A Novel Method for Approximating Object Location Error in Bounding Box Detection Algorithms Using a Monocular Camera

Many autonomous vehicles and advanced driver-assistance systems are equipped with front-facing cameras that detect and track objects using deep-learning-based algorithms. However, the localization capability of monocular cameras is often overlooked. In this paper, a novel method for estimating the pixel-wise error in a detected object's location versus its ground truth is proposed. As the object moves away from the camera, the pixel errors are shown to be normally distributed with unique spreads along the image's vertical axis (y-pixel). The pixel error appears to be smaller as objects get farther away, while at the same distance range, objects have similar error distribution across the camera's horizontal view. The horizontal axis (x-pixel) error appears to be smaller while the distance moves further away. However, the x-pixel location along a constant y-pixel row has no impact on the error distribution. The estimated x and y-pixel error distributions can in turn be used to form a spatial error distribution for finding the location of a detected object within a certain confidence interval. The spatial errors are then projected onto the world coordinate system using a camera transformation matrix to give a more realistic sense of what this error means. The results show that location estimation using monocular cameras generates an elliptical error distribution around the object with a larger error in the y-pixel direction compared to the x-pixel direction. This error distribution can be important to fuse information from multiple range-detecting sensors as well as multi-vehicle and multi-object tracking. The uncertainty characterization for position measurement, as demonstrated in this paper is an essential element of tracking and, is sensor and algorithm dependent.