id: 02205022
dt: a
an: 02205022
au: Lindblad, Joakim
ti: Surface volume estimation of digitized hyperplanes using weighted local
    configurations.
so: Andres, Eric (ed.) et al., Discrete geometry for computer imagery. 12th
    international conference, DGCI 2005, Poitiers, France, April 13‒15,
    2005. Proceedings. Berlin: Springer (ISBN 3-540-25513-3/pbk). Lecture
    Notes in Computer Science 3429, 252-262 (2005).
py: 2005
pu: Berlin: Springer
la: EN
cc: 
ut: surface volume estimation; marching cubes; digital hyperplanes; 4D; cell
    tiling
ci: 
li: doi:10.1007/b135490
ab: Summary: 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 $2 \times 2 \times 2 \times 2$ 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.
rv: