Robust Tracking of Human Motion

This technical report presents a combined solution for two problems, one: tracking objects in 3D space and estimating their trajectories and second: computing the similarity between previously estimated trajectories and clustering them using the similarities that we just computed. For the first part, trajectories are estimated using an EKF formulation that will provide the 3D trajectory up to a constant. To improve accuracy, when occlusions appear, multiple hypotheses are followed. For the second problem we compute the distances between trajectories using a similarity based on LCSS formulation. Similarities are computed between projections of trajectories on coordinate axes. Finally we group trajectories together based on previously computed distances, using a clustering algorithm. To check the validity of our approach, several experiments using real data were performed.

Beta-Reduction As Unification

We define a unification problem ^UP with the property that, given a pure lambda-term M, we can derive an instance Gamma(M) of ^UP from M such that Gamma(M) has a solution if and only if M is beta-strongly normalizable. There is a type discipline for pure lambda-terms that characterizes beta-strong normalization; this is the system of intersection types (without a "top" type that can be assigned to every lambda-term). In this report, we use a lean version LAMBDA of the usual system of intersection types. Hence, ^UP is also an appropriate unification problem to characterize typability of lambda-terms in LAMBDA. It also follows that ^UP is an undecidable problem, which can in turn be related to semi-unification and second-order unification (both known to be undecidable).