AUTO GMM-SAMT: An Automatic Object Tracking System for Video Surveillance in Traffic Scenarios

Abstract

A complete video surveillance system for automatically tracking shape and position of objects in traffic scenarios is presented. The system, called Auto GMM-SAMT, consists of a detection and a tracking unit. The detection unit is composed of a Gaussian mixture model- (GMM-) based moving foreground detection method followed by a method for determining reliable objects among the detected foreground regions using a projective transformation. Unlike the standard GMM detection the proposed detection method considers spatial and temporal dependencies as well as a limitation of the standard deviation leading to a faster update of the mixture model and to smoother binary masks. The binary masks are transformed in such a way that the object size can be used for a simple but fast classification. The core of the tracking unit, named GMM-SAMT, is a shape adaptive mean shift- (SAMT-) based tracking technique, which uses Gaussian mixture models to adapt the kernel to the object shape. GMM-SAMT returns not only the precise object position but also the current shape of the object. Thus, Auto GMM-SAMT achieves good tracking results even if the object is performing out-of-plane rotations.

1. Introduction

Moving object detection and object tracking are important and challenging tasks not only in video surveillance applications but also in all kinds of multimedia technologies. A lot of research has been performed on these topics giving rise to numerous detection and tracking methods. A good survey of detection as well as tracking methods can be found in [1]. Typically, an automatic object tracking system consists of a moving object detection and the actual tracking algorithm [2, 3].

In this paper, we propose Auto GMM-SAMT, an automatic object detection and tracking system for video surveillance of traffic scenarios. We assume that the traffic scenario is recorded diagonally from above, such that moving objects on the ground (reference plane) can be considered as flat on the reference plane. Since the objects in traffic scenarios are mainly three-dimensional rigid objects like cars or airplanes, we take advantage of the fact that even at low frame rates the shape of the 2D mapping of a three-dimensional rigid object changes less than the mapping of a three-dimensional nonrigid object. Although Auto GMM-SAMT was primarily desgined for visual monitoring of airport aprons, it can also be applied for similar scenarios like traffic control or video surveillance of streets and parking lots as long as the above mentioned assumptions of the traffic scenario are valid. As can be seen in Figure 1 the surveillance system combines a detection unit and a tracking unit using a method for determining and matching reliable objects based on a projective transformation.

Figure 1

Auto GMM-SAMT: a video surveillance system for visual monitoring of traffic scenarios based on GMM-SAMT.

The aim of the detection unit is to detect moving foreground regions and store the detection result in a binary mask. A very common solution for moving foreground detection is background subtraction. In background subtraction a reference background image is subtracted from each frame of the sequence and binary masks with the moving foreground objects are obtained by thresholding the resulting difference images. The key problem in background subtraction is to find a good background model. Commonly a mixture of Gaussian distributions is used for modeling the color values of a particular pixel over time [4–6]. Hence, the background can be modeled by a Gaussian mixture model (GMM). Once the pixelwise GMM likelihood is obtained, the final binary mask is either generated by thresholding [4, 6, 7] or according to more sophisticated decision rules [8–10]. Although the Gaussian mixture model technique is quite successful, the obtained binary masks are often noisy and irregular. The main reason for this is that spatial and temporal dependencies are neglected in most approaches. Thus, the method of our detection unit improves the standard GMM method by regarding spatial and temporal dependencies and integrating a limitation of the standard deviation into the traditional method. While the spatial dependency and the limitation of the standard deviation lead to clear and noiseless object boundaries, false positive detections caused by shadows and uncovered background regions so called ghosts can be reduced due to the consideration of the temporal dependency. By combining this improved detection method with a fast shadow removal technique, which is inspired by the technique of [3], the quality of the detection result is further enhanced and good binary masks are obtained without adding any complex and computational expensive extensions to the method.

Once an object is detected and classified as reliable, the actual tracking algorithm can be initialized. In [1] tracking methods are divided into three main categories: point tracking, kernel tacking, and silhouette tracking. Due to its ease of implementation, computational speed, and robust tracking performance, we decided to use a mean shift-based tracking algorithm [11], which belongs to the kernel tracking category. In spite of its advantages traditional mean shift has two main drawbacks. The first problem is the fixed scale of the kernel or the constant kernel bandwidth. In order to achieve a reliable tracking result of an object with changing size, an adaptive kernel scale is necessary. The second drawback is the use of a radial symmetric kernel. Since most objects are of anisotropic shapes, a symmetric kernel with its isotropic shape is not a good representation of the object shape. In fact if not specially treated, the symmetric kernel shape may lead to an inclusion of background information into the target model, which can even cause tracking failures. An intuitive approach of solving the first problem is to run the algorithm with three different kernel bandwidths, former bandwidth and former bandwidth ±10%, and to choose the kernel bandwidth which maximizes the appearance similarity (±10% method) [12]. A more sophisticated method using difference of Gaussian mean shift kernel in scale space has been proposed in [13]. The method provides good tracking results but is computationally very expensive. And both methods are not able to adapt to the orientation or the shape of the object.

