Analyzing point patterns with linear structures has recently been of interest in e.g. neuroscience and geography. To detect anisotropy in such cases, we introduce a functional summary statistic called the cylindrical $K$-function. A class of models for anisotropic spatial point processes, called Poisson line cluster point processes, is also introduced. Parameter estimation based on moment methods or Bayesian inference for this model is discussed when the underlying Poisson line process and the cluster memberships are treated as hidden processes. To illustrate the methodologies, we analyze two and three-dimensional real point pattern data sets.

Keywords: anisotropy, Bayesian inference, directional $K$-function, minicolumn hypothesis, Poisson line process, three-dimensional point pattern analysis.