Reliable, efficient shared autonomy requires balancing human operation and robot automation on complex tasks, such as dexterous manipulation. Adding to the difficulty of shared autonomy is a robot's limited ability to perceive the 6 degree-of-freedom pose of objects, which is essential to perform manipulations those objects afforded. Inspired by Monte Carlo Localization, we propose a generative human-in-the-loop approach to estimating object pose. We characterize the performance of our mixed-initiative 3D registration approach using 2D pointing devices via a user study. Seeking an analog for Fitts's Law for 3D registration, we introduce a new evaluation framework that takes the entire registration process into account instead of only the outcome. When combined with estimates of registration confidence, we posit that mixed-initiative registration will reduce the human workload while maintaining or even improving final pose estimation accuracy.