An improved, efficient method for mapping world points from an environment (e.g., points generated by a LIDAR sensor of an autonomous vehicle) to locations (e.g., pixels) within rolling-shutter images taken of the environment is provided. This improved method allows for accurate localization of the world point in a rolling-shutter image via an iterative process that converges in very few iterations. The method poses the localization process as an iterative process for determining the time, within the rolling-shutter exposure period of the image, at which the world point was imaged by the camera. The method reduces the number of times the world point is projected into the normalized space of the camera image, often converging in three or fewer iterations.