Geodesic Conformal Risk Control for Provably Safe Image Segmentation

Applying Conformal Risk Control (CRC) to image segmentation via standard pixel-wise thresholding often yields severely fragmented predictions under strict instance-level risk constraints. To address this, we propose Geodesic Conformal Risk Control (GeoCRC), a framework that ensures spatially coherent predictions while rigorously bounding the connected-component miss risk. GeoCRC leverages Isotonic Regression calibration to identify reliable seed regions and define traversal costs. Through multi-source geodesic propagation, it constructs a topologically well-behaved, nested family of regions parameterized by a geodesic radius, which is then calibrated using an instance-level miss loss. Theoretically, GeoCRC inherits the distribution-free marginal risk guarantees of standard CRC. Extensive experiments demonstrate that GeoCRC strictly satisfies user-specified risk constraints while drastically reducing spatial fragmentation and false-positive noise compared to baseline methods.