For safe operation, a robot must be able to avoid collisions in uncertain environments. Existing approaches for motion planning with uncertainties often make conservative assumptions about Gaussianity and the obstacle geometry. While visual perception can deliver a more accurate representation of the environment, its use for safe motion planning is limited by the inherent miscalibration of neural networks and the challenge of obtaining adequate datasets. In order to address these imitations, we propose to employ ensembles of deep semantic segmentation networks trained with systematically augmented datasets to ensure reliable probabilistic occupancy information. For avoiding conservatism during motion planning, we directly employ the probabilistic perception via a scenario-based path planning approach. A velocity scheduling scheme is applied to the path to ensure a safe motion despite tracking inaccuracies. We demonstrate the effectiveness of the systematic data augmentation in combination with deep ensembles and the proposed scenario-based planning approach in comparisons to state-of-the-art methods and validate our framework in an experiment involving a human hand.