An eigen decomposition based rank parameter selection approach for the NRSFM algorithm

Non-rigid structure from motion (NRSFM) with an affine structure from motion (aSFM) kernel (NRSFM-aSFM) is a relative novel and robust 3D shape recovery algorithm to the abrupt deformations. Nevertheless, the estimated 3D shapes generally fluctuate with the variation of rank parameter, i.e., the number of shape bases. Therefore, it is necessary to develop an effective method to select the rank parameter. In this paper, we propose an eigen decomposition based rank parameter selection approach, which can automatically select the optimal or an approximately optimal rank parameter for the NRSFM-aSFM algorithm. In the proposed method, a symmetric matrix is first constructed to simplify the singular value estimation. Further, the QR decomposition based iterations are carried out to compute the eigenvalues of the observation matrix. Finally, the rank parameter is estimated according to the cumulative sum of eigenvalues by setting a referred threshold value. The experimental results on several widely used sequences demonstrate the effectiveness and feasibility of the proposed method.