Measuring Crowd Collectiveness

Transcription

1 Measuring Crowd Collectieness Bolei Zhou, Xiaoou Tang,3, and Xiaogang Wang,3 Department of Information Engineering, The Chinese Uniersity of Hong Kong Department of Electronic Engineering, The Chinese Uniersity of Hong Kong 3 Shenzhen Institutes of Adanced Technology, Chinese Academy of Sciences zhoubolei@gmail.com, xtang@ie.cuhk.edu.hk, xgwang@ee.cuhk.edu.hk Abstract Collectie motions are common in crowd systems and hae attracted a great deal of attention in a ariety of multidisciplinary fields. Collectieness, which indicates the degree of indiiduals acting as a union in collectie motion, is a fundamental and uniersal measurement for arious crowd systems. By integrating path similarities among crowds on collectie manifold, this paper proposes a descriptor of collectieness and an efficient computation for the crowd and its constituent indiiduals. The algorithm of the Collectie Merging is then proposed to detect collectie motions from random motions. We alidate the effectieness and robustness of the proposed collectieness descriptor on the system of self-drien particles. We then compare the collectieness descriptor to human perception for collectie motion and show high consistency. Our experiments regarding the detection of collectie motions and the measurement of collectieness in ideos of pedestrian crowds and bacteria colony demonstrate a wide range of applications of the collectieness descriptor.. Introduction One of the most captiating phenomena in nature is the collectie motion of crowds. From bacterial colonies and insect swarms to fish shoal, collectie motions widely exist in different crowd systems and reflect the ordered macroscopic behaiors of constituent indiiduals. Many interdisciplinary efforts hae been made to explore the underlying principles of this phenomenon. Physicists treat crowds as sets of particles and use equations from fluid mechanics to characterize indiidual moements and their interactions [9]. Behaioral studies show that complex crowd behaiors may result from repeated simple interactions among its constituent indiiduals, i.e., indiiduals locally coordi- Data and codes are aailable at A) B) Figure. A) Collectie motions of human crowd, fish shoal, and bacterial colony. B) Spatially coherent structures, i.e., Collectie Manifold, emerging in these crowds. Since indiiduals in a crowd system only coordinate their behaiors in their neighborhood, indiiduals at a distance may hae low elocity correlation een though they are on the same collectie manifold. An example of this is the red indiidual and the green indiidual. Thus, accurately measuring the collectieness of crowd and its constituent indiiduals is challenging. Colored dash links represent neighborhoods. nate their behaiors with their neighbors then the crowd is self-organized into collectie motion without external control [, 7]. Meanwhile, animal aggregation is considered as an eolutionary adantage for species surial, since the integrated whole of indiiduals can generate complex patterns, quickly process information, and engage in collectie decision-making []. One remarkable obseration of collectie motions in different crowd systems is that some spatially coherent structures often emerge from the moements of crowd, such as the arch-like macro structures in the human crowd, the fish shoal and the bacterial colony shown in Fig.. We refer to the spatially coherent structure of collectie motion as Collectie Manifold. Fig. illustrates one important structural property of collectie manifold: behaior consistency remains high among indiiduals in local neighborhood, but 3

2 low among those that are far apart, een on the same collectie manifold. In fact, indiiduals in crowds only hae limited local sensing range, and often base their moements on locally acquired information such as the positions and motions of their neighbors. Some empirical studies hae explored the importance of topological relations and information transmission among neighboring indiiduals in crowd []. Howeer, there is a lack of quantitatie analysis of this structural property of crowds. Collectieness describes the degree of indiiduals acting as a union in collectie motion. It depends on multiple factors, such as the decision making of indiiduals and crowd density. Quantitatiely measuring this uniersal property and comparing it across different crowd systems are important in order to understand the general principles of arious crowd