Motion trajectories provide rich spatiotemporal information about an object's activity. This paper presents novel classification algorithms for recognizing object activity using object motion trajectory. In the proposed classification system, trajectories are segmented at points of change in curvature, and the subtrajectories are represented by their principal component analysis (PCA) coefficients. We first present a framework to robustly estimate the multivariate probability density function based on PCA coefficients of the subtrajectories using Gaussian mixture models (GMMs). We show that GMM-based modeling alone cannot capture the temporal relations and ordering between underlying entities. To address this issue, we use hidden Markov models (HMMs) with a data-driven design in terms of number of states and topology (e.g., left-right versus ergodic). Experiments using a database of over 5700 complex trajectories (obtained from UCI-KDD data archives and Columbia University Multimedia Group) subdivided into 85 different classes demonstrate the superiority of our proposed HMM-based scheme using PCA coefficients of subtrajectories in comparison with other techniques in the literature.

No abstract

Motion trajectories provide rich spatio-temporal information about an object's activity. The trajectory information can be obtained using a tracking algorithm on data streams available from a range of devices including motion sensors, video cameras, haptic devices, etc. Developing view-invariant activity recognition algorithms based on this high dimensional cue is an extremely challenging task. This paper presents efficient activity recognition algorithms using novel view-invariant representation of trajectories. Towards this end, we derive two Affine-invariant representations for motion trajectories based on curvature scale space (CSS) and centroid distance function (CDF). The properties of these schemes facilitate the design of efficient recognition algorithms based on hidden Markov models (HMMs). In the CSS-based representation, maxima of curvature zero crossings at increasing levels of smoothness are extracted to mark the location and extent of concavities in the curvature. The sequences of these CSS maxima are then modeled by continuous density (HMMs). For the case of CDF, we first segment the trajectory into subtrajectories using CDF-based representation. These subtrajectories are then represented by their Principal Component Analysis (PCA) coefficients. The sequences of these PCA coefficients from subtrajectories are then modeled by continuous density hidden Markov models (HMMs). Different classes of object motions are modeled by one Continuous HMM per class where state PDFs are represented by GMMs. Experiments using a database of around 1750 complex trajectories (obtained from UCI-KDD data archives) subdivided into five different classes are reported.

Abstract-This paper presents a novel motion trajectory-based compact indexing and efficient retrieval mechanism for video sequences. Assuming trajectory information is already available, we represent trajectories as temporal ordering of subtrajectories. This approach solves the problem of trajectory representation when only partial trajectory information is available due to occlusion. It is achieved by a hypothesis testing-based method applied to curvature data computed from trajectories. The subtrajectories are then represented by their principal component analysis (PCA) coefficients for optimally compact representation. Different techniques are integrated to index and retrieve subtrajectories, including PCA, spectral clustering, and string matching. We assume a query by example mechanism where an example trajectory is presented to the system and the search system returns a ranked list of most similar items in the dataset. Experiments based on datasets obtained from University of California at Irvine's KDD archives and Columbia University's DVMM group demonstrate the superiority of our proposed PCA-based approaches in terms of indexing and retrieval times and precision recall ratios, when compared to other techniques in the literature.

No abstract