Classical morphological image processing, where the same structuring element is used to process the whole image, has its limitations. Consequently, adaptive mathematical morphology is attracting more and more attention.So far, however, the use of non-flat adaptive structuring functions is very limited. This work presents a method for defining quadratic structuring functions from the well known local structure tensor, building on previous work for flat adaptive morphology. The result is a novel approach to adaptive mathematical morphology, suitable for enhancement and linking of directional features in images. Moreover, the presented strategy can be quite efficiently implemented and is easy to use as it relies on just two user-set parameters which are directly related to image measures.