We introduce linear methods for model-based tracking of nonrigid 3D objects and for acquiring such models from video. 3D motions and flexions are calculated directly from image intensities without information-lossy intermediate results. Measurement uncertainty is quantified and fully propagated through the inverse model to yield posterior mean (PM) and/or mode (MAP) pose estimates. A Bayesian framework manages uncertainty, accommodates priors, and gives confidence measures. We obtain highly accurate and robust closed-form estimators by minimizing information loss from non-reversible (inner-product and least-squares) operations, and, when unavoidable, performing such operations with the appropriate error norm. For model acquisition, we show how to refine a crude or generic model to fit the video subject. We demonstrate with tracking, model refinement, and super-resolution texture lifting from low-quality low-resolution video.