  Many state-of-the-art delineation methods rely on supervised machine learning
algorithms. As a result, they require manually annotated training data, which
is tedious to obtain. Furthermore, even minor classification errors may
significantly affect the topology of the final result. In this paper we propose
a generic approach to addressing both of these problems by taking into account
the influence of a potential misclassification on the resulting delineation. In
an Active Learning context, we identify parts of linear structures that should
be annotated first in order to train a classifier effectively. In a
proofreading context, we similarly find regions of the resulting reconstruction
that should be verified in priority to obtain a nearly-perfect result. In both
cases, by focusing the attention of the human expert on potential
classification mistakes which are the most critical parts of the delineation,
we reduce the amount of required supervision. We demonstrate the effectiveness
of our approach on microscopy images depicting blood vessels and neurons.
