A robustness measure for singular point and index estimation in discretized orientation and vector fields

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