  The identification of singular points or topological defects in discretized
vector fields occurs in diverse areas ranging from the polarization of the
cosmic microwave background to liquid crystals to fingerprint recognition and
bio-medical imaging. Due to their discrete nature, defects and their
topological charge cannot depend continuously on each single vector, but they
discontinuously change as soon as a vector changes by more than a threshold.
Considering this threshold of admissible change at the level of vectors, we
develop a robustness measure for discrete defect estimators. Here, we compare
different template paths for defect estimation in discretized vector or
orientation fields. Sampling prototypical vector field patterns around defects
shows that the robustness increases with the length of template path, but less
so in the presence of noise on the vectors. We therefore find an optimal
trade-off between resolution and robustness against noise for relatively small
templates, except for the "single pixel" defect analysis, which cannot exclude
zero robustness. The presented robustness measure paves the way for uncertainty
quantification of defects in discretized vector fields.
