Assumptions (i.e., data models) must be formulated to relate the observed image intensities to motion, and other constraints (i.e., motion models) must be added to solve problems like motion segmentation, optical flow computation, or motion recognition. The motion models are supposed to capture known, expected or learned properties of the motion field ; this implies to somehow introduce spatial coherence or more generally contextual information. The latter can be formalized in a probabilistic way with local conditional densities as in Markov models. It can also rely on predefined spatial supports (e.g., blocks or pre-segmented regions). The classic mathematical expressions associated with the visual motion information are of two types. Some are continuous variables to represent velocity vectors or parametric motion models. The others are discrete variables or symbolic labels to code motion detection (binary labels), motion segmentation (numbers of the motion regions or layers) or motion recognition output (motion class labels).

Analyzing fluid motion is essential in number of domains and can rarely be handled using generic computer vision techniques. In this particular application context, we study several distinct problems. We first focus on the estimation of dense velocity maps from image sequences. Fluid flows velocities cannot be represented by a single parametric model and must generally be described by accurate dense velocity fields in order to recover the important flow structures at different scales. Nevertheless, in contrast to standard motion estimation approach, adapted data model and higher order regularization are required in order to incorporate suitable physical constraints. In a second step, analyzing such velocity fields is also a source of concern. When one wants to detect particular events, to segment meaningful areas, or to track characteristic structures, dedicated methods must be devised and studied.

Tracking problems that arise in target motion analysis (TMA) and video analysis are highly non-linear and multi-modal, which precludes the use of Kalman filter and its classic variants. A powerful way to address this class of difficult filtering problems has become increasingly successful in the last ten years. It relies on sequential Monte Carlo (SMC) approximations and on importance sampling. The resulting sample-based filters, also called particle filters, can, in theory, accommodate any kind of dynamical models and observation models, and permit an efficient tracking even in high dimensional state spaces. In practice, there is however a number of issues to address when it comes to difficult tracking problems such as long-term visual tracking under drastic appearance changes, or multi-object tracking.