The collection of moving object data is becoming more and more common, and therefore there is an increasing need for the efficient analysis and knowledge extraction of these data in different application domains. Trajectory data are normally available as sample points, and do not carry semantic information, which is of fundamental importance for the comprehension of these data. Therefore, the analysis of trajectory data becomes expensive from a computational point of view and complex from a user's perspective. Enriching trajectories with semantic geographical information may simplify queries, analysis, and mining of moving object data. In this paper we propose a data preprocessing model to add semantic information to trajectories in order to facilitate trajectory data analysis in different application domains. The model is generic enough to represent the important parts of trajectories that are relevant to the application, not being restricted to one specific application. We present an algorithm to compute the important parts and show that the query complexity for the semantic analysis of trajectories will be significantly reduced with the proposed model.

We present an algorithm for polyline (and polygon) similarity testing that is based on the double-cross formalism. To determine the degree of similarity between two polylines, the algorithm first computes their generalized polygons, that consist of almost equally long line segments and that approximate the length of the given polylines within an ε-error margin. Next, the algorithm determines the double-cross matrices of the generalized polylines and the difference between these matrices is used as a measure of dissimilarity between the given polylines. We prove termination of our algorithm and show that its sequential time complexity is bounded by O " (, where N1 and N2 are the number of vertices of the given polylines. We apply our method to query-by-sketch, indexing of polyline databases, and classification of terrain features and show experimental results for each of these applications.

Abstract. A key issue in clustering data, regardless the algorithm used, is the definition of a distance function. In the case of trajectory data, different distance functions have been proposed, with different degrees of complexity. All these measures assume that trajectories are error-free, which is essentially not true. Uncertainty is present in trajectory data, which is usually obtained through a series of GPS of GSM observations. Trajectories are then reconstructed, typically using linear interpolation. A first source of error in trajectory are the GPS observations themselves, since many reported points lie outside the road network. Thus, the users position must be matched to a map, leading to the problem of map matching. A well-known model to deal with uncertainty in a trajectory sample, uses the notion of space-time prisms (also called beads), to estimate the positions where the object could have been, given a maximum speed. Thus, we can replace a (reconstructed) trajectory by a necklace (intuitively, a a chain of prisms), connecting consecutive trajectory sample points. When it comes to clustering, the notion of uncertainty requires appropriate distance functions. The main contribution of this paper is the definition of a distance function that accounts for uncertainty, together with the proof that this function is also a metric, and therefore it can be used in clustering. We also present an algorithm that computes the distance between the chains of prisms corresponding to two trajectory samples. Finally, we discuss some preliminary results, obtained clustering a set of trajectories of cars in the center of the city of Milan, using the distance function introduced in this paper.