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1 2003 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.

2 LEARNING A MULTI-CAMERA TOPOLOGY T J Ellis, D Makris, J K Black Digital Imaging Research Centre, Kingston University, UK t.ellis@kingston.ac.uk Abstract We report an investigation to determine the topology of an arbitrary network of video cameras observing an environment. The topology is learnt in an unsupervised manner by temporal correlation of objects transiting between adjacent camera viewfields. We extract this information in two steps, firstly identifying the principal entry and exit zones associated with each camera view, and then establishing the correspondence or links between the exit zones of one camera to the entry zones of an adjacent one by accumulating evidence from many trajectory observations. A significant benefit of the method is that it doesn t rely on establishing correspondence between trajectories. In addition to generating the topological structure, the method also results in a measure of inter-camera transition times, which can be used to support predictive tracking across the camera network. 1. Introduction A typical video surveillance installation comprises a potentially large network of cameras that are used to maintain remote observation of the environment (e.g. a car park or shopping mall). The cameras are usually placed to maximise the spatial coverage and also to ensure adequate visibility of key locations such as doorways or vulnerable sites (e.g. automatic cash-teller machines - ATM s). A significant part of the current research effort in multi-camera video surveillance has focused on combining multiple views from cameras with overlapping fields-of-view (FOV), identifying the same object in each view with the aim of minimising the likelihood of losing track of the object. This is most often associated with the ability to maintain tracking as the object passes through occlusion or to compensate for poor target visibility, but multiple views can also help to increase the accuracy of the location estimation. However, less attention has been directed to the problem of establishing the correspondence between nonoverlapped cameras and determining the topology of the camera network. In most cases, non-overlapped cameras are more prevalent, given the desire to maximize the spatial coverage afforded by the camera network. Such information can of course be specified manually following the installation of the camera system, perhaps linked to an existing geometric model, such as a floor plan. However this approach is inflexible, non-adaptive and subject to operator error. Knowledge of the topology is important for enabling targets to be tracked as they move throughout the environment monitored by the camera network. It can be used to assist the tracking of targets as they move between adjacent camera views, supporting prediction of target re-appearance. In addition, for a security surveillance application, it is of benefit to establish a full track history of each target in the environment, allowing the activity (and ultimately, the behaviour) of the target to be interpreted from its complete trajectory. In order to integrate the track data from multiple cameras, it is useful to consider the visibility of targets within the entire environment, and not just each camera view separately. Four region visibility criteria can be identified (see figure 1): 1. visible FOV (field-of-view) - this defines the regions that an individual camera will image. In cases where the camera view extends to the horizon, a practical limit on the view range is imposed by the finite spatial resolution of the camera. 2. camera FOV - encompasses all the regions within the camera view, including occluded regions. 3. network FOV - encompasses the visible FOV's of all the cameras in the network. Where a region is occluded in one camera s visible FOV, it may be observable within another FOV. 4. virtual FOV - covers the network FOV and all spaces in between the camera FOV s within which the target must exist. The boundaries of the system represent locations from which previously unseen targets can enter the network. The aim of this research is to automatically recover the topology of the network FOV, and to determine some of the parameters of the virtual FOV, in particular, the expected disappearance period when targets undergo occlusion. In section 2 we consider several alternative approaches to tackling the task, and review related research. In section 3 we develop an approach based on temporal correlation, using an EM-based solution and a

