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3D object detection serves as a crucial basis of visual perception, motion prediction, and planning for automated driving. To apply an algorithm for this purpose, the detection of all types of road users in real-time is an essential condition. In this paper, we propose an approach that projects the 3D points of image-based bounding box proposals into so-called grid map patches. These patches are used to estimate the exact dimensions of the 3D box with the help of a lightweight CNN. The complete proposed processing chain is parallelized and implemented on a GPU. This makes our approach the fastest stereo-based 3D object detector on the KITTI benchmark while still achieving results that are within the range of the best image-based algorithms.