behaiors. Furthermore, this measurement plays important roles in many applications, such as monitoring the transition of a crowd system from disordered to ordered s- tates, studying the correlation between collectieness and crowd properties such as population density, characterizing the dynamic eolution of collectie motion, and comparing the collectieness of different crowd systems. Most existing crowd sureillance technologies [, 7] cannot compare crowd behaiors across different scenes because they lack uniersal descriptors with which to characterize crowd dynamics. Monitoring collectieness is also useful in crowd management, control of swarming desert locusts [], preention of disease spreading [], and many other fields. Howeer, this important property lacks accurate measurements. Existing works [3, 9] simply measured the aerage elocity of all the indiiduals to indicate the collectieness of the whole crowd, which is neither accurate nor robust. The collectieness of indiiduals in crowd is also illdefined. In this paper, by quantifying the topological properties of collectie manifold of crowds, we propose a descriptor of collectieness for crowd systems as well as their constituent indiiduals. Based on collectieness, an algorithm called Collectie Merging is proposed to detect collectie motions from random motions. We alidate the effectieness and robustness of the proposed collectieness on selfdrien particles [9]. It is further compared to human motion perception for collectie motion on a new ideo dataset with ground-truth. In addition, our experiments of detecting collectie motions and measuring crowd collectieness in ideos of pedestrian crowds and bacterial colony demonstrate the wide applications of the collectieness descriptor... Related Works Scientific studies on collectie motion in crowd systems can be categorized as empirical or theoretical; a compact reiew can be found in []. In the computer ision community, crowd motion analysis has become an actie research Cardinality of a set. [.] i i-th element of a ector. e ector with all elements as. W n n power of a matrix W. max(x, y) maximum alue of x and y. Table. Notations used in the paper. topic in recent years. Many approaches hae focused on segmenting the motion patterns and learning the pedestrian behaiors. For example, Rabaud et al. [] and Zhou et al. [] detected independent/collectie motions for object counting and clustering. Lin et al. [] and Ali et al. [] segmented motion fields generated by crowds. Zhou et al. [7] used a mixture of dynamic systems to learn pedestrian dynamics and applied it to crowd simulation. There are other works of crowd behaior analysis on sureillance applications, such as abnormal actiity detection [3, ] and semantic region analysis [, ]. Kratz et al. [] proposed efficiency to measure the difference between the actual motion and intended motion of pedestrians for tracking and abnormality detection. Howeer, none of the aboementioned measured the collectieness of crowd behaiors or explored its potential applications.. Measuring Collectieness A crowd is more than a gathering of indiiduals. Under certain circumstances, indiiduals in a crowd are organized into a unity with different leels of collectie motions. Thus, crowd collectieness should be determined by the collectieness of its constituent indiiduals, which reflects the similarity of the indiidual s behaior to others in the same crowd system. We introduce collectieness in a bottom-up manner: from behaior consistency in neighborhoods of indiiduals to that among all pairwise indiiduals, then from indiidual collectieness to crowd collectieness... Behaior Consistency in Neighborhood We first measure the similarity of indiidual behaiors in neighborhood. When indiidual j is in the neighborhood of i, i.e., j N (i) at time t, the similarity is defined as w t (i, j) = max(c t (i, j), ), () where C t (i, j) is the elocity correlation at t between i and j. N is defined as K-nearest-neighbor, motiated by existing empirical studies of collectie motion, which hae shown that animals maintain local interaction among neighbors with a fixed number of neighbors on topological distance, rather than with all neighbors within a fixed spatial distance []. Thus, w t (i, j) [, ] measures an indiidual s behaior consistency in a neighborhood. This pairwise similarity would be unreliable if two indiiduals are not neighbors because of the property of collectie manifold 3