3 statistically-derived peak detection threshold. Section 4 presents results from applying the algorithm to trajectory data acquired from an online camera network comprising 6 video cameras. Section 5 provides a brief discussion of the benefits of our approach, and section 6 gives some conclusions and identifies some areas for further work. camera location building viewfield overlapped viewfield Figure 1. Visibility criteria for camera network. 2. Alternative approaches For overlapped cameras, viewpoint registration can be achieved by a variety of methods. Cameras can be calibrated to a common world coordinate system by detecting visible landmarks with known 3D coordinates. As a consequence of the wide inter-camera baseline typically involved in outdoor surveillance placement, automatic detection of corresponding landmarks can be challenging, particularly for complex scenes, and manual correspondence is commonly undertaken. An alternative to camera calibration allows the correspondence of the common ground plane between pairs of cameras using the homography. The homography can be learnt by observing temporally co-incident events, and then estimating the spatial transformation needed to bring the cameras into correspondence (e.g. see [1]). There are a number of approaches we might use to automatically determine the connectivity or spatial adjacency of the camera network, for both overlapped and non-overlapped cameras. An obvious method would be to extend the single camera tracking algorithm across multiple views. However, in a busy environment where many objects are being tracked simultaneously, the main problem lies in establishing the correct correspondence. This would demand a means of unambiguously identifying objects as they leave one camera view and recognising the same object as it enters the adjacent view. This might be achieved if the system were able to select highly distinctive targets, ensuring that only easilytracked subjects were used in establishing the connectivity. An alternative solution would be to calibrate the system by having only a single target move at a steady pace around all the typical paths in the environment, allowing the system to learn all the connections without ambiguity. Whilst such an approach is attractive in its simplicity, it has several drawbacks for a real surveillance system. Firstly, it requires an explicit setup phase in which this calibration is undertaken. If any of the cameras are moved (deliberately or accidentally) the system will need recalibration. Secondly, it cannot be applied to pre-recorded video data, where there is no access to the site prior to the video analysis. Thirdly, it fails to provide statistics on the frequency and variability of traffic transiting between the camera views. This correspondence-based approach has been used by a number of other researchers. Huang and Russell [3] describe an algorithm for corresponding vehicles traveling along a motorway between a pair of widely separated cameras. They use spatial, temporal and appearance features of tracked objects in one view to match to those appearing after some expected transition period in the next view. Javed et al [4] have used a similar approach, applying it to the task we study in this paper (i.e. a non-overlapping multi-camera network). They correspond individual tracks between camera views without explicitly identifying entry and exit zones and can generate a consistent labelling of tracked objects. However, they apply it to a much simpler environment, using only small numbers of observations to validate the operation. Finally, Stauffer [11] has considered the problem automatically recognizing common regions in overlapping camera views using the rich information from many track correspondences across multiple cameras and computing the camera homography. A second paper [10] considers the detection of entry and exit zones (which he refers to as source and sinks), but these are restricted to identifying the links within a single camera view. A second possibility is to use a 3D calibration of the cameras in the network with a common world co-ordinate system. In this case it is possible to determine the geometric relationship between adjacent cameras, and allow the calculation of minimum length path differences between two views. However, this approach suffers from lack of knowledge of the actual paths that are taken by moving objects. It would be beneficial to combine this calibration information with a semantically-labelled geometric (CAD) model of the environment, from which actual path lengths might be computed, but this compromises the aim to create an adaptive online system. If a calibration of the camera network has already been undertaken, it is possible to use a 3D (ground plane) predictive tracker to treat the inter-camera regions as an occlusion. An example of this is shown in figure 1, where the pedestrian is tracked on the ground plane using a 3D (linear) Kalman filter [1]. As can be seen in the figure,

4 even though the target trajectory in the occluded region is not linear, the noise model of the filter can compensate for minor violations to the model. (Note: the kink in the longer red trajectory is not associated with a decision change by the linear tracker, but as a consequence of back-projecting the trajectory, given where the object appeared in the second camera s FOV.) Y 320 (m etr es) track1 track2 Trajectory Prediction Between Camera Field of Views camera-2 camera X (metres) Figure 2. a), b) Two adjacent camera viewpoints; c) ground plane map with two superimposed trajectories; d) views and trajectories re-projected onto ground plane. An alternative approach, which we develop in this paper, eliminates the requirement to correspond individual tracks and hence is not susceptible to failure of the recognition capability of the tracking algorithm. It achieves this by searching for a consistent temporal correlation of targets leaving one camera FOV and appearing in that of another. This approach requires no pre-knowledge of the camera network geometry or the environment, but does assume the targets maintain a similar speed when un-observed. Whilst it would be possible to establish the camera network topology through only a single, reliable observation (e.g. as for the calibration walker described above), in practice we wish to determine a measure of confidence in using the inherently noisy and un-reliable track data by accumulating statistics from many observations. As a consequence, we adopt a strategy that eliminates the need to correspond individual trajectories by learning over a long time period using a large number of trajectories. 