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We present an approach to analyze mixing in flow fields by extracting vortex and strain features as extremal structures of derived scalar quantities that satisfy a duality property: They indicate vortical as well as high-strain (saddle-type) regions. Specifically, we consider the Okubo-Weiss criterion and the recently introduced MZ criterion. Although the first is derived from a purely Eulerian framework, the latter is based on Lagrangian considerations. In both cases, high values indicate vortex activity, whereas low values indicate regions of high strain. By considering the extremal features of those quantities, we define the notions of a vortex and a strain skeleton in a hierarchical manner: The collection of maximal zero-dimensional, one-dimensional, and 2D structures assemble the vortex skeleton; the minimal structures identify the strain skeleton. We extract those features using scalar field topology and apply our method to a number of steady and unsteady 3D flow fields.