3 illustrated in Fig.B. A better behaior consistency based on the structural property of collectie manifold is proposed below... Behaior Consistency on Collectie Manifold Since similarity cannot be accurately estimated when t- wo indiiduals are at a distance, we propose a new pairwise similarity based on an important topological structure of collectie manifold: paths, which represent the connectiity of the network associated with a graph []. In crowd systems, paths hae important roles in information transmission and communication among constituent indiiduals. Thus, path-based similarity can better characterize the behaior consistency among indiiduals in a crowd. Let W be the weighted adjacency matrix of the graph associated with a crowd set C, where an edge w t (i, j) is the similarity between indiidual i and j in its neighborhood defined in Eq.. Let γ l = {p p... p l } (p = i, p l = j) denote a path of length l through n- odes p, p,..., p l on W between indiidual i and j. Then ν γl = l k= w t(p k, p k+ ) is defined as the path similarity on a specific path γ l. Since there can be more than one path of length l between i and j, let the set P l contain all the paths of length l between i and j; then the l-path similarity is defined as ν l (i, j) = γ l P l ν γl (i, j). () ν l (i, j) can be efficiently computed with Theorem. Theorem. ν l (i, j) is the (i, j) entry of matrix W l..3. Indiidual Collectieness from Path Similarity Since l-path similarity ν l (i, j) measures the behaior consistency between i and j at l-path scale, we define the indiidual collectieness of indiidual i at l-path scale as ϕ l (i) = j C ν l (i, j) = [W l e] i. (3) Fig.B plots the aerage ϕ l (in log scale) with l = 3 in a synthetic collectie crowd shown in Fig.A. The alue of aerage ϕ l exponentially increases with l, because the number of paths between two nodes in a well connected graph increases exponentially with the path length. To further measure crowd collectieness, we should integrate the indiidual collectieness at all path scales; that is, {ϕ,..., ϕ l,..., ϕ }. Howeer, due to the exponential increase of ϕ l with l shown in Fig.B, indiidual collectieness at different path scales cannot be directly summed. Therefore, we define a generating function to integrate all path similarities. =. =.9.9 φ z l φl A) B) l 3 C) l 3 Figure. A) Synthetic crowd from Self-Drien Particles in collectie motion (details of SDP are gien in Section 3). B) Plot of aerage ϕ l (in log scale) with l. C) Regularization of path similarity. Indiidual collectieness at lower l-path scales make a greater contribution to the oerall indiidual collectieness... Crowd Collectieness with Regularization Generating function regularization is used to assign a meaningful alue for the sum of a possibly diergent series [7]. There are different forms of generating functions. We define the generating function for the l-path similarities as ϖ i,j = z l ν l (i, j), () l= where z is a real-alued regularization factor, and z l can be interpreted as the weight for l-path similarity. z < and cancels the effect that ϕ l exponentially increases with l. ϖ i,j can be computed with Theorem. Theorem. ϖ i,j is the (i, j) entry of matrix Z, where. ρ(w) denotes the spectral radius of matrix W. Indiidual collectieness from the generating function regularization on all the path similarities can be written as Z = (I zw) I and < z < ρ(w) ϕ(i) = z l ϕ l (i) = [Ze] i. () l= In Fig.C, we let z =.9 ρ(w) and plot the aerage zl ϕ l which approaches as l increases. The summation of regularized indiidual collectieness from all path scales conerges. z controls the conergence rate and the relatie contributions of path similarities with different lengths to ϕ. The crowd collectieness of a crowd system C is then defined as the mean of all the indiidual collectieness, which can be explicitly written in a closed form as = C C i= ϕ(i) = C e ((I zw) I)e. () captures the structural property of the whole dataset. Such structure-based descriptors are also effectiely used in general data clustering [, 3]. 3. Properties of the Collectieness We derie some important properties of collectieness. 33

