Abstract-In this paper, a new conditional formulation of classical filtering methods is proposed. This formulation is dedicated to image sequence based tracking. These conditional filters allow solving systems whose measurements and state equation are estimated from the image data. In particular, the model that is considered for point tracking combines a state equation relying on the optical flow constraint and measurements provided by a matching technique. Based on this, two point trackers are derived. The first one is a linear tracker well-suited to image sequences exhibiting global dominant motion. This filter is determined through the use of a new estimator, called the conditional linear minimum variance estimator. The second one is a nonlinear tracker, implemented from a conditional particle filter. It allows tracking of points whose motion may be only locally described. These conditional trackers significantly improve results in some general situations. In particular, they allow dealing with noisy sequences, abrupt changes of trajectories, occlusions and cluttered background.

A new strategy called the Deepest Minimum Criterion (DMC) is presented for optimally obtaining an affine transformation of a given unbiased estimator, when a-priori information on the parameters is known. Here, it is considered that the samples are drawn from a distribution parametrized by an unknown deterministic vector parameter. The a-priori information on the true parameter vector is available in the form of a known subset of the parameter space to which the true parameter vector belongs. A closed form exact solution is given for the non-linear DMC problem in which it is known that the true parameter vector belongs to an ellipsoidal ball and the covariance matrix of the unbiased estimator does not depend on the parameters. A closed form exact solution is also given for the Min-Max strategy for this same case.

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We consider the problem of motion detection by background subtraction. An accurate estimation of the background is only possible if we locate the moving objects; meanwhile, a correct motion detection is achieved if we have a good available background model. This work proposes a new direction in the way such problems are considered. The main idea is to formulate this class of problem as a joint decision-estimation unique step. The goal is to exploit the way two processes interact, even if they are of a dissimilar nature (symbolic-continuous), by means of a recently introduced framework called mixed-state Markov random fields. In this paper, we will describe the theory behind such a novel statistical framework, that subsequently will allows us to formulate the specific joint problem of motion detection and background reconstruction. Experiments on real sequences and comparisons with existing methods will give a significant support to our approach. Further implications for video sequence inpainting will be also discussed.