Mean shift-based methods which are not only adapting the kernel scale but also the orientation of the kernel are presented in [14–17]. The method of [14] focuses on face tracking and uses ellipses as basic face models; thus it cannot easily be generalized for tracking other objects since adequate models are required. Like in [15] scale and orientation of a kernel can be obtained by estimating the second-order moments of the object silhouette, but that is of high computational costs. In [16] mean shift is combined with adaptive filtering to obtain kernel scale and orientation. The estimations of kernel scale and orientation are good, but since a symmetric kernel is used, no adaptation to the actual object shape can be performed. Therefore, in [17] asymmetric kernels are generated using implicit level set functions. Since the search space is extended by a scale, and an orientation dimension, the method simultaneously estimates the new object position, scale, and orientation. However the method can only estimate the objects orientation for in-plane rotations. In case of 3D or out-of-plane rotations none of the mentioned algorithms is able to adapt to the shape of the object.

Therefore, for the tracking unit of Auto GMM-SAMT we developed GMM-SAMT, a mean shift-based tracking method which is able to adapt to the object contour no matter what kind of 3D rotation the object is performing. During initialization the tracking unit generates an asymmetric and shape-adapted kernel from the object mask delivered by the previous units of Auto GMM-SAMT. During the tracking the kernel scale is first adapted to the current object size by running the mean shift iterations in an extended search space. The scale-adapted kernel is then fully adapted to the current contour of the object by a segmentation process based on a maximum a posteriori estimation considering the GMMs of the object and the background histogram. Thus, a good fit of the object shape is retrieved even if the object is performing out-of-plane rotations.

The paper is organzied as follows. In Section 2 the detection of moving foreground regions is explained while Section 3 describes the determination of reliable objects among the detected foreground regions. GMM-SAMT, the core of Auto GMM-SAMT, is presented in Section 4. The whole system (Figure 1) is evaluated in Section 5 and finally conclusions are drawn in Section 6.

2. Moving Foreground Detection

2.1. GMM-Based Background Subtraction

As proposed in [4] the probability of a certain pixel in frame having the color value is given by the weighted mixture of Gaussian distributions:

(1)

where is the color vector and the weight for the respective Gaussian distribution. is an -by- covariance matrix of the form , because it is assumed that the RGB color channels have the same standard deviation and are independent from each other. While the latter is certainly not the case, by this assumption a costly matrix inversion can be avoided at the expense of some accuracy. To update the model for a new frame it is checked if the new pixel color matches one of the existing Gaussian distributions. A pixel with color matches a Gaussian if

(2)

where is a user-defined parameter. If matches a distribution, the model parameters are adjusted as follows:

(3)

where is the learning rate and according to [6]. For unmatched distributions only a new has to be computed following (4):

(4)

The other parameters remain the same. The Gaussians are now ordered by the value of the reliability measure in such a way that with increasing subscript the reliability decreases. If a pixel matches more than one Gaussian distribution, the one with the highest reliability is chosen. If the constraint in (2) is not fulfilled and a color value cannot be assigned to any of the distributions, the least probable distribution is replaced by a distribution with the current value as its mean value, a low prior weight, and an initially high standard deviation and is rescaled.

A color value is regarded to be background with higher probability (lower ) if it occurs frequently (high ) and does not vary much (low ). To determine the background distributions a user-defined prior probability is used:

(5)

The rest distributions are foreground.

2.2. Temporal Dependency

The traditional method takes into account only the mean temporal frequency of the color values of the sequence. The more often a pixel has a certain color value, the greater is the probability of occurrence of the corresponding Gaussian distribution. But the direct temporal dependency is not taken into account.

