The ability of autonomous vehicles (AVs) to detect three-dimensional objects is crucial for motion planning, object tracking and safe driving. This task is especially challenging for systems using only monocular cameras, for which depth estimation presents special difficulties. In this paper, we discuss the subsystem of 3D object detection in bird's-eye-view (BEV) for a single camera in an AV system. The subsystem consists of two parts. First, it estimates the contour of the object's projection polygon in BEV based on 2D detection and drivable area segmentation (a planar ground model is used). Second, it simplifies the object's projection by fitting the obtained polygon to a rotated bounding box. For this part we propose a new L-shape model-based fitting algorithm. It assumes that the vertices of the input polygon belong to two adjacent sides of the fitted bounding box. We compared this algorithm with a naive approach which minimizes the bounding box's area and with adaptations of algorithms from a paper solving a similar problem with LiDAR point clouds. The L-shape algorithm outperformed the alternatives.