This paper presents ERODE, an efficient outlier detector with a quality similar to that of standard RANSAC but at a fraction of its computational cost. In contrast to RANSAC-based methods which follow a hypothesis-and-verify approach, ERODE employs instead the whole set of observations together with a robust kernel to perform robustified least-squares minimization. Our proposal has important practical applications among computer vision problems, which we demonstrate with stereovisual odometry experiments with both simulated and real data.