Robustness of topological defects in discrete domains

Topological defects are singular points in vector fields, important applications ranging from fingerprint detection to liquid crystals biomedical imaging. In discretized topological and their charge identified by finite differences or finite-step paths around the tentative defect. As is (half) integer, it cannot depend continuously on each input a discrete domain. Instead, switches discontinuously when vectors change beyond certain amount, making analysis of error prone noisy data. We improve existing methods for identification proposing robustness measure (i) location defect, (ii) existence total within given area, (iii) annihilation defect pair, (iv) formation pair. Based proposed measure, we show that domains can be with optimal trade-off between localization precision robustness. The enables uncertainty quantification nematic fields (orientation fields) polar (vector fields).