Monocular 3D object detection has recently shown promising results, however there remain challenging problems. One of those is the lack of invariance to different camera intrinsic parameters, which can be observed across different 3D object datasets. Little effort has been made to exploit the combination of heterogeneous 3D object datasets. In contrast to general intuition, we show that more data does not automatically guarantee a better performance, but rather, methods need to have a degree of 'camera independence' in order to benefit from large and heterogeneous training data. In this paper we propose a category-level pose estimation method based on instance segmentation, using camera independent geometric reasoning to cope with the varying camera viewpoints and intrinsics of different datasets. Every pixel of an instance predicts the object dimensions, the 3D object reference points projected in 2D image space and, optionally, the local viewing angle. Camera intrinsics are only used outside of the learned network to lift the predicted 2D reference points to 3D. We surpass camera independent methods on the challenging KITTI3D benchmark and show the key benefits compared to camera dependent methods.