Linear Embeddings in Non-Rigid Structure from Motion

This paper proposes a method to recover the embedding of the possible shapes assumed by a deforming non-rigid object by comparing triplets of frames from an orthographic video sequence. We assume that we are given features tracked with no occlusions and no outliers but possible noise, an orthographic camera and that any 3D shape of a deforming object is a linear combination of several canonical shapes. By exploiting any repetition in the object motion and defining an ordering between triplets of frames in a Generalized Non-Metric Multi-Dimensional Scaling framework, our approach recovers the shape coefficients of the linear combination, independently from other structure and motion parameters. From this point, a good estimate of the remaining unknowns is obtained for a final optimization to perform full non-rigid structure from motion. Results are presented on synthetic and real image sequences and our method is found to perform better than current state of the art.