Alternative tilings for improved surface area estimates by local counting algorithms

In this paper, we first review local counting methods for perimeter estimat ion of piecewise smooth binary figures on square, hexagonal, and triangular grids. We verify that better perimeter estimates, using local counting alg orithms, can be obtained using hexagonal or triangular grids. We then compa re surface area estimates using local counting techniques for binary three- dimensional volumes under the three semi-regular polyhedral tilings: the cu bic, truncated octahedral, and rhombic dodecahedral tilings. It is shown th at for surfaces of random orientation with a uniform distribution, the expe cted error of surface area estimates is smaller for the truncated octahedra l and rhombic dodecahedral tilings than for the standard cubic or rectangul ar prism tilings of space. Additional properties of these tessellations are reviewed and potential applications of better surface area estimates are d iscussed. (C) 1999 Academic Press.