Trajectory based video analysis in multi-camera setups

PhDThis thesis presents an automated framework for activity analysis in multi-camera setups. We start with the calibration of cameras particularly without overlapping views. An algorithm is presented that exploits trajectory observations in each view and works iteratively on camera pairs. First outliers are identified and removed from observations of each camera. Next, spatio-temporal information derived from the available trajectory is used to estimate unobserved trajectory segments in areas uncovered by the cameras. The unobserved trajectory estimates are used to estimate the relative position of each camera pair, whereas the exit-entrance direction of each object is used to estimate their relative orientation. The process continues and iteratively approximates the configuration of all cameras with respect to each other. Finally, we refi ne the initial configuration estimates with bundle adjustment, based on the observed and estimated trajectory segments. For cameras with overlapping views, state-of-the-art homography based approaches are used for calibration. Next we establish object correspondence across multiple views. Our algorithm consists of three steps, namely association, fusion and linkage. For association, local trajectory pairs corresponding to the same physical object are estimated using multiple spatio-temporal features on a common ground plane. To disambiguate spurious associations, we employ a hybrid approach that utilises the matching results on the image plane and ground plane. The trajectory segments after association are fused by adaptive averaging. Trajectory linkage then integrates segments and generates a single trajectory of an object across the entire observed area. Finally, for activities analysis clustering is applied on complete trajectories. Our clustering algorithm is based on four main steps, namely the extraction of a set of representative trajectory features, non-parametric clustering, cluster merging and information fusion for the identification of normal and rare object motion patterns. First we transform the trajectories into a set of feature spaces on which Meanshift identi es the modes and the corresponding clusters. Furthermore, a merging procedure is devised to re fine these results by combining similar adjacent clusters. The fi nal common patterns are estimated by fusing the clustering results across all feature spaces. Clusters corresponding to reoccurring trajectories are considered as normal, whereas sparse trajectories are associated to abnormal and rare events. The performance of the proposed framework is evaluated on standard data-sets and compared with state-of-the-art techniques. Experimental results show that the proposed framework outperforms state-of-the-art algorithms both in terms of accuracy and robustness

Deep Decision Trees for Discriminative Dictionary Learning with Adversarial Multi-Agent Trajectories

With the explosion in the availability of spatio-temporal tracking data in modern sports, there is an enormous opportunity to better analyse, learn and predict important events in adversarial group environments. In this paper, we propose a deep decision tree architecture for discriminative dictionary learning from adversarial multi-agent trajectories. We first build up a hierarchy for the tree structure by adding each layer and performing feature weight based clustering in the forward pass. We then fine tune the player role weights using back propagation. The hierarchical architecture ensures the interpretability and the integrity of the group representation. The resulting architecture is a decision tree, with leaf-nodes capturing a dictionary of multi-agent group interactions. Due to the ample volume of data available, we focus on soccer tracking data, although our approach can be used in any adversarial multi-agent domain. We present applications of proposed method for simulating soccer games as well as evaluating and quantifying team strategies.Comment: To appear in 4th International Workshop on Computer Vision in Sports (CVsports) at CVPR 201

Cluster-based feedback control of turbulent post-stall separated flows

We propose a novel model-free self-learning cluster-based control strategy for general nonlinear feedback flow control technique, benchmarked for high-fidelity simulations of post-stall separated flows over an airfoil. The present approach partitions the flow trajectories (force measurements) into clusters, which correspond to characteristic coarse-grained phases in a low-dimensional feature space. A feedback control law is then sought for each cluster state through iterative evaluation and downhill simplex search to minimize power consumption in flight. Unsupervised clustering of the flow trajectories for in-situ learning and optimization of coarse-grained control laws are implemented in an automated manner as key enablers. Re-routing the flow trajectories, the optimized control laws shift the cluster populations to the aerodynamically favorable states. Utilizing limited number of sensor measurements for both clustering and optimization, these feedback laws were determined in only $O(10)$ iterations. The objective of the present work is not necessarily to suppress flow separation but to minimize the desired cost function to achieve enhanced aerodynamic performance. The present control approach is applied to the control of two and three-dimensional separated flows over a NACA 0012 airfoil with large-eddy simulations at an angle of attack of $9^\circ$, Reynolds number $Re = 23,000$ and free-stream Mach number $M_\infty = 0.3$. The optimized control laws effectively minimize the flight power consumption enabling the flows to reach a low-drag state. The present work aims to address the challenges associated with adaptive feedback control design for turbulent separated flows at moderate Reynolds number.Comment: 32 pages, 18 figure

Computing Similarity between a Pair of Trajectories

With recent advances in sensing and tracking technology, trajectory data is becoming increasingly pervasive and analysis of trajectory data is becoming exceedingly important. A fundamental problem in analyzing trajectory data is that of identifying common patterns between pairs or among groups of trajectories. In this paper, we consider the problem of identifying similar portions between a pair of trajectories, each observed as a sequence of points sampled from it. We present new measures of trajectory similarity --- both local and global --- between a pair of trajectories to distinguish between similar and dissimilar portions. Our model is robust under noise and outliers, it does not make any assumptions on the sampling rates on either trajectory, and it works even if they are partially observed. Additionally, the model also yields a scalar similarity score which can be used to rank multiple pairs of trajectories according to similarity, e.g. in clustering applications. We also present efficient algorithms for computing the similarity under our measures; the worst-case running time is quadratic in the number of sample points. Finally, we present an extensive experimental study evaluating the effectiveness of our approach on real datasets, comparing with it with earlier approaches, and illustrating many issues that arise in trajectory data. Our experiments show that our approach is highly accurate in distinguishing similar and dissimilar portions as compared to earlier methods even with sparse sampling