4 Algorithm Collectie Merging INPUT: {x i, i i C} t. :Compute W from K-NN using Eq.. :Z = (I zw) I. 3:Set the entry Z(i, j) to if Z(i, j) κ, otherwise to. :Extract the connected components of the thresholded Z. Property. (Strong Conergence Condition) Z conerges when z < K. It is computationally expensie to choose z by comparing it with ρ(w), especially for a large crowd system, since we need to compute the eigenalues of W to get ρ(w) with complexity O(n 3 ). According to Property, the alue of z can be determined without computing ρ(w). Property. (Bounds of ) zk zk, if z < K. The equality stands when W = A, where A is the adjacency matrix from K-nearest-neighbor. W = A indicates that there are perfect elocity correlations among neighbors; that is, w t (i, j) = if j N (i) for any i, which means that all the constituent indiiduals in neighborhood moe in the same direction. For simplicity, in most of our experiments we let K = and z =., so the upper bound of is. Relations among, K and z are briefly discussed in Section.3. Property 3. (Upper bound of entries of Z) ϖ i,j < z zk, for eery entry (i,j) of Z. This property will be used in the following algorithm for detecting collectie motion patterns from clutters.. Collectie Motion Detection Based on the collectieness descriptor, we propose an algorithm called Collectie Merging to detect collectie motions from time-series data with noises (see Algorithm ). Gien spatial locations x i and elocities i of indiiduals i C at time t, we first compute W. By thresholding the alues on Z, we can easily remoe outlier particles with low collectieness and get the clusters of collectie motion patterns as the connected components from thresholded Z. As for the threshold κ, according to the bound in Property 3 we let κ = αz zk where. < α <.. Based on the accurate measurement of collectieness, this four-lined algorithm can be implemented in real time. It has potential applications in time-series clustering and actiity analysis. In the experiment section, we demonstrate its effectieness for detecting collectie motions in arious ideos.. Ealuation on Self-Drien Particles We take the Self-Drien Particle model (SDP) [9] to e- aluate the proposed collectieness, because SDP has been used extensiely for studying collectie motion and shows high similarity with arious crowd systems in nature [, ]. Importantly, the groundtruth of collectieness in SDP is.7 =. =... Frame No. Frame Frame Figure 3. Emergence of collectie motion in SDP. At the beginning, is low since the spatial locations and moing directions of indiiduals are randomly assigned. The behaiors of indiiduals gradually turn into collectie motion from random moements, and accurately reflects the phase transition of crowd dynamics. Here K =, z =., and η =. The upper bound of is. known for ealuation. SDP was firstly proposed to inestigate the emergence of collectie motion in a system of particles. These simple particles are drien with a constant speed, and the directions of their elocities are updated to the aerage direction of the particles in their neighborhood at each frame. It is shown that the leel of random perturbation η on the aligned direction in neighborhood would cause the phase transition of this crowd system from disordered moements into collectie motion. The update of elocity direction θ for eery indiidual i in SDP is θ i (t + ) = θ j (t) j N (i) + θ, (7) where θ j j N (i) denotes the aerage direction of elocities of particles within the neighborhood of i, θ is a random angle chosen with a uniform distribution within the interal [ ηπ, ηπ]. η tunes the leel of alignment... Crowd Collectieness of SDP As shown in Fig.3, we compute crowd collectieness at each time t. monitors the emergence of collectie motion oer time. At initialization, the spatial locations and elocity directions of all the particles are randomly assigned. The crowd gradually turns into the state of collectie motion. accurately records this phase transition. As η increases, particles in SDP become disordered. As shown in Fig., accurately measures the collectieness of crowd systems under different leels of random perturbation η. For a comparison, Fig.B plots the aerage normal- i i ized elocity = N N i=, which was commonly used as a measure of collectieness in existing works [3, 9]. From the large standard deiation of under multiple simulations with the same η, we see that is unstable and sensitie to initialization conditions of SDP. On the contrary, shows its robustness on measuring crowd collectieness. In our implementation of SDP, the absolute alue of elocity =.3, the number of indiiduals N =, and interaction radius r =. Experimental results in [9] hae shown that these three parameters only hae a marginal effect on the general behaiors of SDP. 3

