  We present a new certification method for image and point cloud segmentation
based on randomized smoothing. The method leverages a novel scalable algorithm
for prediction and certification that correctly accounts for multiple testing,
necessary for ensuring statistical guarantees. The key to our approach is
reliance on established multiple-testing correction mechanisms as well as the
ability to abstain from classifying single pixels or points while still
robustly segmenting the overall input. Our experimental evaluation on synthetic
data and challenging datasets, such as Pascal Context, Cityscapes, and
ShapeNet, shows that our algorithm can achieve, for the first time, competitive
accuracy and certification guarantees on real-world segmentation tasks. We
provide an implementation at https://github.com/eth-sri/segmentation-smoothing.
