Mode-Shape Interpretation: Re-Thinking Modal Space For Recovering Deformable Shapes

This paper describes an on-line approach for estimating non-rigid shape and camera pose from monocular video sequences. We assume an initial estimate of the shape at rest to be given and represented by a triangulated mesh, which is encoded by a matrix of the distances between every pair of vertexes. By applying spectral analysis on this matrix, we are then able to compute a low-dimensional shape basis, that in contrast to standard approaches, has a very direct physical interpretation and requires a much smaller number of modes to span a large variety of deformations, either for inextensible or extensible configurations. Based on this low-rank model, we then sequentially retrieve both camera motion and non-rigid shape in each image, optimizing the model parameters with bundle adjustment over a sliding window of image frames. Since the number of these parameters is small, specially when considering physical priors, our approach may potentially achieve real-time performance. Experimental results on real videos for different scenarios demonstrate remarkable robustness to artifacts such as missing and noisy observations.