5 ..... A).... η B) =.9 =. η η = =. =. η=. Figure. A) and with increasing η. The bars indicate the standard deiations of these two measurements. The large deiations of show that is unstable and sensitie to initialization of SDP. At each η, simulation repeats for times. B) For a low η, all the indiiduals are in a global collectie motion, and is close to the upper bound. For a relatiely larger η, indiiduals form multiple clusters of collectie motions. For a high η, indiiduals moe randomly and is low. Frame Frame A) φ B).... φ Figure. A) Two frames of the mixed-crowd system and their histograms of indiidual collectieness. After a while, self-drien particles are organized into clusters of collectie motions. The histogram of ϕ t is clearly separated into two modes. B) By remoing particles with indiidual collectieness lower than., we can extract self-drien particles in collectie motions. Blue and red points represent self-drien particles and outliers. The number of outliers is equal to that of self-drien particles and η =... Collectieness in Mixed Crowd Systems SDP assumes that all the indiiduals are homogeneous. Studies on complex systems [] hae shown that indiiduals in most crowd systems in nature are inhomogeneous. To ealuate the robustness of our collectieness descriptor, we extend SDP to a mixed-crowd model by adding outlier particles, which do not hae alignment in neighborhoods and moe randomly all the time. We measure indiidual collectieness in this mixed-crowd system. As shown in Fig.A, indiiduals are randomly initialized at the start, so the histogram of indiidual collectieness has a single mode. When self-drien particles gradually turn into clusters of collectie motions, there is a clear separation between two modes in the histogram of indiidual collectieness. By remoing indiiduals with collectieness smaller than., we can effectiely extract collectiely moing self-drien particles from outliers as shown in Fig.B. =. =.7 = 33. =. = 3. =.9 l.... zlφ A) zlφ l l l 3 l K=3, z=.3 K=, z=. K=, z=.3 K=, z=. K=, z=.3 K=, z=. zlφ B).... η C) l.... K= K= K= Figure. A) Regularized indiidual collectieness on l-path scale z l ϕ l as η = and z = at three different leels of collectie K motions. In each diagrams, the left-hand side shows the aerage z l ϕ l with l = 3 and the right-hand side shows the isualization of all the alues of z l ϕ l (i) with l = 3 and i =. Since the conergence condition is not satisfied, become unstable when SDP is in a high leel of collectie motion. B) with increasing η at different K and z in SDP. C) Gien a fixed K, the upper bound of grows fast when z approaches to, which K makes unstable..3. Conergence Condition of Collectieness Property shows that Z conerges when z < K. What happens if z K? We let z = K and plot the regularized indiidual collectieness of l-path scales [zϕ, z ϕ,..., z l ϕ l ] in Fig.. As the SDP gradually turns into collectie motion, z l ϕ l with large l-path scale approaches to, which makes l= zl ϕ l non-conergent, and crowd collectieness unstable. There are two parameters z and K for computing collectieness in practical applications. K defines the size of neighborhood and z makes the series summation conerge. K affects similarity estimation in neighborhood. A large K makes the estimation inaccurate, while a small K is sensitie to noise. Empirically it could be % % of C. In all our experiments, we fix K =. z is constrained by K in Property. With different K and z, the upper bound of aries, as shown in Fig.B. With a larger upper bound, the deriatie d dη is larger and the measurement is more sensitie to the change of crowd motion. can also be re-scaled to [, ] diided by the upper bound. Thus, by tuning z and K we can control the sensitiity of collectieness in practical applications. The upper bound of grows quickly when z approaches to K, which makes the alue of unstable, as shown in Fig.C. The ideal range is. K < z <. K. z.... 3

