This work proposes novel hyperparameter-free losses for single view 3D reconstruction with morphable models (3DMM). We dispense with the hyperparameters used in other works by exploiting geometry, so that the shape of the object and the camera pose are jointly optimized in a sole term expression. This simplification reduces the optimization time and its complexity. Moreover, we propose a novel implicit regularization technique based on random virtual projections that does not require additional 2D or 3D annotations. Our experiments suggest that minimizing a shape reprojection error together with the proposed implicit regularization is especially suitable for applications that require precise alignment between geometry and image spaces, such as augmented reality. We evaluate our losses on a large scale dataset with 3D ground truth and publish our implementations to facilitate reproducibility and public benchmarking in this field.