Semantic segmentation is among the most promising tools for the perception of safety-critical applications such as automated driving. Deep neural networks have defined the state-of-the-art in this task over the past decade. However, some of these models still often suffer from shortcomings related to their reliability. Namely, they (i) provide unsatisfactory information on the quality and reliability of their prediction and (ii) give rise to incorrect predictions in open world scenarios because they are trained on a predefined set of semantic classes. Objects outside this predefined semantic space are usually called out-of-distribution (OoD) objects. Recently, we have proposed a pixel-wise, gradient-based uncertainty approach [29] to address both of these problems. We have presented an efficient method to calculate learning gradients based on auxiliary labels during inference and compared our approach with other methods that address either or both modes of shortcoming of the segmentation model. In this extended version, we emphasize a detailed analysis of hyperparameters of our method, as well as gradient depth used to compute uncertainty scores. Our numerical experiments show the ability of the gradient uncertainty to estimate the prediction quality and detect OoD objects at negligible computational overhead.