6 Score= =.3 =. Score= =.9 =. =. =. =.3 =. =.9 =. =. =.9 =. =. =. =. =. =. =.73 =.7 =.7 =.79 Low score =. =.7 Score= =.9 =. Score= =. =.9 Score=7 =.7 =.7 Score=9 =. =. Score=9 =.7 =.7 Medium Score=7 High A). Figure 7. Histogram of collectie scores of all the ideos in the Collectie Motion Database and some representatie ideo frames, along with their collectie scores,, and. The three rows are from the three collectieness categories.... B) Frame No. Figure 9. A) Detecting collectie motions from crowd ideos. Keypoints with the same color belong to the same cluster of collectie motion. Red crosses are detected outliers. B) Monitoring crowd dynamics with collectieness. Two frames indicate the representatie states of the crowd.. Further Ealuation and Applications We ealuate the consistency between our collectieness and human perception, and apply the proposed descriptor and algorithm to arious ideos of pedestrian crowds and bacterial colony. ness for this ideo. We compute using the same motion features as a comparison baseline. Fig.7 shows the collectie scores,, and for some representatie ideos. Fig.A scatters the collectie scores with and of all the ideos, respectiely. There is a high correlation between collectie scores and, and the proposed collectieness is consistent with human perception. The second is the classification accuracy based on the collectieness descriptor. We diide all the ideos into three categories by majority oting of subjects rating, and then ealuate how the proposed collectieness descriptor can classify them. Histograms of and for the three categories are plotted effectiely in Fig.B. has better discrimination capability than. Fig.C plots the ROC cures and the best accuracies which can be achieed with all the possible decision boundaries for binary classification of high and low, high and medium, and medium and low categories based on and, respectiely. can better classify different leels of collectie motions than, especially on the binary classification of high-medium categories and medium-low categories of ideos. It indicates our collectieness descriptor can delicately measure the dynamic state of crowds. Classification failures come from two sources. Since there are gray areas between high-medium and medium-low collectie motions, some samples are een difficult for humans to reach consensus and are also difficult to our descriptor. Meanwhile collectieness may not be properly computed due to tracking failures, projectie distortion and.. Human Perception for Collectie Motion To quantitatiely ealuate the proposed crowd collectieness, we compare it with human motion perception on a new Collectie Motion Database, and then analyze the consistency and correlation with human-labeled ground-truth for collectie motion. The Collectie Motion Database consists of 3 ideo clips from crowded scenes. clips are selected from Getty Image [], 97 clips are captured or collected by us. This database contains different leels of collectie motions with frames per clips. Some representatie frames are shown in Fig. 7. To get the groundtruth, subjects are inited to rate all ideos independently. A subject is asked to rate the leel of collectie motions in a ideo from three options: low, medium, and high. We propose two criteria to ealuate the consistency between human-labeled ground-truth and the proposed collectieness descriptor. The first is the correlation between the human scores and our collectieness descriptor. We count the low option as, the medium one as, and the high one as. Since each ideo is labeled by ten subjects, we sum up all the scores as the collectie score for this ideo. The range of collectie scores is [, ]. The histogram of collectie scores for the whole database is plotted in Fig.7. We compute the crowd collectieness at each frame using the motion features extracted with a generalized KLT (gklt) tracker deried from [], and take aeraged oer frames as the collectie3

7 Score Score A) Correlation=.7. Correlation=.9. 3 Low Medium High.... Low Medium High ROC cure: High-Low.... ROC cure: High-Medium.... ROC cure: Medium-Low. B).... C) D).... High-Low Best Accuracy Boundary High-Medium Best Accuracy Boundary....3 Medium-Low Best Accuracy Boundary Score= =. =. Score=9 =. =. Figure. A) Scatters of collectie scores with and for all the ideos. B) Histograms of and for the three categories of ideos. C) ROC cures and best accuracies for high-low, high-medium, and medium-low classification. D) Failure examples of collectieness. special scene structures. Two failure examples are shown in Fig.D. The computed collectieness in the two ideos is low because the KLT tracker does not capture the motions well due to the perspectie distortion and the extremely low frame rate, while all subjects gie high scores because of the regular pedestrian and traffic flows in the scenes... Collectie Motion Detection in Videos We detect collectie motions from ideos in the Collectie Motion Database. Collectie motion detection in crowd ideos is challenging due to the short and fragmented nature of extracted trajectories, as well as the existence of outlier trajectories. Fig.9A shows the detected collectie