Representing videos by densely extracted local space-time features has recently become a popular approach for analysing actions. In this study, the authors tackle the problem of categorising human actions by devising bag of words (BoWs) models based on covariance matrices of spatiotemporal features, with the features formed from histograms of optical flow. Since covariance matrices form a special type of Riemannian manifold, the space of symmetric positive definite (SPD) matrices, non-Euclidean geometry should be taken into account while discriminating between covariance matrices. To this end, the authors propose to embed SPD manifolds to Euclidean spaces via a diffeomorphism and extend the BoW approach to its Riemannian version. The proposed BoW approach takes into account the manifold geometry of SPD matrices during the generation of the codebook and histograms. Experiments on challenging human action datasets show that the proposed method obtains notable improvements in discrimination accuracy, in comparison with several state-of-the-art methods.
Wang al @cite_12 demonstrate that dense sampling approaches consistently outperform space-time interest point based methods for human action categorisation. A dense sampling at regular positions in space and time guarantees good coverage of foreground motions as well as of surrounding context. To characterise local patterns ( motion, appearance, or shape), the descriptors divide small 3D volumes into a grid of @math cells and for each cell the related information is accumulated. Examples are HOG and HOF @cite_34 , HOG3D @cite_33 , and 3D SIFT @cite_4 .
@cite_34 @cite_4 @cite_33 @cite_12
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For volume rendering of regular grids the display of view-plane aligned slices has proven to yield both good quality and performance. In this paper we demonstrate how to merge the most important extensions of the original 3D slicing approach, namely the pre-integration technique, volumetric clipping, and advanced lighting. Our approach allows the suppression of clipping artifacts and achieves high quality while offering the fiexibility to explore volume data sets interactively with arbitrary clip objects. We also outline how to utilize the proposed volumetric clipping approach for the display of segmented data sets. Moreover, we increase the rendering quality by implementing efficient over-sampling with the pixel shader of consumer graphics accelerators. We give prove that at least 4-times over-sampling is needed to reconstruct the ray integral with sufficient accuracy even with pre-integration. As an alternative to this brute-force over-sampling approach we propose a hardware-accelerated ray caster which is able to perform over-sampling only where needed and which is able to gain additional speed by early ray termination and space leaping. In high-dimensional magnetic resonance imaging applications, time-consuming, sequential acquisition of data samples in the spatial frequency domain ( @math -space) can often be accelerated by accounting for dependencies in linear reconstruction, at the cost of noise amplification that depends on the sampling pattern. Common examples are support-constrained, parallel, and dynamic MRI, and @math -space sampling strategies are primarily driven by image-domain metrics that are expensive to compute for arbitrary sampling patterns. It remains challenging to provide systematic and computationally efficient automatic designs of arbitrary multidimensional Cartesian sampling patterns that mitigate noise amplification, given the subspace to which the object is confined. To address this problem, this paper introduces a theoretical framework that describes local geometric properties of the sampling pattern and relates them to the spread in the eigenvalues of the information matrix described by its first two spectral moments. This new criterion is then used for very efficient optimization of complex multidimensional sampling patterns that does not require reconstructing images or explicitly mapping noise amplification. Experiments with in vivo data show strong agreement between this criterion and traditional, comprehensive image-domain- and @math -space-based metrics, indicating the potential of the approach for computationally efficient (on-the-fly), automatic, and adaptive design of sampling patterns. In this paper, we propose a non-local structured prior for volumetric multi-view 3D reconstruction. Towards this goal, we present a novel Markov random field model based on ray potentials in which assumptions about large 3D surface patches such as planarity or Manhattan world constraints can be efficiently encoded as probabilistic priors. We further derive an inference algorithm that reasons jointly about voxels, pixels and image segments, and estimates marginal distributions of appearance, occupancy, depth, normals and planarity. Key to tractable inference is a novel hybrid representation that spans both voxel and pixel space and that integrates non-local information from 2D image segmentations in a principled way. We compare our non-local prior to commonly employed local smoothness assumptions and a variety of state-of-the-art volumetric reconstruction baselines on challenging outdoor scenes with textureless and reflective surfaces. Our experiments indicate that regularizing over larger distances has the potential to resolve ambiguities where local regularizers fail. This paper introduces a video representation based on dense trajectories and motion boundary descriptors. Trajectories capture the local motion information of the video. A dense representation guarantees a good coverage of foreground motion as well as of the surrounding context. A state-of-the-art optical flow algorithm enables a robust and efficient extraction of dense trajectories. As descriptors we extract features aligned with the trajectories to characterize shape (point coordinates), appearance (histograms of oriented gradients) and motion (histograms of optical flow). Additionally, we introduce a descriptor based on motion boundary histograms (MBH) which rely on differential optical flow. The MBH descriptor shows to consistently outperform other state-of-the-art descriptors, in particular on real-world videos that contain a significant amount of camera motion. We evaluate our video representation in the context of action classification on nine datasets, namely KTH, YouTube, Hollywood2, UCF sports, IXMAS, UIUC, Olympic Sports, UCF50 and HMDB51. On all datasets our approach outperforms current state-of-the-art results.