Lane estimation for autonomous driving can beformulated as a curve estimation problem, where local sensordata provides partial and noisy observations of spatial curves.The number of curves to estimate may be initially unknown andmany of the observations may be outliers or false detections(due e.g. to to tree shadows or lens flare). The challenges lie indetecting lanes when and where they exist, and updating laneestimates as new observations are made.This paper describes an efficient probabilistic lane estimationalgorithm based on a novel curve representation. The keyadvance is a principled mechanism to describe many similarcurves as variations of a single basis curve. Locally observed roadpaint and curb features are then fused to detect and estimateall nearby travel lanes. The system handles roads with complexgeometries and makes no assumptions about the position andorientation of the vehicle with respect to the roadway.We evaluate our algorithm with a ground truth datasetcontaining manually-labeled, fine-grained lane geometries forvehicle travel in two large and diverse datasets that include morethan 300,000 images and 44km of roadway. The results illustratethe capabilities of our algorithm for robust lane estimation in theface of challenging conditions and unknown roadways.