motions by Collectie Merging on nine ideos, along with their computed and. The detected collectie motion patterns correspond to a ariety of behaiors, such as group walking, lane formation, and different traffic modes, which are of a great interest for further ideo analysis and scene understanding. The estimated crowd collectieness also aries across scenes and reflects different leels of collectie motions in ideos. Howeer, cannot accurately reflect the collectieness of crowd motions in these ideos. Furthermore, the proposed crowd collectieness can be used to monitor crowd dynamics. Fig.9B shows an example in which the collectieness changes abruptly when two groups of pedestrians pass each other. Such eents indicate rapid phase transition of a crowd system or some critical point has been reached. They are useful for crowd control and scientific studies..3. Collectie Motions in Bacterial Colony In this experiment, we use the proposed collectieness to study collectie motions emerging in a bacterial colony. The wild-type Bacillus subtilis colony grows on agar substrates, and bacteria inside the colony freely swim on the agar surface. The real motion data of indiidual bacteri-. Correlation=.9 3 Frame No. Correlation=. A). Bacteria Number Bacteria Number B) 3 Frame No. C) =. =. =.7 Frame Frame 93 =. =.7 =.9 =.3 Frame 3 Frame 33 =. Figure. A) The crowd collectieness of the bacterial colony and the bacteria number change oer time; their correlation is high. B) The aerage normalized elocity of the bacterial colony and the bacteria number change oer time; their correlation is low. C) Representatie frames of collectie motion patterns detected by Collectie Merging and their and. Arrows with different colors indicate different clusters of detected collectiely moing bacteria. Red crosses indicate detected randomly moing bacteria. a comes from []. There are bacteria moing around at eery frame. Fig.AB plot and with the number of bacteria oer time. Fig.C shows representatie frames and collectie motion patterns detected by Collectie Merging. Crowd density was proed to be one of the key factors for the formation of collectie motion [, 9]. A lot of scientific studies are conducted to analyze their correlation. For the same type of bacteria in the same enironment, bacteria collectieness should monotonically increase with density. Fig.A shows that bacteria density has a much better correlation with than. Our proposed collectieness measurement has good potentials for scientific studies. 37

8 7. Conclusions and Future Work We hae proposed a collectieness descriptor for crowd systems as well as their constituent indiiduals along with the efficient computation. Collectie Merging can be used to detect collectie motions from randomly moing outliers. We hae alidated the effectieness and robustness of the proposed collectieness on the system of self-drien particles, and shown the high consistency with human perception for collectie motion. Further experiments on ideos of pedestrian crowds and bacteria colony demonstrate its potential applications in ideo sureillance and scientific s- tudies. As a new uniersal descriptor for arious types of crowd systems, the proposed crowd collectieness should inspire many interesting applications and extensions in future work. Indiiduals in a crowd system can moe collectiely in a single group or in seeral groups with different collectie patterns, een though the system has the same alue of. Our single collectieness measurement can be well extended to a spectrum ector of characterizing collectieness at different length scales. It is also desirable to enhance the descriptie power of collectieness by modeling its spatial and temporal ariations. The enhanced descriptor can be applied to cross-scene crowd ideo retrieal, which is difficult preiously because uniersal properties of crowd systems could not be well quantitatiely measured. Collectieness also proides useful information in crowd saliency detection and abnormality detection. This paper is an important starting point in these exciting research directions. Acknowledgment This work is partially supported by the General Research Fund sponsored by the Research Grants Council of Hong Kong (Project No. CUHK7 and CUHK7) and National Natural Science Foundation of China (Project No.7 and 99). The first author would like to thank Deli Zhao and Wei Zhang for aluable discussions and Hepeng Zhang for sharing bacteria data. 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