
354 Spatial Point Patterns: Methodology and Applications with R
(9.64) are g ood approxima tions when the pixels are small. Examples include distance transforms
(e.g., Z(u) is the distance from u to the nearest geolo gical fault), spatial coordinates, and kern el-
smoothed g eochemical a ssay values. In the le ast optimistic case, Z is a discontinuous function, such
as the indicator of a very irregular spatial do main such as a rock outcrop. The approximations ( 9.59)
and (9.62)–(9.64) can then give rise to considerable bias, even for quite small pixel sizes [34].
Replacing pixel co unts by pr esence-absence indicators causes a loss of statistical ...