Robust relational trees by scale-space filtering

A relational tree (RT) is a signal representation used to discriminate between multidimensional signals with arbitrary nonlinear monotonic distortion. The use of RTs is limited by noise. Scale-space filtering takes advantage of the inherently scale-like properties of an RT to provide a more robust signal representation across distortions. Some methods and properties of Gaussian scale-space filtering of RTs are examined. Scale trees (STs) and conventionally filtered (fixed-scale) RTs have been shown to be subsets of this process. Since the effect of scale-space filtering is to move segmentation uncertainty toward the leaves of the tree, other operations performed in the tree domain, such as filtering, can be optimized as well.<>