Partitions of unity play an important rôle as amplitude-preserving windows for nonstationary type filters. Multidimensional partitions of unity can be constructed by combining one-dimensional partitions as factors. By grouping neighbouring windows, arbitrary nonuniform partitions of unity can be formed, which can greatly reduce computation times.
The Gaussian function displays a host of desirable properties, making it particularly well suited for use as an "atom" in multidimensional partitions of unity.
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