Surface Volume Estimation of Digitized Hyperplanes Using Weighted Local Configurations

  • Joakim Lindblad
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3429)


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.


surface volume estimation marching cubes digital hyperplanes 4D cell tiling 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Joakim Lindblad
    • 1
  1. 1.Centre for Image AnalysisUppsala UniversityUppsalaSweden

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