Detection and tracking of vehicles captured by traffic surveillance cameras is a key component of intelligent traffic systems. In this paper a novel method of detecting 3D bounding boxes of vehicles is presented. Using the known geometry of the surveilled scene, we propose an algorithm to construct a perspective transformation. The transformation enables us to simplify the problem of detecting 3D bounding boxes to detecting 2D bounding boxes with one additional parameter. We can therefore utilize modified 2D object detectors based on deep convolutional networks to detect 3D bounding boxes of vehicles. Known 3D bounding boxes of vehicles can be utilized to improve results on tasks such as fine-grained vehicle classification or vehicle re-identification. We test the accuracy of our detector by comparing the accuracy of speed measurement on the BrnoCompSpeed dataset with the existing state of the art method. Our method decreases the mean error in speed measurement by 22 % (1.10 km/h to 0.86 km/h) and the median error in speed measurement by 33 % (0.97 km/h to 0.65 km/h mean), while also increasing the recall (83.3 % to 89.3 %).