Perception-based neural network controllers are increasingly used in autonomous systems that rely on visual inputs to operate in the real world. Ensuring the safety of such systems under uncertainty is challenging. Existing verification techniques typically focus on Lp-bounded perturbations in the pixel space, which fails to capture the low-dimensional structure of many real-world effects. In this work, we introduce a novel verification framework for perception-based controllers that can generate outer-approximations of reachable sets through explicitly modeling uncertain observations with geometric perturbations. Our approach constructs a boundable mapping from states to images, enabling the use of state-based verification tools while accounting for uncertainty in perception. We provide theoretical guarantees on the soundness of our method and demonstrate its effectiveness across benchmark control environments. This work provides a principled framework for certifying the safety of perception-driven control systems under realistic visual perturbations.