To detect the static background regions and to enhance adaptation of the model to these regions, a parameter is introduced to measure the number of cases where the color of a certain pixel was matched to the same distribution in subsequent frames:

(6)

where is the distribution which matched the pixel color in the previous frame and is the current Gaussian distribution. If exceeds a threshold , the factor is multiplied by a constant :

(7)

The factor is now temporal dependent and is the initial user-defined . In regions with static image content the model is now faster updated as background. Since the method does not depend on the parameters and , the detection is also ensured in uncovered regions. In the top row of Figure 2 the original frame of sequence Parking_lot and the corresponding background estimated using GMMs combined with the proposed temporal dependency approach is shown. The detection results of the standard GMM method with different values of are shown in the bottom row of Figure 2. While the standard method detects a lot of either false positives or false negatives, the method considering temporal dependency obtains quite a good mask.

Figure 2

A frame of sequence Parking_lot and the corresponding detection results of the proposed method compared to the traditional method. First row: original frame (a) and background estimated by the proposed method with temporal dependency (α₀ = 0.001, s = 10, u_min = 15) (b). Bottom row: standard method with α = 0.001 (c) and α = 0.01(d).

2.3. Spatial Dependency

In the standard GMM method, each pixel is treated separately and spatial dependency between adjacent pixels is not considered. Therefore, false positives caused by noise-based exceedance of in (2) or slight lighting changes are obtained. Since the false positives of the first type are small and isolated image regions, the ones of the second type cover larger adjacent regions as they mostly appear at the border of shadows, the so-called penumbra. Through spatial dependency both kinds of false positives can be eliminated.

Since in the case of false positives the color value of is very close to the mean of one of the distributions, at least for one distribution a small value is obtained for . In general this is not the case for true foreground pixels. Instead of generating a binary mask we create a mask with weighted foreground pixels. For each pixel its weighted mask value is estimated according to the following equation:

(8)

The background pixels are still weighted with zero while the foreground pixels are weighted according to the minimum distance between the pixel and the mean of the background distributions. Thus, foreground pixels with a larger distance to the background distributions get a higher weight. To use the spatial dependency as in [18], where the neighborhood of each pixel is considered, the sum of the weights in a square window is computed. By using a threshold the number of false positives is reduced and a binary mask is estimated from the weighted mask according to

(9)

In Figure 3(b) part of a binary mask for sequence Parking_lot obtained by GMM method considering temporal as well as spatial dependency is shown.

Figure 3

Detection result of the proposed method with temporal dependency (a) compared to the proposed method with temporal and spatial dependencies (b) for sequence Parking_lot ( and ).

2.4. Background Quality Enhancement

If a pixel in a new frame is not described very well by the current model, the standard deviation of a Gaussian distribution modelling the foreground might increase enourmously. This happens most notably when the pixel's color value deviates tremendously from the mean of the distribution and large values of are obtained during the model update. The larger gets, the more color values can be matched to the Gaussian distribution. Again this increases the probability of large values of .

Figure 4 illustrates the changes of the standard deviation over time for the first 150 frames of sequence Street modeled by 3 Gaussians. The minimum, mean, and maximum standard deviations of all Gaussian distributions for all pixels are shown (dashed lines). The maximum standard deviation increases over time and reaches high values. Hence, all pixels which are not assigned to one of the other two distributions will be matched to the distribution with the large value. The probability of occurrence increases and the distribution will be considered as a background distribution. Therefore, even foreground colors are easily but falsely identified as background colors. Thus, we suggest to limit the standard deviation to the initial standard deviation value as demonstrated in Figure 4 by the continuous red line. In Figure 5 the traditional method (left background) is compared to the one where the standard deviation is restricted to the initial value (right background). By examining the two backgrounds it is clearly visible that the limitation of the standard deviation improves the quality of the background model, as the dark dots and regions in the left background are not contained in the right background.

Figure 4

Maximum, mean, and minimum standard deviation of all Gaussian distribution of all pixels for the first 150 frames of sequence Street .

Figure 5

Background estimated for sequence Street without (a) and with limited standard deviation (b). Ellipse marks region, where detection artefacts are very likely to occur.

