LOCAL ESTIMATION OF DISPLACEMENT DENSITY FOR ABNORMAL BEHAVIOR DETECTION P.L.M. Boutte/roy, A. Bouzerdoum, S.L. Phung SECTE, Faculty of informatics, Wollongong University, Northfields Av., Wollongong, 2522 NSW, Australia. ABSTRACT Detecting abnormal behavior in video sequences has be- come a crucial task with the development of automatic video- surveillance systems. Here, we propose an algorithm which locally models the probability distribution of objects be- havioral features. A temporal Gaussian mixture with lo- cal update is introduced to estimate the local probability distribution. The update of the feature probability distribu- tion is thus temporal and local, allowing a smooth transition for neighboring locations. The integration of local infor- mation in the estimation provides a fast adaptation along with an efficient discrimination between normal and abnor- mal behavior. The proposed technique is evaluated on both synthetic and real data. Synthetic data simulates different scenarios occurring in road traffic, and illustrates how the model adapts to local conditions. Real data demonstrates the ability of the system to detect abnormal behavior due to the presence of pedestrians and animals on highways. In all tested scenarios the system identifies abnormal and normal behavior correctly. 1. INTRODUCTION The last decade witnessed a rise in the development of ab- normal behavior detection (ABD) systems due to the in- creasing demand in visual surveillance and security. The outcomes of ABD development are tremendous, leading to automatic and instantaneous notification of abnormal events in public places. Abnormal behavior detection is a challeng- ing problem because it is a high-level process requiring the integration of various techniques such as feature selection, trajectory modeling, dimensionality reduction and density estimation. Moreover, most of these fields are still active areas of research; global optimal solutions are yet to be found for many problems. Abnormal behavior detection al- gorithms can be divided into two sub-categories: algorithms concerned with the characterization of the body posture and those concerned with the analysis of object trajectories. The algorithm proposed in this paper falls in the latter category. A. Beghdadi L2TI, Institut Galilee, Univ. Paris 13, 99, avenue J. B. Clement, 93430 Villetaneuse, France. Trajectory-based analysis is concerned with modeling the distribution of objects' feature vectors consisting of the object coordinates and behavioral features such as vector flow, object size, colors, etc. This combination of local and behavioral features determines whether the behavior is normal or not. ABD techniques traditionally rely upon the learning of a global distribution of the feature vector over the entire feature space, regardless of the nature of the fea- ture (local or behavioral). Hidden Markov models are typi- cally used to model the global distribution [1, 2, 3]. Neural networks have also been used for ABD with some success [4]. In particular, self organizing maps (SOMs) have at- tracted attention due to their ability to preserve the topol- ogy of the input data [5, 6]. Johnson and Hogg have also proposed to model the probability distribution of a feature vector composed of the position and the vector flow of the object using a competitive neural network [7] and a global Gaussian mixture model [8]. The algorithm proposed herein differs from the afore- mentioned techniques in that the local (or position) feature vector is not integrated in the distribution estimate but is rather used as a parameter to index the pdf estimate. A map of local probability distributions for the behavioral features is thus generated. The benefits are twofold: first, the dimen- sionality of the feature vector is reduced; second, integrat- ing the local feature in the distribution estimate augments the rate of false detection for abnormal behavior. Indeed, global estimation of local feature is, by definition, inade- quate. The paper is organized as follows. Section 2 fo- cuses on the probability density modeling with Gaussian mixtures. In particular, subsection 2.2 introduces the con- cept of spatio-temporal Gaussian mixture applied to behav- ioral features. Subsection 2.3 is concerned with the update equations of the spatio-temporal Gaussian mixture. Sec- tion 3 presents experimental results for abnormal behavior detection using synthetic and real data, followed by the con- clusion in Section 4. 1-4244-2376-7/08/$20.00 ©20081EEE 386