3. Methodology We adopt a two stage algorithm for detecting connected zones first detecting entry and exit zones, then temporally correlating the disappearance and reappearance of tracked objects between views. The entry and exit zones correspond to regions in the image where the majority of targets appear in or disappear from the camera FOV. These zones typically coincide with the borders of the image, but are also associated with long-term occlusions created by buildings and other large structures that objects can move behind. The advantage of creating these zones is that the second step (identifying the temporal correlations) need only be applied to a small number of discrete regions. In addition, we are also able to determine the popularity (i.e. frequency of use) of the links. We use a statistical analysis to identify the topology of the camera network and to support tracking within the blind areas of the Virtual FOV. This statistical analysis is based on trajectory data derived from single tracking modules attached to each camera of the system. Entry/exit zones for each camera FOV are learnt automatically using the EM algorithm [9] and are also used to construct an activity-based semantic scene model [7]. The zones are created by clustering the spatial distributions of track starting coordinates (i.e. the first observation associated with each trajectory) and the finishing coordinates, for entry and exit zones respectively. The method is able to reject incorrect zones that are associated with noisy trajectory data, which result from failure of the single camera tracker and from spurious motion activity in the scene. We represent all the entry/exit zones of the camera FOV s collectively as a network of nodes (similar to the topological representation in [7]). The links of the network represent transitions between the entry/exit zones, which are either visible (through the Network FOV), or invisible (through the blind areas). A markovian chain or a HMM can be overlaid on the topological representation [8], to provide a probabilistic framework for activity analysis and long-term prediction. Visible links are automatically learnt [6], [7] using trajectories derived by a single-camera tracker [12] or overlapped multiple camera tracker [1]. Visible links are physically represented in spatial terms (distance). However, the challenge is to identify the invisible links and this is the focus of the method proposed in this paper. Invisible links are estimated in temporal terms and more specifically by pdfs that shows the distribution of the target transition periods through the blind areas. When targets move along an invisible link from zone i to zone j, the surveillance system observes them disappearing at zone i with rate d i (t) and re-appearing at zone j with rate r i (t). A correlation of the two signals d i (t), r j (t), can indicate both the existence of the link and the transition time pdf.

5 environment is shown in figure 3. Figure 4 shows the camera views re-projected onto a common ground plane Figure 3. Ground plane depiction of the 6 camera network shown in results section. Major entry and exit zones indicated by blue ellipses. We implement the correlation of the signals by accumulating co-occurrences of disappearing events at zone i and appearing events at j, in a discrete-time buffer C ij (τ). More specifically, for a given disappearing event at zone i at time t 1, we check for appearing events at zone j at time t 2, t 2 [t 1 -T,t 1 +T], where T is a parameter that defines the time-search window. When such an event is detected, then C ij(τ) is updated: C t t +.5 C t t ij ( ) ij ( 2 1 ) + 1 Time-buffers C ij (τ) are estimated for each possible pair i, j [1, N], where N is the total number of entry/exit zones from all the camera visible FOVs. If a link exists, then the C ij (τ) function has a clear peak which indicates the most popular time-transition value. We detect possible links using two different methods: a) a statistical test which detects peak values based on a threshold estimated from the mean and variance of the transition time pdf, according to: thr = avg C τ + ω std C τ (1) ( ( )) () ij ( ) The weight, ω, is determined empirically, because the noise is not always well-modelled as white. b) by fitting K Gaussian functions to the C ij (τ), using EM. One of the Gaussian s is expected to represent the actual transition-time distribution, while the remaining K-1 Gaussian s represent noise resulting from random cooccurrences. 4. Results We have applied the learning algorithm described in section 3 to a network of six video cameras distributed around a building. A ground-plane layout of the ij Figure 4. Ground plane re-projection of the six camera views onto a common world coordinate ground plane. Figure 5. Detected entry zones. Note, vehicles travel on the left-hand side of the road.