2.5. Single Step Shadow Removal

Even though the consideration of spatial dependency can avert the detection of most penumbra pixels, the pixels of the deepest shadow, the so-called umbra, might still be detected as foreground objects. Thus, we combined our detection method with a fast shadow removal scheme inspired by the method of [3]. Since a shadow has no affect on the hue but changes the saturation and decreases the luminance, possible shadow pixels can be determined as follows. To find the true shadow pixels, the luminance change is determined in the RGB space by projecting the color vector onto the background color value . The projection can be written as . A luminance ratio is defined as to measure the luminance difference between and while the angle between the color vector and the background color value measures the saturation difference. Each foreground pixel is classified as a shadow pixel if the following two terms are both statisfied:

(10)

where is the maximum allowed darkness, is the maximum allowed brightness, and and are the maximum allowed angle separation for penumbra and umbra. Compared to the shadow removal scheme described in [3], the proposed technique supresses penumbra and umbra simultaneously while the method of [3] has to be run twice. More details can be found in [19].

3. Determination of Reliable Objects

After the GMM-based background subtraction it has to be decided which of the detected foreground pixels in the binary mask represent true and reliable object regions. In spite of its good performance the background subtraction unit still needs a few frames to adjust when an object, which has not been moving for a long time, suddenly starts to move. During this period uncovered background regions, also referred to as ghosts, can be detected as foreground. To avoid a tracking of these wrong detection results we have to distinguish between reliable (true objects) and nonreliable objects (uncovered background). Since it does not make sense to track objects which only appear in the scene for a few frames, these objects are also considered as nonreliabel objects.

The unit for determining reliable objects among the detected foreground regions consists mainly of a connected component analysis (CCA) and a matching process, which performs a projective transformation to be able to incorporate the size information as a useful matching criterion. Connected component analysis (CCA) is applied on the binary masks to determine connected foreground regions, to fill small holes of the foreground regions, and to compute the centroid of each detected foreground region. CCA can also be used to compute the area size of each foreground region. In general size is an important feature to descriminate different objects. But since the size of moving objects changes while the object moves towards or away from the camera, the size information obtained from the binary masks is not very useful. Especially in video surveillance systems which are operating with low frame rates like 3 to 5 fps the size of a moving object might change drastically. Therefore, we transform the binary masks as if they were estimated from a sequence which has been recorded by a camera with top view. Figure 6 shows the original and the transformed versions of two images and their corresponding binary masks.

Figure 6

Original frames and binary masks of sequence Airport (a) and the transformed versions (b). In the orginial binary masks the object size changes according to the movement of the objects, while in the transformed binary masks the object sizes stay more or less constant and the ratio of the object sizes is kept.

According to a projective transformation each pixel of the original view is projected onto the image plane of a virtual camera with a top view of the recorded scene. The direct link between a pixel in the original camera plane and its corresponding pixel in the camera plane of the virtual camera is given by

(11)

where is the transformation or homography matrix and is the th row of . To perform the projective transformation which is also called homography the according homography matrix is needed. The homography matrix can be estimated either based on extrinsic and intrinsic camera parameters and three point correspondences or based on at least four point correpondences. We worked with point correspondences only, which were chosen manually between one frame of the surveillance sequence and a satellite imagery of the scene. By estimating the vector product and regarding that we get a system of equations of the form , where is a matrix and ; see [20] for details. Since only two linear independent equations exist in , can be reduced to a matrix and the following equation is obtained:

(12)

If four point correspondences are known, the matrix can be estimated from (12) except for a scaling factor. To avoid the trivial solution the scaling factor is set to the norm . Since in our case always more than four point correspondences are known, one can again use the norm as an additional condition and use the basic direct linear transformation (DLT) algorithm [20] for estimating or the set of equations in (12) has to be turned into an inhomogeneous set of linear equations. For the latter one entry of has to be chosen such that . For example, with we obtain the following equations from (12):

(13)

where is an 8-dimensional vector consisting of the first 8 elements of . Concatenating the equations from more than four point correspondences a linear set of equations of the form of is obtained which can be solved by a least squares technique.

In case of airport apron surveillance or other surveillance scenarios where the scene is captured from a (slanted) top view position, moving objects on the ground can be considered as flat compared to the reference plane. Thus, in the transformed binary masks the size of the detected foreground regions almost does not change over the sequence, compare masks in Figure 6. Hence, we can now use the size for detecting reliable objects. Since airplanes and vehicles are the most interesting objects on the airport apron, we only keep detected regions which are bigger than a certain size in the transformed binary image. In most cases can also be used to distinguish between airplanes and other vehicles. After removing all foreground regions which are smaller than , the binary mask is transformed back into the original view. All remaining foreground regions in two subsequent frames are then matched by estimating the shortest distance between the centroids. We define a foreground region as a reliable object, if the region is detected and matched in subsequent frames.

