A traditional strategy for analysing `spatial pattern' is based on
measuring certain distances in the image. Distances in spatial
processes may be regarded as waiting times, and the methods of
survival analysis can be applied to them.
`Edge effects' in spatial statistics are difficulties caused by our
inability to observe a spatial process outside the sampling region.
There is a close analogy between edge effects and the censoring of
survival times. This motivates a censored data approach to the
estimation of various distance distributions in spatial point
processes and random sets. Analogues of the Kaplan-Meier estimator
can be constructed for a continuum of observations.
Survival analysis concepts, such as the hazard rate, have a useful
interpretation in spatial statistics. So also does the `J function',
the ratio of the survival functions of two distance distributions for
the process. We give examples of applications to ecological and
geological data.
A weakness of traditional methods has been their restriction to spatially
homogeneous patterns. The techniques of survival analysis allow us to
develop practical techniques for model-based survival analysis of
spatial datasets, including models of spatially-varying texture, and
of the dependence of texture on covariates. Applications include
spatial epidemiology and image understanding.