6 Figure 5 and 6 show the entry and exit zones automatically identified from the trajectory analysis. Trajectories were gathered during a 12 hour daylit period, using 3203, 4250, 4894, 12746, 1451 and trajectories respectively from the cameras 1-6 (numbered raster-scan top left to bottom right). The zones are depicted with an ellipse plotted with the center and at one standard deviation. The colours have particular no significance. The zone detection has failed to detect two entry/exit regions in camera 1 view (bottom left and bottom right), though these have been found in the heavily overlapping camera 2 view. Similarly, the exit zone in the middle of camera 3 has been missed. ground plane distances shown in table 2 are generated from a camera calibration using ground survey data of visible scene landmarks. Figure 7. Distribution of trajectories exiting camera 3, zone 3 (right image) and entering camera 2, zone 1(left image). Histograms (identical) show distribution of temporal correlations. Left histogram shows peak detection threshold. Right histogram shows three gaussian mixture models fitted to distribution. Figure 6. Detected exit zones. Figure 7 shows the temporal distribution of trajectories exiting from camera 3, zone 3 and entering camera 2, zone 1, depicted in 7a and 7b (ellipses plotted in red). The peak detection threshold is plotted onto the distribution (7c), and is calculated at 31.7 from equation (1) in section 3. The weight value (w) is set empirically to a value of 4.0. The histogram (7c) plots the occurrence of over a time range of +/- 50 seconds from when the target was detected inside the exit zone. The second histogram (7d) shows the result of the gaussian mixture modeling of the pdf using EM. The mixture model generates a good fit to the peak, and less accurately to the noise. In comparison, the temporal correlation distribution shown in figure, taken from a road scene, shows that EM does not model the peak well. In general, the simpler peak detection algorithm had a significant detection performance advantage over the EM approach, and the results we present in tables 1 and 2 and figure 9 were generated using this method. The results corresponding to Figure 8. Temporal correlation distribution for road vehicle scene. EM generates a poor model fit in d). Table 1 summarises the results of the inter-camera correspondence for all the cameras and zones in the network. Matches have not been allowed for zones within the same camera view, as this generates many more matches (corresponding to the detection of the principal

7 routes within a single view, see [8]) and lack of space precludes their presentation here. As can be seen, the detected peaks are not especially sensitive to the computed threshold. The Time column shows the time difference associated with the peak. Zero values of the transition time corresponds to pairs where zones are overlapped in space. This can be verified in table 2, where it can be seen the inter-zone distance (associated with a zero time difference) have low values (< 4m). It can also be seen, for example, in camera 4, zone 1 and camera 6, zone 7 (c4z1 & c6z7, plotted in yellow) for which the camera ground plane data indicates are only 1.2m apart. Negative values indicate entry zones that feed into the exit zone (barring those from the same view, which have been excluded, as described earlier). Table 2 provides a validation of the corresponded zones. The column Distance represents the ground plane distance between ellipse centers of the entry and exit zones in each pair of camera views. This is calculated using the camera calibration parameters. The Speed column computes the average transition speed of trajectories between the two zones. The computed speeds are consistent with the pedestrian and vehicle traffic speeds that might be expected in these environments. In this case, the first two entries correspond to pedestrians, and the rest to vehicles. Table 1. Inter-camera zone correspondences identified. Paired colours used in figure 6 are: red, green, yellow, magenta, cyan, blue. Exit zone Entry zone thresh Peak size Time (sec) colou r c2z1 c3z R c3z3 c2z G c4z1 c6z Y c4z5 c6z M c5z3 c3z C c5z4 c3z B c5z4 c4z G c6z3 c4z R c6z3 c4z G c6z4 c4z B c6z4 c5z Y c6z7 c4z M c6z7 c4z C Figure 8 shows the full camera network, and the corresponded zones, which are marked in the same colour. In order to reduce the overall range of colours used, we cycle through them twice. Hence, to determine the actual correspondence the colour coding and entry/exit codes (shown in table 1) must be used to correctly interpret the correspondence. For example, the two narrow zones linking cameras 2 and 3 (shown in red and green ellipses) correspond to the bi-directional traffic between these two zones (c2z1 & c3z3 and c3z3 and c2z9). Figure 9. Paired entry and exit zones are shown in different colours, some of which are repeated (see table 1). Table 2. Validation of zone correspondences. Exit zone Entry zone Time dif (sec) Distanc e (m) Speed (m/s) c2z1 c3z c3z3 c2z c4z1 c6z c4z5 c6z c5z3 c3z c5z4 c3z c5z4 c4z c6z3 c4z c6z3 c4z c6z4 c4z c6z4 c5z c6z7 c4z c6z7 c4z

