Recent years have seen the emergence of very effective ConvNet-based object detectors that have reconfigured the computer vision landscape. As a consequence, new approaches that propose object-based reasoning to solve traditional problems, such as camera pose estimation, have appeared. In particular, these methods have shown that modelling 3D objects by ellipsoids and 2D detections by ellipses offers a convenient manner to link 2D and 3D data. Following that promising direction, we propose here a novel object-based pose estimation algorithm that does not require any sensor but a RGB camera. Our method operates from at least two object detections, and is based on a new paradigm that enables to decrease the Degrees of Freedom (DoF) of the pose estimation problem from six to three, while two simplifying yet realistic assumptions reduce the remaining DoF to only one. Exhaustive search is performed over the unique unknown parameter to recover the full camera pose. Robust algorithms designed to deal with any number of objects as well as a refinement step are introduced. Effectiveness of the method has been assessed on the challenging T-LESS and Freiburg datasets.