Camera or object pose calculation is described, for example, to relocalize a mobile camera (such as on a smart phone) in a known environment or to compute the pose of an object moving relative to a fixed camera. The pose information is useful for robotics, augmented reality, navigation and other applications. In various embodiments where camera pose is calculated, a trained machine learning system associates image elements from an image of a scene, with points in the scene's 3D world coordinate frame. In examples where the camera is fixed and the pose of an object is to be calculated, the trained machine learning system associates image elements from an image of the object with points in an object coordinate frame. In examples, the image elements may be noisy and incomplete and a pose inference engine calculates an accurate estimate of the pose.