A large part of computer vision research is devoted to building models and algorithms aimed at understanding human appearance and behaviour from images and videos. Ultimately, we want to build automated systems that are at least as capable as people when it comes to interpreting humans. Most of the tasks that we want these systems to solve can be posed as a problem of inference in probabilistic models. Although probabilistic inference in general is a very hard problem of its own, there exists a very powerful class of inference algorithms, variational inference, which allows us to build efficient solutions for a wide range of problems.

In this thesis, we consider a variety of computer vision problems targeted at modeling human appearance and behaviour, including detection, activity recognition, semantic segmentation and facial geometry modeling. For each of those problems, we develop novel methods that use variational inference to improve the capabilities of the existing systems.

First, we introduce a novel method for detecting multiple potentially occluded people in depth images, which we call DPOM. Unlike many other approaches, our method does probabilistic reasoning jointly, and thus allows to propagate knowledge about one part of the image evidence to reason about the rest. This is particularly important in crowded scenes involving many people, since it helps to handle ambiguous situations resulting from severe occlusions. We demonstrate that our approach outperforms existing methods on multiple datasets.

Second, we develop a new algorithm for variational inference that works for a large class of probabilistic models, which includes, among others, DPOM and some of the state-of-the-art models for semantic segmentation. We provide a formal proof that our method converges, and demonstrate experimentally that it brings better performance than the state-of-the-art on several real-world tasks, which include semantic segmentation and people detection. Importantly, we show that parallel variational inference in discrete random fields can be seen as a special case of proximal gradient descent, which allows us to benefit from many of the advances in gradient-based optimization.

Third, we propose a unified framework for multi-human scene understanding which simultaneously solves three tasks: multi-person detection, individual action recognition and collective activity recognition. Within our framework, we introduce a novel multi-person detection scheme, which relies on variational inference and jointly refines detection hypotheses instead of relying on suboptimal post-processing. Ultimately, our model takes as an inputs a frame sequence and produces a comprehensive description of the scene. Finally, we experimentally demonstrate that our method brings better performance than the state-of-the-art.

Fourth, we propose a new approach for learning facial geometry with deep probabilistic models and variational methods. Our model is based on a variational autoencoder with multiple sets of hidden variables, which are capturing various levels of deformations, ranging from global to local, high-frequency ones. We experimentally demonstrate the power of the model on a variety of fitting tasks. Our model is completely data-driven and can be learned from a relatively small number of individuals.