The detection result of a reliable object already being tracked is compared to the tracking result of GMM-SAMT to check if the detection result is still valid; see Figure 1. The comparison is also used as a final refinement step for the GMM-SAMT results. In case of very similar object and background color the tracking result might miss small object segments at the border of the object, which might be identified as object regions during the detection step and can be added to the object shape. Also small object segments at the border of the object, which are actually background regions, can be identified and corrected by comparing the tracking result with the detection result. For objects, which are considered as realiable for the first time, the mask of the object is used to build the shape adaptive kernel and to estimate the color histogram of the object for generating the target model as described in Sections 4.1 and 4.2. After the adaptive kernel and target model are estimated, GMM-SAMT can be initialized.

4. Object Tracking Using GMM-SAMT

4.1. Mean Shift Tracking Overview

Mean shift tracking discriminates between a target model in frame and a candidate model in frame . The target model is estimated from the discrete density of the objects color histogram (whereas ). The probability of a certain color belonging to the object with the centroid is expressed as , which is the probability of the feature occuring in the target model. The candidate model is defined analogous to the target model; for more details see [21, 22]. The core of the mean shift method is the computation of the offset from an old object position to a new position by estimating the mean shift vector:

(14)

where is a symmetric kernel with bandwidth defining the object area and is the weight of which is defined as

(15)

where is the histogram bin index function and is the impulse function. The similarity between target and candidate model is measured by the discrete formulation of the Bhattacharya coefficient:

(16)

The aim is to minimize the distance between the two color distributions as a function of in the neighborhood of a given position . This can be achieved using the mean shift algorithm. By running this algorithm the kernel is recursively moved from to according to the mean shift vector.

4.2. Asymmetric Kernel Selection

Standard mean shift tracking is working with a symmetric kernel. But an object shape cannot be described properly by a symmetric kernel. Therefore, the use of isotropic or symmetric kernels will always cause an influence of background information on the target model, which can even lead to tracking errors. To overcome these difficulties we are using an asymmetric and anisotropic kernel [17, 21, 23]. Based on the object mask generated by the detection unit of Auto GMM-SAMT an asymmetric kernel is constructed by estimating for each pixel inside the mask its normalized distance to the object boundary:

(17)

where the distance from the boundary is estimated by iteratively eroding the outer boundary of the object shape and adding the remaining object area to the former object area. In Figure 7 an object, its mask, and the mask-based asymmetric kernel are shown.

Figure 7

Object in image (a), object mask (b), and asymmetric object kernel retrieved from object mask (c).

4.3. Mean Shift Tracking in Spatial-Scale-Space

Instead of running the algorithm only in the local space the mean shift iterations are performed in an extended search space consisting of the image coordinates and a scale dimension as described in [17]. Thus, the object's changes in position and scale can be evaluated through the mean shift iterations simultaneously. To run the mean shift iterations in the joint search space a 3D kernel consisting of the product of the spatial object-based kernel from Section 4.2 and a kernel for the scale dimension

(18)

is defined. The kernel for the scale dimension is a 1D Epanechnikov kernel with the kernel profile if and 0 otherwise, where . The mean shift vector given in (14) can now be computed in the joint space as

(19)

with , where is the scale update.

Given the object mask for the initial frame the object centroid and the target model are computed. To make the target model more robust the histogram of a specified neighborhood of the object is also estimated and bins of the neighborhood histogram are set to zero in the target histogram to eliminate the influence of colors which are contained in the object as well as in the background. In case of an object mask with a slightly different shape than the object shape too many object colors might be supressed in the target model, if the direct neighbored pixels are considered. Therefore, the directly neighbored pixels are not included in the considered neighborhood. The mean shift iterations are then performed as described in [17, 23] and the new position of the object as well as a scaled object shape will be determined, where the latter can be considered as a first shape estimate.

4.4. Shape Adaptation Using GMMs

After the mean shift iterations have converged, the final shape of the object is evaluated from the first estimate of the scaled object shape. Thus, the image is segmented using the mean shift method according to [22]. For each segment being only partly included in the found object area we have to decide if it still belongs to the object shape or to the background. Therefore, we learn two Gaussian mixture models, one modeling the color histogram of the background and one the histogram of the object. The GMMs are learned at the beginning of the tracking based on the corresponding object binary mask. Since we are working in RGB color space, the multivariate normal density distribution of a color value is given by

(20)

where is the mean and is a 3 × 3 covariance matrix. The Gaussian mixture model for an image area is given by

