Marching cubes: A high resolution 3D surface construction algorithm
SIGGRAPH '87 Proceedings of the 14th annual conference on Computer graphics and interactive techniques
Skeletons in N dimensions using shape primitives
Pattern Recognition Letters
Digital Planar Segment Based Polyhedrization for Surface Area Estimation
IWVF-4 Proceedings of the 4th International Workshop on Visual Form
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 digital distance transforms in four dimensions
Discrete Applied Mathematics
A Comparative Evaluation of Length Estimators
ICPR '02 Proceedings of the 16 th International Conference on Pattern Recognition (ICPR'02) Volume 4 - Volume 4
Isosurface Construction in Any Dimension Using Convex Hulls
IEEE Transactions on Visualization and Computer Graphics
Surface area estimation of digitized 3D objects using weighted local configurations
Image and Vision Computing
Multigrid convergence and surface area estimation
Proceedings of the 11th international conference on Theoretical foundations of computer vision
Surface area estimation of digitized 3D objects using quasi-Monte Carlo methods
Pattern Recognition
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We present a method for estimating the surface volume of four-dimensional objects in discrete binary images. A surface volume weight is assigned to each 2 × 2 × 2 × 2 configuration of image elements. The total surface volume of a digital 4D object is given by a summation of the local volume contributions. Optimal volume weights are derived in order to provide an unbiased estimate with minimal variance for randomly oriented digitized planar hypersurfaces. Only 14 out of 64 possible boundary configurations appear on planar hypersurfaces. We use a marching hypercubes tetrahedrization to assign surface volume weights to the non-planar cases. The correctness of the method is verified on four-dimensional balls and cubes digitized in different sizes. The algorithm is appealingly simple; the use of only a local neighbourhood enables efficient implementations in hardware and/or in parallel architectures.