8 5. Discussion The methodology we have developed, based on a statistical analysis of the trajectory data, has several advantages compared to the more deterministic approach of the predictive tracker (e.g. the Kalman filter). The predictive tracker inevitably suffers from poor performance if the inter-connection path in the blind space is not a linear path. However, the temporal correlation is not constrained by this problem. In addition, the method assumes no prior information about the camera network. Another advantage of our method is that it is able to cope with multiple hypotheses, where an exit zone may connect to several entry zones. The equivalent predictive tracker would need a particle filter or similar. 6. Conclusions and Further Work We have presented a method to learn both the topological and temporal transition characteristics in a multi-camera network using only (un-reliable) trajectory data acquired independently from single view target tracking. The temporal correlation allows correspondence of zones without the need to correspond individual trajectories across cameras, and consequently provides a more robust detection. The algorithm (zone detection and correlation) operate entirely un-supervised, and are thus suitable for use in real surveillance systems that must operate autonomously over long periods of time. The solution learns typical transition times between camera views, enabling a simple modeling of these occlusion regions. One disadvantage of our the approach is that it does not account for targets that move at significantly different speeds for instance, a zone shared by both pedestrian and vehicle traffic. A solution that we are currently implementing is to compute not a temporal correlation, but a distance covered correlation between zones. In this case, we can correct the time delay between disappearance and reappearance using the target s known ground speed as it enters the exit zone. From an understanding of the multi-camera topology, we can now extend the semantically-rich, activity-related scene model (described in [8]) across the camera network, enabling activity detection and interpretation across the entire surveillance environment. [2] Grimson W E L, Stauffer C, Romano R, Lee L, Using adaptive tracking to classify and monitor activities in a site, CVPR98, Santa Barbara, USA, June [3] Huang T, Russell S, Object identification in a Bayesian context, in Proc. of IJCAI, [4] Javed O, Rasheed R, Shafique K, Shah M, "Tracking Across Multiple Cameras with Disjoint Views", 9th IEEE International Conference on Computer Vision (ICCV), Nice, France, October [5] Kettnaker V, Zabih R, Bayesian multi-camera surveillance, Proc. IEEE CVPR99, pp , [6] Makris D, Ellis T, Finding Paths in Video Sequences, British Machine Vision Conference 2001 (BMVC2001), vol.1, pp , Manchester, UK, September 10-13, [7] Makris D, Ellis T, Path Detection in Video Surveillance, Image and Vision Computing, vol.20/12, pp , October [8] Makris D, Ellis T, Spatial and Probabilistic Modeling of Pedestrian Behaviour, British Machine Vision Conference 2002 (BMVC2002), vol.2, pp , Cardiff, UK, September 2-5, [9] Makris D, Ellis T, Automatic Learning of an Activity-based Semantic Scene Model, IEEE International Conference on Advanced Video and Signal Based Surveillance 2003 (AVSS2003), pp , Miami, FL, USA, July [10] Stauffer C, Estimating Tracking Sources and Sinks, IEEE Conference on Computer Vision and Pattern Recognition 2003 (CVPR2003), Madison, Wisconsin, USA, June [11] Stauffer C, Tieu K, Automated multi-camera planar tracking correspondence modelling, IEEE Conference on Computer Vision and Pattern Recognition 2003 (CVPR2003), Madison, Wisconsin, USA, June [12] Xu M, Ellis T Partial Observation vs. Blind Tracking through Occlusion, Proc. BMVC, Cardiff, pp , September References [1] Black J, Ellis T, Rosin P Multi View Image Surveillance and Tracking, IEEE Workshop on Motion and Video Computing, Orlando, pp , December 2002.

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