Trajectories Comparing Based on Matching and Distance Evaluation Within Stiefel and Grassmann Manifolds
Résumé
In this paper, we are interested in comparing human trajectories using skeleton information provided by a consumer RGB-D sensor. In fact, 3D human joints given by skeletons offer an important information for human motion analysis. In this context, the use of manifolds has grown considerably in the computer vision community in recent years. The main contribution of this study resides in working jointly with two manifolds. The matching of the trajectories is performed in Stiefel manifold and dissimilarity measure is carried out in Grassmann manifold. Indeed, trajectories of motions are provided by the projection in the Stiefel manifold. Then, the Stiefel distance is used within the dynamic time warping in order to define the appropriate matching between a reference trajectory and a test one. This allows avoiding that the rotation within the motion will be ignored, as it is the case with the Grassmann manifold. Then, the dissimilarity is evaluated using the Grassmann distance to compare motions while being invariant against rotation. Realized experiments on standard challenging datasets prove that the proposed method, for the comparison of human trajectories with different sizes, performs accurately compared to existing manifold-based methods.
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