(21)

where is the a priori probability of distribution , which can also be interpreted as the weight for the respective Gaussian distribution. To fit the Gaussians of the mixture model to the corresponding color histogram the parameters are estimated using the expectation maximization (EM) algorithm [24]. During the EM iterations, first the probability (at iteration step ) of all data samples to belong to the th Gaussian distribution is calculated by Bayes' theorem:

(22)

which is known as the expectation step. In the subsequent maximization step the likelihood of the complete data is maximized by re-estimating the parameters :

(23)

The updated parameter set is then used in the next iteration step . The EM algorithm iterates between these two steps and converges to a local maximum of the likelihood. Thus, after convergence the GMM will be fitted to the discrete data giving a nice representation of the histogram; see Figure 8. Since the visualization of a GMM modeling a three-dimensional histogram is rather difficult to understand, Figure 8 shows two GMMs modeling only the histogram of the green color channel of the car in sequence Parking_lot. The accuracy of a GMM depends on the number of Gaussians. Hence, the GMM with Gaussian distributions models the histogram more accurate than the model with Gaussians. Of course, depending on the histogram in some cases a GMM with a higher number of Gaussian distributions might be necessary, but for our purpose a GMM with Gaussians showed to be a good trade-off between modeling accuracy and parameter estimation.

Figure 8

Modeling the histogram of the green color channel of the car in sequence Parking_lot with (a) and Gaussians (b).

To decide for each pixel if it belongs to the GMM of the object or to the background GMM we use maximum a posteriori (MAP) estimation. Using log-likelihoods the typical form of the MAP estimate is given by

(24)

where indicates that a pixel, or more precise its color value , belongs to the object () or the background class (), and is the corresponding a priori probability. To set to an appropriate value object and background area of the initial mask are considered.

Based on the number of its object and background pixels, a segment is assigned as an object or background segment. If more than 50% of the pixels of a segment belong to the object class, the segment is assigned as an object segment; otherwise the segment is considered to belong to the background. The tracking result is then compared to the according detection result of the GMM-based background subtraction method. Segments of the GMM-SAMT result, which match the detected moving foreground region, are considered as true moving object segments. But segments which are not at least partly included in the moving foreground region of the background subtraction result are discarded, since they are most likely wrongly assigned as object segments due to errors in the MAP estimation caused by very similar foreground and background colors. Hence, the final object shape consists only of segments complying with the constraints of the background subtraction as well as the constraints of the GMM-SAMT procedure. Thus, we obtain quite a trustworthy representation of the final object shape from which the next object-based kernel is generated. Finally, the next mean shift iterations of GMM-SAMT can be initialiezed.

5. Experimental Results

The performance of Auto GMM-SAMT was tested on several sequences showing typical traffic scenarios recorded outside. To show that the detection method itself is also applicable for other surveillance scenarios, it was also tested on indoor surveillance sequences. In particular, the detection method was tested on two indoor sequences provided by [9] and three outdoor sequences, while the tracking and overall performance of Auto GMM-SAMT was tested on five outdoor sequences. For each sequence at least 15 ground truth frames were either manually labeled or taken from [9]. Overall the performance of Auto GMM-SAMT was evaluated on a total of 200 sample frames.

After parameter testing the GMM methods achieved good detection results for all sequences with Gaussians, , , and , whereas the parameters for temporal dependency and and for spatial dependency were set to and . Due to the very different illumination conditions in the indoor and outdoor scenarios, the learning rate and the shadow removal parameters were chosen separately for indoor sequences and outdoor sequences; see Table 2.

Detection results for the indoor sequences Shopping_Mall and Airport_Hall can be seen in Figure 9 while detection results for outdoor scenarios are shown in Figure 10. In particular, the images shown from left to right in each row of Figure 9 and of Figure 10 are the input frame, the ground truth, the standard GMM result, and the result of the Auto GMM-SAMT detection unit. By comparing the results, one can clearly see that for both scenarios the detection unit of Auto GMM-SAMT achieves much better binary masks than the standard GMM method. To further evaluate the detection performance the information retrieval measurements Recall and Precision were computed by comparing the detection results to the ground truth as follows:

(25)

For sequences Shopping_Mall and Airport_Hall the ground truths of [9] were taken, while for all other sequences the ground truths were manually labeled. The Recall and Precision scores given in Table 1 confirm the impression of the visual inspection, since for all test sequences the detection unit of Auto GMM-SAMT achieves better results as the standard GMM method. In addition to the information retrieval measurements, we also calculated the even more significant measure:

(26)

Again the visual impression is confirmed. The scores of the standard GMM method and of the Auto GMM-SAMT detection unit are compared in the last column of Table 1.

