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Multiview video plus depth is emerging as the most flexible format for three-dimensional video representation, as witnessed by the current standardization efforts by ISO and ITU. In particular, in depth representation, arguably the most important information lies in object contours. As a consequence, an interesting approach consists in performing a lossless coding of object contours, possibly followed by a lossy coding of per-object depth values. In this context, we propose a new technique for lossless coding of object contours, based on the elastic deformation of curves. Using the square-root velocity representation for the elements of the space of curves, we can model a continuous evolution of elastic deformations between two reference contour curves. An elastically deformed version of the reference contours can be sent to the decoder with a reduced coding cost and used as side information to improve the lossless coding of the actual contour. Experimental results on several multiview video sequences show remarkable gains with respect to the reference techniques and to the state of the art.