Abstract
As a fundamental and challenging problem, non-rigid structure-from-motion (NRSfM) has attracted a large amount of research interest. It is worth mentioning that NRSfM has been applied to dynamic scene understanding and motion segmentation. Especially, a motion segmentation approach combining NRSfM with the subspace representation has been proposed. However, the current subspace representation for non-rigid motions clustering do not take into account the inherent sequential property, which has been proved vital for sequential data clustering. Hence this paper proposes a novel framework to segment the complex and non-rigid motion via an ordered subspace representation method for the reconstructed 3D data, where the sequential property is properly formulated in the procedure of learning the affinity matrix for clustering with simultaneously recovering the 3D non-rigid motion by a monocular camera with 2D point tracks. Experiment results on three public sequential action datasets, BU-4DFE, MSR and UMPM, verify the benefits of method presented in this paper for classical complex non-rigid motion analysis and outperform state-of-the-art methods with lowest subspace clustering error (SCE) rates and highest normalized mutual information (NMI) in subspace clustering and motion segmentation fields.
Highlights
Modeling and analysis of non-rigid motions from image sequence are challenging problems in computer vision due to complex deformable pattern and shape structure, for example, dynamic scenes, human body activities, expressive or talking faces, etc
Motivated by ordered subspace clustering (OSC) and QOSC, we introduce a penalty term to penalize the similarity between consecutive columns of the low rank representation Z from reconstructed 3D motion data X, we obtain the following non-rigid structure-from-motion (NRSfM) model: λ min k X − XZ k2F + k Z k∗ + λ1 k ZSk2,1 + λ2 k X k∗ + λ3 k Ek1
One reprehensive method is the subspace segmentation via quadratic programming (SSQP) [18], which introduces a quadratic term to force the block-diagonal feature for clustering, and it has been proved that SSQP satisfies the block-diagonal feature on the assumption of orthogonal linear subspaces [18]
Summary
Modeling and analysis of non-rigid motions from image sequence are challenging problems in computer vision due to complex deformable pattern and shape structure, for example, dynamic scenes, human body activities, expressive or talking faces, etc. Dai et al [6,7] adopted a simple subspace to model non-rigid 3D shapes and proposed a “prior-free” method for NRSfM problem, where there is no prior assumption about the non-rigid or camera motions. The sequence property of non-rigid motion has not been considered in current methods, which is ubiquitous in motion segmentation and other applications involved in sequential data. It is proved by ordered subspace clustering (OSC) [16,17] methods which is recently proposed, that clustering using sequential or ordered properties will improve clustering accurancy significantly.
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