journal of Mathematical Imaging and Vision
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We present a method for estimating surface area of three-dimensional objects in discrete binary images. A surface area weight is assigned to each 2x2x2 configuration of voxels. The total surface area of a digital object is given by a summation of the local area contributions. Optimal area weights are derived in order to provide an unbiased estimate with minimum variance for randomly oriented digitized planar surfaces. Due to co-appearance of certain voxel combinations, the optimal solution is not uniquely defined for planar surfaces. A Monte Carlo-based optimization of the estimator performance on the distribution of digitized balls of increasing radii is performed in order to uniquely determine the optimal surface area weights. The method is further evaluated on various objects in a range of sizes. A significant reduction of the error for small objects is observed. The algorithm is appealingly simple; the use of only a small local neighborhood enables efficient implementations in hardware and/or in parallel architectures.