  Regionalization is the task of dividing up a landscape into homogeneous
patches with similar properties. Although this task has a wide range of
applications, it has two notable challenges. First, it is assumed that the
resulting regions are both homogeneous and spatially contiguous. Second, it is
well-recognized that landscapes are hierarchical such that fine-scale regions
are nested wholly within broader-scale regions. To address these two
challenges, first, we develop a spatially constrained spectral clustering
framework for region delineation that incorporates the tradeoff between region
homogeneity and spatial contiguity. The framework uses a flexible, truncated
exponential kernel to represent the spatial contiguity constraints, which is
integrated with the landscape feature similarity matrix for region delineation.
To address the second challenge, we extend the framework to create fine-scale
regions that are nested within broader-scaled regions using a greedy, recursive
bisection approach. We present a case study of a terrestrial ecology data set
in the United States that compares the proposed framework with several baseline
methods for regionalization. Experimental results suggest that the proposed
framework for regionalization outperforms the baseline methods, especially in
terms of balancing region contiguity and homogeneity, as well as creating
regions of more similar size, which is often a desired trait of regions.
