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From Sequence to Trajectory and Vice Versa: Solving the Inverse QTC Problem and Coping with Real-World Trajectories

Spatial interactions between agents carry information of high value to human observers, as exemplified by the high-level interpretations that humans make when watching the Heider and Simmel movie, or other such videos which just contain motions of simple objects, such as points, lines and triangles. However, not all the information contained in a pair of continuous trajectories is important; and thus the need for qualitative descriptions of interaction trajectories arises. Towards that purpose, Qualitative Trajectory Calculus (QTC) has been proposed in (Van de Weghe, 2004). However, the original definition of QTC handles uncorrupted continuous-time trajectories, while real-world signals are noisy and sampled in discrete-time. Also, although QTC presents a method for transforming trajectories to qualitative descriptions, the inverse problem has not yet been studied. Thus, in this paper, after discussing several aspects of the transition from ideal QTC to discrete-time noisy QTC, we introduce a novel algorithm for solving the QTC inverse problem; i.e. transforming qualitative descriptions to archetypal trajectories that satisfy them. Both of these problems are particularly important for the successful application of qualitative trajectory calculus to Human-Robot Interaction.