A method for approximating missing data in spatial patterns

Abstract

Spatial patterns such as historical landscape records or digital photographs are often plagued by large numbers of missing or otherwise corrupted data points or pixels that cannot be easily reproduced. A method is described in which a simple stochastic cellular automaton is used to produce fictitious fractal data at arbitrarily many spatial points such that the resulting pattern mimics the morphological features of the actual pattern. The method is simple to implement, preserves all the existing data, has no adjustable parameters, and can be used to fill in regions of arbitrary size and shape, even outside the region for which data are available. Furthermore, it reduces to more conventional interpolation methods when only a few isolated data points are missing.