For the problem of action detection, most existing methods require that relevant portions of the action of interest in training videos have been manually annotated with bounding boxes. Some recent works tried to avoid tedious manual annotation , and proposed to automatically identify the relevant portions in training videos. However, these methods only concerned the identification in either spatial or temporal domain, and may get irrelevant contents from another domain. These irrelevant contents are usually undesirable in the training phase, which will lead to a degradation of the detection performance. This paper advances prior work by proposing a joint learning framework to simultaneously identify the spatial and temporal extents of the action of interest in training videos. To get pixel-level localization results, our method uses dense trajectories extracted from videos as local features to represent actions. We first present a trajectory split-and-merge algorithm to segment a video into the background and several separated foreground moving objects. In this algorithm, the inherent temporal smoothness of human actions is exploited to facilitate segmentation. Then, with the latent SVM framework on segmentation results, spatial and temporal extents of the action of interest are treated as latent variables that are inferred simultaneously with action recognition. Experiments on two challenging datasets show that action detection with our learned spatial and temporal extents is superior than state-of-the-art methods.

Non-rigid structure-from-motion (NRSfM) is the process of recovering time-varying 3D structures and poses of a deformable object from an uncalibrated monocular video sequence. Currently, most NRSfM algorithms utilize a non- degenerate assumption for non-rigid object deformations whereby the 3D structures of a non-rigid object can be assumed to be a linear combination of basis shapes with full rank three. Unfortunately, this assumption will produce extra degrees-of-freedom when the non-rigid object has some degenerate deformations with shape bases of rank less than three. These extra degrees-of-freedom will yield spurious shape deformations due to non-negligible noise in real applications, which will cause substantial reconstruction errors. To solve this problem, we propose a low-rank shape deformation model to represent 3D structures of degenerate deformations. When modeling degenerate deformations, the proposed model exploits the rank-deficient nature of degenerate deformations in addition to the low-rank property of non-rigid objects' trajectories, thus providing a more accurate and compact representation compared with existing models. Based on this model, we formulate the NRSfM problem as two coherent optimization problems. These problems are solved with iterative non-linear optimization algorithms. Experiments on synthetic and motion capture data are conducted. The results exhibit the significant advantages of our approach over state-of-the-art NRSfM algorithms for the 3D recovery of non-rigid objects with degenerate deformations.