413 research outputs found
SEGMENTATION, RECOGNITION, AND ALIGNMENT OF COLLABORATIVE GROUP MOTION
Modeling and recognition of human motion in videos has broad applications in behavioral biometrics, content-based visual data analysis, security and surveillance, as well as designing interactive environments. Significant progress has been made in the past two decades by way of new models, methods, and implementations. In this dissertation, we focus our attention on a relatively less investigated sub-area called collaborative group motion analysis. Collaborative group motions are those that typically involve multiple objects, wherein the motion patterns of individual objects may vary significantly in both space and time, but the collective motion pattern of the ensemble allows characterization in terms of geometry and statistics. Therefore, the motions or activities of an individual object constitute local information. A framework to synthesize all local information into a holistic view, and to explicitly characterize interactions among objects, involves large scale global reasoning, and is of significant complexity. In this dissertation, we first review relevant previous contributions on human motion/activity modeling and recognition, and then propose several approaches to answer a sequence of traditional vision questions including 1) which of the motion elements among all are the ones relevant to a group motion pattern of interest (Segmentation); 2) what is the underlying motion pattern (Recognition); and 3) how two motion ensembles are similar and how we can 'optimally' transform one to match the other (Alignment). Our primary practical scenario is American football play, where the corresponding problems are 1) who are offensive players; 2) what are the offensive strategy they are using; and 3) whether two plays are using the same strategy and how we can remove the spatio-temporal misalignment between them due to internal or external factors. The proposed approaches discard traditional modeling paradigm but explore either concise descriptors, hierarchies, stochastic mechanism, or compact generative model to achieve both effectiveness and efficiency.
In particular, the intrinsic geometry of the spaces of the involved features/descriptors/quantities is exploited and statistical tools are established on these nonlinear manifolds. These initial attempts have identified new challenging problems in complex motion analysis, as well as in more general tasks in video dynamics. The insights gained from nonlinear geometric modeling and analysis in this dissertation may hopefully be useful toward a broader class of computer vision applications
A revisit to Bang-Jensen-Gutin conjecture and Yeo's theorem
A path (cycle) is properly-colored if consecutive edges are of distinct
colors. In 1997, Bang-Jensen and Gutin conjectured a necessary and sufficient
condition for the existence of a Hamilton path in an edge-colored complete
graph. This conjecture, confirmed by Feng, Giesen, Guo, Gutin, Jensen and
Rafley in 2006, was laterly playing an important role in Lo's asymptotical
proof of Bollob\'as-Erd\H{o}s' conjecture on properly-colored Hamilton cycles.
In 1997, Yeo obtained a structural characterization of edge-colored graphs that
containing no properly colored cycles. This result is a fundamental tool in the
study of edge-colored graphs. In this paper, we first give a much shorter proof
of the Bang-Jensen-Gutin Conjecture by two novel absorbing lemmas. We also
prove a new sufficient condition for the existence of a properly-colored cycle
and then deduce Yeo's theorem from this result and a closure concept in
edge-colored graphs.Comment: 13 pages, 5 figure
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Discriminative virtual views for cross-view action recognition
We propose an approach for cross-view action recognition by way of ‘virtual views’ that connect the action descriptors extracted from one (source) view to those extracted from another (target) view. Each virtual view is associated with a linear transformation of the action descriptor, and the sequence of transformations arising from the sequence of virtual views aims at bridging the source and target views while preserving discrimination among action categories. Our approach is capable of operating without access to labeled action samples in the target view and without access to corresponding action instances in the two views, and it also naturally incorporate and exploit corresponding instances or partial labeling in the target view when they are available. The proposed approach achieves improved or competitive performance relative to existing methods when instance correspondences or target labels are available, and it goes beyond the capabilities of these methods by providing some level of discrimination even when neither correspondences nor target labels exist.Engineering and Applied Science
Properly Edge-colored Theta Graphs in Edge-colored Complete Graphs
With respect to specific cycle-related problems, edge-colored graphs can be considered as a generalization of directed graphs. We show that properly edge-colored theta graphs play a key role in characterizing the difference between edge-colored complete graphs and multipartite tournaments. We also establish sufficient conditions for an edge-colored complete graph to contain a small and a large properly edge-colored theta graph, respectively
Observer-based Leader-following Consensus for Positive Multi-agent Systems Over Time-varying Graphs
This paper addresses the leader-following consensus problem for discrete-time
positive multi-agent systems over time-varying graphs. We assume that the
followers may have mutually different positive dynamics which can also be
different from the leader. Compared with most existing positive consensus works
for homogeneous multi-agent systems, the formulated problem is more general and
challenging due to the interplay between the positivity requirement and
high-order heterogeneous dynamics. To solve the problem, we present an extended
version of existing observer-based design for positive multi-agent systems. By
virtue of the common quadratic Lyapunov function technique, we show the
followers will maintain their state variables in the positive orthant and
finally achieve an output consensus specified by the leader. A numerical
example is used to verify the efficacy of our algorithms
Exact solutions for nonlinear trapped lee waves in the -plane approximation
In this paper, we construct exact solutions that character three-dimensional,
nonlinear trapped lee waves propagation superimposed on longitudinal
atmospheric currents in the -plane approximation. The solutions obtained
are presented in Lagrangian coordinates, and are Gerstner-like solutions. In
the process, we also derive the dispersion relation and analyze the density,
pressure and the vorticity qualitatively
Learning multi-modal densities on discriminative temporal interaction manifold for group activity recognition
While video-based activity analysis and recognition has received much attention, existing body of work mostly deals with single object/person case. Coordinated multi-object activities, or group activities, present in a variety of applications such as surveillance, sports, and biological monitoring records, etc., are the main focus of this paper. Unlike earlier attempts which model the complex spatial temporal constraints among multiple objects with a parametric Bayesian network, we propose a Discriminative Temporal Interaction Manifold (DTIM) framework as a data-driven strategy to characterize the group motion pattern without employing specific domain knowledge. In particular, we establish probability densities on the DTIM, whose element, the discriminative temporal interaction matrix, compactly describes the coordination and interaction among multiple objects in a group activity. For each class of group activity we learn a multi-modal density function on the DTIM. A Maximum a Posteriori (MAP) classifier on the manifold is then designed for recognizing new activities. Experiments on football play recognition demonstrate the effectiveness of the approach
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