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.

中文翻译：

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一种利用单目相机逼近边界框检测算法中目标位置误差的新方法

许多自动驾驶汽车和先进的驾驶员辅助系统都配备了前置摄像头，可以使用基于深度学习的算法检测和跟踪物体。然而，单目相机的定位能力往往被忽视。在本文中，提出了一种新方法，用于估计检测到的对象的位置与其地面实况的像素级误差。当物体远离相机时，像素误差呈正态分布，沿着图像的垂直轴（y 像素）具有独特的分布。随着物体离得越远，像素误差似乎越小，而在相同的距离范围内，物体在相机的水平视图中具有相似的误差分布。距离越远，水平轴（x 像素）误差似乎越小。然而，沿恒定 y 像素行的 x 像素位置对误差分布没有影响。估计的 x 和 y 像素误差分布又可用于形成空间误差分布，以便在某个置信区间内找到检测到的对象的位置。然后使用相机变换矩阵将空间误差投影到世界坐标系上，以更真实地了解该误差的含义。结果表明，使用单目相机的位置估计会在物体周围产生椭圆误差分布，与 x 像素方向相比，y 像素方向的误差更大。这种误差分布对于融合来自多个距离检测传感器以及多车辆和多目标跟踪的信息非常重要。