For each particle video data has the same 5 channels, image brightness, green minus red channel, green minus blue channel, x gradient and y gradient as the flow estimation algorithm. The process of computation is shown in Fig. Propagation: Particles terminating in an adjacent frame are extended into the current frame according to the forward and reverse optical flow fields.

To propagate particle i from frame t-1 to t, use the flow field:. Linking: To quantify relative particle motion, our algorithm need create links between particles. It simply link each particle to its N nearest neighbors.

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Using links from adjacent frames reduces temporal linking variability, while still allowing links to appear and disappear as particles pass by one another. For each link i, j , it computes a squared motion difference according to the flow vectors:.

Optimization: The core of the particle video algorithm is optimization process which can remodify the particle position caused by particle drift problem in long-segment diffusion process. The distortion term measures relative motion relative motion between the particles.

If two linked particles move in different directions, they will have a larger distortion term. If they move in the same direction, they will have a smaller distortion term and L i t denotes the set of particles linked to particle i in frame t.

### Table of Contents

The algorithm optimizes Eq. A system of equations is obtained by taking partial derivatives which the algorithm solves for dx i t and dy i t :. The dx i t and dy i t values produced by solving this system are added to the current particle positions x i t and y i t. Small groups clustering algorithm is always inspired by McPhail and Wohlstein hypothesize, who present the only objective measure known of in the social science literature to determine which people are traveling together through the scene.

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In their literature, groups in crowd are determined by the three test: 1 any two people who are within a fixed distance, 2 any two contiguous people are judged to have the same speed and 3 any two contiguous people traveling at the same speed whose directions of motion are the same. These tests have generally been applied by researchers who analyze video surveillance. Potential groups are identified in crowd regions using spectral clustering based on robust measurement to particle video trajectories.

Measurement: Taking into account the group-level crowd obstructed by neighboring pedestrian, the individual template tracking is not practical to operate. So the proposed measurement strategy not any longer rigidly adheres to traditional individual trajectory measurement. Particle trajectories similarity is analyzed in tracked crowd to judge the distribution of group people.

To detect group formation, the particles from crowds are tracked to measure the similarity with its neighbor across time. If two or more particles keep consistent similarity among them in a certain period of time, the method considers they belong to the same group. The similarity criterion concerned is not only the space distance and motion velocity distance but also appearance channel distance which is peculiar to video particle trajectory. The appearance channel especially in color and gradient channels have the character about the moderate insensibility to changes in lighting and reflectance which facilitates judging the particle trajectory in outdoor environment.

Denote the trajectory of a particle in the scene as a set of tuples s, v, c, t , where s is the position vector of the particle and the v is the motion velocity at frame t, c is the channel vector about particle appearance. In comparison with McPhail and Wohlstein frame-based test, the extended method is to an aggregated pairwise similarity measure between two trajectories over time:.

Compute the weight parameter w by overlap time and T max which is set to the value of the longer existing time between particle i and j. The others weight parameters are set along with video size change. Clustering algorithm: The identify groups algorithm based on a spectral clustering approach that starts with particle trajectory similarity measured in section A. In order to achieve more effectively clustering analysis, a diagonal matrix is constructed to group the particle trajectories, as shown in Table 1. The similarity S ij between particle p i and p j is computed by Eq.

Otherwise, the two clusters are considered negatively related and thus the location p i p j of adjacency matrix is set as 0. The adjacency matrix is demonstrated in Table 1. To summarize, starting from large number of particle trajectories, the similarity matrix of each other from three aspects, location, motion velocity and appearance channel is constructed to include all particle trajectories information.

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Then the spectral clustering uses the eigenvectors of the matrix to denote original data. In the end, it clusters them into k clusters via k-means. Compare to traditional clustering algorithm, such as K-means, it is added the step of reducing dimensions by calculation of the eigenvectors. It makes the algorithm more robust and better performance than traditional ones and it is much suitable to the complicated trajectory data.

The method has been tested on videos of some scenes captured in our campus, some are shown in Fig. In the test dataset Fig. Seen from the larger group, it is difficult to identify individual from each other and much harder to track with them by traditional temple tracking algorithm. By using video particle tracking algorithm, crowd are tracked and particle trajectories are presented as shown in Fig.

In the clustering algorithm, the basic parameters is generally required to tune for a given sequence, depending on the video frame size, the crowd density and the speed of individuals and the distance threshold in this test video sequences both are set to The clustered groups result can be obviously noticed. More results are shown in Fig. There are three groups walking in the surveillance view and two groups are very close in our view angle.

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In traditional distance cluster method, they are exceedingly judged to the same group in error. Identifying groups based on a spectral clustering approach is concerned not only the space distance and motion velocity distance but also appearance channel distance. This study describes a novel approach for detecting human groups in videos. The framework of detection and tracking algorithm can serve as a prior step for group clustering algorithm analysis.

The proposed algorithm involves crowd detection and tracking. Finding that extracting accurate and continuous trajectories in obstruct crowd is the key point for successful detection of human groups. It was found that particle trajectories in the algorithm of particle motion estimation in tracking crowd are much reliable.

Finally, analysis the character of trajectories in human crowd to cluster them based on spectral clustering algorithm. Experimental results obtained by using our test video sequences have shown that our system is effective in detect small group people in crowd for uncontrolled environment of surveillance videos.

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Search in Google Scholar. Information Technology Journal, DOI: Detection result of motion regions, a The different original frames and b The detected crowds are in blue color. The process of computing the particle trajectory, 1: Propagate, 2: Link and 3: Optimize using particle video.

Form the matrix Y from X by renormalizing each of X's rows to have unit length i. Treating each row of Y as a point in R k , cluster them into k clusters via k-means. Finally, assign the particle p i to cluster j if and only if row i of the matrix Y was assigned to cluster j. The experiment result of the first video sequence, a The motion crowd are detected from three different frame in the first video sequence, b Trajectories corresponding with a and c Clustering results show the different groups by two colors even if they are so closed.

Another video sequences are tested with our algorithm, a Detection results, b Corresponding trajectories and c Clustering results show the three different groups by three different colors. Chen, D. Huang, Motion-based unusual event detection in human crowds. Description with markdown optional :.

Higher is better for the metric. Uses extra training data. Data evaluated on. Optical Flow Estimation Edit. State-of-the-art leaderboards Add a result.