Table 1 Recall and Precision and measure of standard GMM and of improved GMM method of the Auto GMM-SAMT detection unit.

Table 2 Learning rate and shadow removal parameters.

Figure 9

Input frame, ground truth, and detection results of standard GMM method and of the Auto GMM-SAMT detection unit are shown from left to right for sequence Shopping_Mall (a) and for sequence Airport_Hall (b).

Figure 10

Input frame, ground truth, and detection results of standard GMM method and of the Auto GMM-SAMT detection unit are shown from left to right for sequences Parking_lot (a), Airport (b), and PETS 2000 (c).

To determine reliable objects among the detected foreground regions the obtained binary masks are transformed using the corresponding homography matrix. The homography matrix is estimated only once at the beginning of a sequence and can then be used for the whole sequence. A recalculation of the homography matrix is not necessary. Thus, the homography estimation can be considered as a calibration step of the surveillance system, which does not influence the computational performance of Auto GMM-SAMT at all. In the transformed mask only foreground regions of interesting size (e.g., ) are kept and considered as possible object regions. For our purpose was set to 2000 pixels for detecting cars and to 75000 pixels for airplanes.

After possible object regions are estimated in the transformed binary mask, the mask is transformed back into the original view. All possible object regions, which could be matched in subsequent frames, are considered as reliabel objects. For each reliable detected object the masked-based kernel is generated. Each object kernel is then used for computing the weighted histogram in the RGB space with  bins. For the scale dimension the Epanechnikov kernel with a bandwidth of is used. For mean shift segmentation a multivariate kernel defined according to (35) in [22] as the product of two Epanechnikov kernels, one for the spatial domain (pixel coordinates) and one for the range domain (color), is used. The bandwidth of the Epanechnikov kernel in range domain was set to , and the bandwidth of the one in spatial domain to . The minimal segment size was set to 5 pixels. Since the colors of an object and the surrounding background do not change to drastically in the considered scenarios, while the object is being tracked, the object and background GMMs for the MAP decision are only estimated at the beginning of the tracking by running the EM algorithm until convergence or for a maximum number of 30 iterations. Since Auto GMM-SAMT is developed for video surveillance of traffic scenarios, which are recorded diagonally from above such that the homography leads to reasonable results, the tracking performance was tested on five outdoor sequences containing mainly three-dimensional rigid objects.

In Figure 11 the performance of Auto-GMM-SAMT after initialization with a suboptimal object mask is illustrated. The first two images in Figure 11 show a binary mask for sequence Parking_lot before and after removing foreground regions of uninteresting size, while the initialization of the Auto GMM-SAMT tracking unit using the refined mask is given in the third image. The tracking result for the subsequent frame of sequence Parking_lot is provided in the fourth image of Figure 11. Despite the uncovered background contained in the initialization mask, Auto GMM-SAMT immediately recovers from this weak initialization. More tracking results of Auto GMM-SAMT for sequences Parking_lot and PETS 2000(ftp://ftp.pets.rdg.ac.uk/pub/PETS2000/) can be seen in Figure 12. In both cases Auto GMM-SAMT is able to track the contour of the cars, even though the cars are performing out-of-plane rotations.

Figure 11

Mask of a car in sequence Parking_lot generated by the Auto GMM-SAMT detection unit, mask after removing foreground regions of uninteresting size, initialization of the Auto GMM-SAMT tracking unit for tracking the car, and the corresponding tracking result for the next frame (shown from left to right).

Figure 12

Tracking results of Auto GMM-SAMT for sequence Parking_lot (a) and for sequence PETS 2000 (b).

In Figure 13 the tracking results of Auto GMM-SAMT (green solid contour) are compared to the results of the standard mean shift tracker combined with the ±10% method (red dotted ellipse). While Auto GMM-SAMT is able to adapt to the shape of the turning airplane, the standard method even fails to fit the scale and the position of the ellipse to the size and location of the airplane; see top row of Figure 13. Beside that, standard mean shift tracking also tends to track only a part of the object. This typical behaviour of the standard mean shift can even lead to tracking failure as, for instance, in the case of the turning car in sequence Follow_me (bottom row of Figure 13).

