Wavelets, boundaries, and the spatial analysis of landscape pattern

Recent developments in remote sensing and geographical information systems make widely available data sets covering large extents with a variety of spatial resolutions, such as digital images and geographic databases, potentially interesting for ecological applications. Such regular lattice data consisting of several million observations are now frequently analyzed for mapping, monitoring, and interpreting landscapes from an ecological, pattern-sensitive perspective. This requires adaptive data description and interpretation, which usually comes in the form of partitioning the data, for example, by the application of boundary-detection and/or classification and segmentation. Such tasks can benefit from utilizing new statistical and image processing tools, including wavelets, because they can characterize global as well as local pattern. This paper briefly introduces the wavelet representation and links it with hierarchical spatial data structures (quadtrees) and extensively used statistical techniques (nested analysis of variance, geostatistics, spectral analysis). The wavelet transformation and its variants are extremely efficient in summarizing or hierarchically approximating very large data sets while focusing on interesting subsets of the studied landscape. The use of wavelets in spatial data analysis and their relevance in characterizing and partitioning landscapes is demonstrated using our own and commercial software (S+WAVELETS) by comparing this representation with other methods. Simulated examples and real data from a grassland field study in Saskatchewan and regional net primary productivity across Ontario derived from satellite images illustrate the methodology.