We present a novel framework for the automatic discovery and recognition of motion primitives in videos of human activities. Given the 3D pose of a human in a video, human motion primitives are discovered by optimizing the motion flux', a quantity which captures the motion variation of a group of skelet al joints. A normalization of the primitives is proposed in order to make them invariant with respect to a subject anatomical variations and data sampling rate. The discovered primitives are unknown and unlabeled and are unsupervisedly collected into classes via a hierarchical non-parametric Bayes mixture model. Once classes are determined and labeled they are further analyzed for establishing models for recognizing discovered primitives. Each primitive model is defined by a set of learned parameters. Given new video data and given the estimated pose of the subject appearing on the video, the motion is segmented into primitives, which are recognized with a probability given according to the parameters of the learned models. Using our framework we build a publicly available dataset of human motion primitives, using sequences taken from well-known motion capture datasets. We expect that our framework, by providing an objective way for discovering and categorizing human motion, will be a useful tool in numerous research fields including video analysis, human inspired motion generation, learning by demonstration, intuitive human-robot interaction, and human behavior analysis.
 This paper presents a novel video descriptor, referred to as Histogram of Oriented Track lets, for recognizing abnormal situation in crowded scenes. Unlike standard approaches that use optical flow, which estimates motion vectors only from two successive frames, we built our descriptor over long-range motion trajectories which is called track lets in the literature. Following the standard procedure, we divided video sequences in spatio-temporal cuboids within which we collected statistics on the track lets passing through them. In particular, we quantized orientation and magnitude in a 2-dimensional histogram which encodes the motion patterns expected in each cuboid. We classify frames as normal and abnormal by using Latent Dirichlet Allocation and Support Vector Machines. We evaluated the effectiveness of the proposed descriptors on three datasets: UCSD, Violence in Crowds and UMN. The experiments demonstrated (i) very promising results in abnormality detection, (ii) setting new state-of-the-art on two of them, and (iii) outperforming former descriptors based on the optical flow, dense trajectories and the social force model. This paper presents a novel video descriptor based on substantial derivative, an important concept in fluid mechanics, that captures the rate of change of a fluid property as it travels through a velocity field. Unlike standard approaches that only use temporal motion information, our descriptor exploits the spatio-temporal characteristic of substantial derivative. In particular, the spatial and temporal motion patterns are captured by respectively the convective and local accelerations. After estimating the convective and local field from the optic flow, we followed the standard bag-of-word procedure for each motion pattern separately, and we concatenated the two resulting histograms to form the final descriptor. We extensively evaluated the effectiveness of the proposed method on five benchmarks, including three standard datasets (Violence in Movies, Violence In Crowd, and BEHAVE), and two new video-survelliance sequences downloaded from Youtube. Our experiments show how the proposed approach sets the new state-of-the-art on all benchmarks and how the structural information captured by convective acceleration is essential to detect violent episodes in crowded scenarios. Approaches inspired by Newtonian mechanics have been successfully applied for detecting abnormal behaviors in crowd scenarios, being the most notable example the Social Force Model (SFM). This class of approaches describes the movements and local interactions among individuals in crowds by means of repulsive and attractive forces. Despite their promising performance, recent socio-psychology studies have shown that current SFM-based methods may not be capable of explaining behaviors in complex crowd scenarios. An alternative approach consists in describing the cognitive processes that gives rise to the behavioral patterns observed in crowd using heuristics. Inspired by these studies, we propose a new hybrid framework to detect violent events in crowd videos. More specifically, (i) we define a set of simple behavioral heuristics to describe people behaviors in crowd, and (ii) we implement these heuristics into physical equations, being able to model and classify such behaviors in the videos. The resulting heuristic maps are used to extract video features to distinguish violence from normal events. Our violence detection results set the new state of the art on several standard benchmarks and demonstrate the superiority of our method compared to standard motion descriptors, previous physics-inspired models used for crowd analysis and pre-trained ConvNet for crowd behavior analysis.