  Perception of obstacles remains a critical safety concern for autonomous
vehicles. Real-world collisions have shown that the autonomy faults leading to
fatal collisions originate from obstacle existence detection. Open source
autonomous driving implementations show a perception pipeline with complex
interdependent Deep Neural Networks. These networks are not fully verifiable,
making them unsuitable for safety-critical tasks.
  In this work, we present a safety verification of an existing LiDAR based
classical obstacle detection algorithm. We establish strict bounds on the
capabilities of this obstacle detection algorithm. Given safety standards, such
bounds allow for determining LiDAR sensor properties that would reliably
satisfy the standards. Such analysis has as yet been unattainable for neural
network based perception systems. We provide a rigorous analysis of the
obstacle detection system with empirical results based on real-world sensor
data.
