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Spatial Point Patterns
book

Spatial Point Patterns

by Adrian Baddeley, Ege Rubak, Rolf Turner
November 2015
Intermediate to advanced content levelIntermediate to advanced
828 pages
33h 11m
English
Chapman and Hall/CRC
Content preview from Spatial Point Patterns
Higher-Dimensional Spaces and Marks 657
When comparing the estimate
b
F(r) with the benchmark value for a Poisson process, w e need to
be aware of a digital artefact. The ‘sphere’ of radius r in the distance tra nsform tha t is, the set of
voxels that lie at most r units from a given voxel according to the distance transform algorithm is
a p olyhedron of fixed shape, even for large values of r. For the spatstat algorithm the volume v(r )
of the d igital sphere o f radius r is roughly 0.78 times the volume of the euc lidean sphere, (4
π
/3)r
3
.
This is a considerable deficit, so the benchmark value sho uld really be calculated b y replacing the
ideal
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Publisher Resources

ISBN: 9781482210217