Visual system identification: learning physical parameters and latent spaces from pixels

In this thesis, we develop machine learning systems that are able to leverage the knowledge of equations of motion (scene-specific or scene-agnostic) to perform object discovery, physical parameter estimation, position and velocity estimation, camera pose estimation, and learn structured latent spaces that satisfy physical dynamics rules. These systems are unsupervised, learning from unlabelled videos, and use as inductive biases the general equations of motion followed by objects of interest in the scene. This is an important task as in many complex real world environments ground-truth states are not available, although there is physical knowledge of the underlying system. Our goals with this approach, i.e. integration of physics knowledge with unsupervised learning models, are to improve vision-based prediction, enable new forms of control, increase data-efficiency and provide model interpretability, all of which are key areas of interest in machine learning. With the above goals in mind, we start by asking the following question: given a scene in which the objects’ motions are known up to some physical parameters (e.g. a ball bouncing off the floor with unknown restitution coefficient), how do we build a model that uses such knowledge to discover the objects in the scene and estimate these physical parameters? Our first model, PAIG (Physics-as-Inverse-Graphics), approaches this problem from a vision-as-inverse-graphics perspective, describing the visual scene as a composition of objects defined by their location and appearance, which are rendered onto the frame in a graphics manner. This is a known approach in the unsupervised learning literature, where the fundamental problem then becomes that of derendering, that is, inferring and discovering these locations and appearances for each object. In PAIG we introduce a key rendering component, the Coordinate-Consistent Decoder, which enables the integration of the known equations of motion with an inverse-graphics autoencoder architecture (trainable end-to-end), to perform simultaneous object discovery and physical parameter estimation. Although trained on simple simulated 2D scenes, we show that knowledge of the physical equations of motion of the objects in the scene can be used to greatly improve future prediction and provide physical scene interpretability. Our second model, V-SysId, tackles the limitations shown by the PAIG architecture, namely the training difficulty, the restriction to simulated 2D scenes, and the need for noiseless scenes without distractors. Here, we approach the problem from rst principles by asking the question: are neural networks a necessary component to solve this problem? Can we use simpler ideas from classical computer vision instead? With V- SysId, we approach the problem of object discovery and physical parameter estimation from a keypoint extraction, tracking and selection perspective, composed of 3 separate stages: proposal keypoint extraction and tracking, 3D equation tting and camera pose estimation from 2D trajectories, and entropy-based trajectory selection. Since all the stages use lightweight algorithms and optimisers, V-SysId is able to perform joint object discovery, physical parameter and camera pose estimation from even a single video, drastically improving data-efficiency. Additionally, due to the fact that it does not use a rendering/derendering approach, it can be used in real 3D scenes with many distractor objects. We show that this approach enables a number of interest applications, such as vision-based robot end-effector localisation and remote breath rate measurement. Finally, we move into the area of structured recurrent variational models from vision, where we are motivated by the following observation: in existing models, applying a force in the direction from a start point and an end point (in latent space), does not result in a movement from the start point towards the end point, even on the simplest unconstrained environments. This means that the latent space learned by these models does not follow Newton’s law, where the acceleration vector has the same direction as the force vector (in point-mass systems), and prevents the use of PID controllers, which are the simplest and most well understood type of controller. We solve this problem by building inductive biases from Newtonian physics into the latent variable model, which we call NewtonianVAE. Crucially, Newtonian correctness in the latent space brings about the ability to perform proportional (or PID) control, as opposed to the more computationally expensive model predictive control (MPC). PID controllers are ubiquitous in industrial applications, but had thus far lacked integration with unsupervised vision models. We show that the NewtonianVAE learns physically correct latent spaces in simulated 2D and 3D control systems, which can be used to perform goal-based discovery and control in imitation learning, and path following via Dynamic Motion Primitives