Frames, the Loewner order and eigendecomposition for morphological operators on tensor fields

Rotation invariance is an important property for operators on tensor fields, but up to now, most methods for morphology on tensor fields had to either sacrifice rotation invariance, or do without the foundation of mathematical morphology: a lattice structure. Recently, we proposed a framework for rotation-invariant mathematical morphology on tensor fields that does use a lattice structure. In addition, this framework can be derived systematically from very basic principles. Here we show how older methods for morphology on tensor fields can be interpreted within our framework. On the one hand this improves the theoretical underpinnings of these older methods, and on the other this opens up possibilities for improving the performance of our method. We discuss commonalities and differences of our method and two methods developed by Burgeth et al.