Figure 13

Tracking results using the standard mean shift tracker combined with the ±10% method (The result of the standard mean shift tracker indicated by the red dotted ellipses is hard to see. Can you please enhance the visibility of the red dotted ellipses?) and Auto GMM-SAMT (green solid contour) for tracking an airplane and a car in sequences Airplane (a) and Follow_me (b), respectively.

The visual evaluation of the tracking results already shows that Auto GMM-SAMT clearly outperforms the standard mean shift algorithm. To further evaluate the tracking result the tracking error in pixels is estimated by computing the averaged euclidean distance of the tracked centroids to the ground truth centroids, see Tables 3 and 4. Since the standard method failes to track the follow-me car, the tracking error is extremly high in that case and does not represent the general performance of the standard mean shift tracker. However, GMM-SAMT and Auto GMM-SAMT also outperform the standard mean shift tracking in all other cases. Recall and Precision as well as the measure were also computed for the tracking results by comparing the number of (correctly) tracked object pixels to the tracking ground truths. The Recall and Precision scores confirm the impression of the visual inspection since for all test sequences Auto GMM-SAMT exceeds the standard mean shift method; see Tables 3 and 4. By taking a look at the scores in Tables 3 and 4, one also recognizes that Auto GMM-SAMT keeps up with the stand alone implementation of GMM-SAMT. This is indeed quite a nice matter of fact, since the stand alone GMM-SAMT is initialized by the user with very precise initial masks, while the automatic estimated masks of the Auto GMM-SAMT detection unit are likely to be less precise; compare Figure 11. Despite Auto GMM-SAMT does not suffer from a loss of quality, for some sequences Auto GMM-SAMT achieves even higher scores.

Table 3 Recall and Precision and measure of standard mean shift tracking and GMM-SAMT.

Table 4 Recall, Precision, and score of Auto GMM-SAMT.

The performance of the detection unit (implemented in C++) is about 29 fps for image resolution on a 2.83 GHz Intel Core 2 Q9550. By using multithreading the performance is further enhanced up to 60.16 fps using 4 threads. Since the tracking unit is implemented in Matlab, it does not perform in real-time yet. But our modifications do not add any computational expensive routines to the mean shift method and the EM-algorithm is only run at the beginning of the tracking. Thus, a good computational performance should also be possible for a C/C++ implementation of the tracking unit.

6. Conclusions

The presented Auto GMM-SAMT video surveillance system shows that the GMM-SAMT algorithm could succesfully be combined with our improved GMM-based background subtraction method. Thus, an automatic object tracking for video surveillance is achieved.

On the one hand Auto GMM-SAMT takes adavantage of GMM-SAMT, which extends the standard mean shift algorithm to track the contour of objects of changing shape without the help of any predefined shape model. Since the tracking unit works with object mask-based kernels, the influence of background colors on the target model is avoided. Thus, the Auto GMM-SAMT tracking unit is much more robust than standard mean shift tracking. Because of adapting the kernel to the current object shape in each frame, Auto GMM-SAMT is able to track the shape of an object even if the object is performing out-of-plane rotations.

On the other hand Auto GMM-SAMT automates the initialization of the tracking algorithm using our improved GMM-based detection algorithm. Because of the limitation of the standard deviation and the consideration of temporal and spatial dependencies in the detection unit, the Auto GMM-SAMT system obtains good binary masks. Even uncovered background regions are relatively fast classified as background due to the spatiotemporal adaptive detection method. Despite this fast adaptation to uncovered background areas, for a few frames false positives caused by uncovered background regions might be contained in the masks. But it is shown that the GMM-SAMT tracking method can also achieve good tracking result when initialized with binary masks of moderate quality as long as the color of object and (uncovered) background is not too similar. Otherwise Auto GMM-SAMT will deliver the first correct object contours after the uncovered background is correctly identified as such by the detection unit. Nevertheless, Auto GMM-SAMT can keep up with the stand alone implementation of GMM-SAMT. In some cases Auto GMM-SAMT performs even better than GMM-SAMT due to the final shape refinement when comparing the tracking results with the background subtraction results. However, in the case of very similar foreground and background colors detection and tracking problems can occur.

In addition, the projective transformation of Auto GMM-SAMT can be considered only as a fast but very simple object classification. Since the classification is not reliable enough for a robust surveillance system, we will focus on other object features as well as on alternative classification techniques in our future work. The consideration of other object features could also help to improve the detection and tracking performance in case of very similar object and background colors. Besides we also plan to investigate the automation of the homography estimation to remove the manual calibration step.