- Research Article
- Open Access
Static Object Detection Based on a Dual Background Model and a Finite-State Machine
EURASIP Journal on Image and Video Processing volume 2011, Article number: 858502 (2010)
Detecting static objects in video sequences has a high relevance in many surveillance applications, such as the detection of abandoned objects in public areas. In this paper, we present a system for the detection of static objects in crowded scenes. Based on the detection of two background models learning at different rates, pixels are classified with the help of a finite-state machine. The background is modelled by two mixtures of Gaussians with identical parameters except for the learning rate. The state machine provides the meaning for the interpretation of the results obtained from background subtraction; it can be implemented as a look-up table with negligible computational cost and it can be easily extended. Due to the definition of the states in the state machine, the system can be used either full automatically or interactively, making it extremely suitable for real-life surveillance applications. The system was successfully validated with several public datasets.
Detecting static objects in video sequences has several applications in surveillance systems such as the detection of illegally parked vehicles in traffic monitoring or the detection of abandoned objects in public safety systems and has attracted the attention of a vast research in the field of video surveillance. Most of the proposed techniques aiming to detect static objects base on the detection of motion, achieved by means of background subtraction, followed by some kind of tracking . Background subtraction is a commonly used technique for the segmentation of foreground regions in video sequences taken from a static camera, which basically consists on detecting the moving objects from the difference between the current frame and a background model. In order to achieve good segmentation results, the background model must be regularly kept updated so as to adapt to the varying lighting conditions and to stationary changes in the scene. Therefore, background subtraction techniques often do not suffice for the detection of stationary objects and are thus supplemented by an additional approach.
Most of the approaches suggested in the recent literature for the detection of static objects rely on tracking information [1–4]. As observed by Porikli et al., . these methods can find difficulties in real-life scenes involving crowds due the large amounts of occlusions and to the shadows casted by moving objects, which turn the object initialization and tracking into a hard problem to solve. Many of the applications where the detection of abandoned objects can be of interest like safety in public environments (airports, railway stations) impose the requirement of coping with crowds.
In order to address the limitations exhibited by tracking-based approaches, Porikli et al. . proposed a pixelwise system which uses dual foregrounds. Therefore, they used two background models with different learning rates, a short-term and a long-term background model. In this way, they were able to control how fast static objects get absorbed by the background models and detect them as those groups of pixels classified as background by the short-term but not by the long-term background model.
A drawback of this system is that temporarily static objects may also become absorbed by the long-term background model after a given time depending on its learning rate. This would lead the system to not detect those static objects anymore and furthermore to detect the uncovered background regions as abandoned objects when they are removed from the scene. To overcome this problem, the long-term background model could be updated selectively. The disadvantage of this approach is that incorrect update decisions might later result in incorrect detection and that the uncovered background could be detected as foreground after removing static objects even if those do not get absorbed by the long-term model if the lighting conditions have changed notably.
The combination of the foreground masks obtained from the subtraction of two background models was already used by  in order to quickly adapt to changes in the scene while preventing foreground objects from being absorbed too fast by the background model. They used the intersection of the foreground masks to selectively update the short-term background model, obtaining a very precise segmentation of moving objects, but they did not consider the problem of detecting new static objects. Recently, Singh et al.  proposed a system for the detection of static objects that also bases on two background models however; it relies on selectively updating the long-term background model, entailing the above-mentioned problem of possibly taking incorrect updating decisions, and on tracking information.
To solve the problem that poses static objects concerning the updating of the long-term background model in dual background systems, we propose a system that, based on the results obtained from a dual background model, classifies the pixels according to a finite-state machine. Therefore, we can define the meaning of obtaining a given result from background subtraction when being in a given state. Thus, the system is able to differentiate between background and static objects that have been absorbed by both background models depending on the pixels history. Furthermore, by adequately designing the states and transitions of the finite-state machine, the system that we define can be used either in a full automatic or in an interactive manner, making it extremely suitable for real-life surveillance applications. After classification, pixels are grouped according to their class and connectivity. The content of this paper has been partially submitted to the IEEE Workshop on Applications of Computer Vision (WACV) 2011 . In the present paper, we provide a detailed insight into the proposed system and some robustness and efficiency implementation issues to further enhance it.
The rest of this paper is organized as follows In Section 2 we briefly describe the task of background subtraction, which sets the basis of our system. Section 3 is devoted to the finite-state machine, including some implementation remarks. Section 4 summarizes some experimental results and the limitations and merits of the proposed system. Section 5 concludes the paper.
2. Background Modelling
Background subtraction is a commonly used approach to detect moving objects in video sequences taken from a static camera. In essence, for every pixel at a given time , the probability of observing the value , given the pixel history , is estimated
and the pixel is classified as background if this probability is bigger than a given threshold or as foreground if not. The estimated model in (1) is known as background model and the pixel classification process as background subtraction. The classification process depends on the pixel history as explicitly denoted in (1). In order to obtain a sensitive detection, the background model must be updated regularly to adapt to varying lighting conditions. Therefore, the background model is a statistical model containing everything in a scene that remains static and depends on the training set used to build it. A study of some well-known background models can be found in [8–10] and references therein.
As observed in , there are many surveillance scenarios where the initial background contains objects that are later removed from the scene (parked cars, static persons that move away, etc.). When these objects move away, they originate a foreground blob that should be correctly classified as a removed object. Although this is an important classification step for an autonomous system, we do not consider this problem in this paper. We assume that, after an initialization time, the background model only contains static objects which do belong to the empty scene. Some approaches on background initialization can be found in [12, 13] and references therein. In , the authors use multiple hypotheses for the background at each pixel by locating periods of stable intensity during the training sequence. The likelihood of each hypothesis is evaluated by using optical flow information from the neighboring pixels. The most likely hypothesis is chosen as background model. In  the background is estimated in a patch by patch manner by selecting the most appropriate candidate patches according to the combined frequency responses of extended versions of candidate patches and their neighbourhood, thus exploiting spatial correlations within small regions.
The result of a background subtraction is a foreground mask , which is a binary image where the pixels classified as foreground are differentiated from those classified as background. In the following, we use the value 1 for those pixels classified as foreground (foreground pixels), and 0 for those classified as background (background pixels). Foreground pixels can be grouped into blobs by means of connectivity properties [14, 15]. Blobs are foreground regions which can belong to one or more objects or even to some parts of different objects in case of occlusions. For brevity in the exposition, we will refer to the detected foreground regions as objects. Accordingly, we will use the term static objects instead of the more precise form static foreground regions.
2.1. Dual Background Models
A statistical background model as defined in (1) provides a description of the static scene. Since the model is updated regularly, objects being introduced in the scene and remaining static will be incorporated into the model at some time. Therefore, regulating the training set or the learning rate used to build the background model, it is possible to adjust how fast new static objects get incorporated into the background model.
Porikli et al.  used this fact to detect new static objects based on the foreground masks obtained from two background models learning at different rates, a short-term foreground mask , and a long-term foreground mask . shows the pixel values corresponding to moving objects and temporarily static objects, as well as shadows and illumination changes that the long-term background model fails to incorporate. contains the moving objects and noise. Depending on the foreground masks values, they postulate the hypotheses shown in Table 1, where and denote the value of the long-term and short-term foreground mask at pixel , respectively. We use this notation in the rest of this paper.
After a given time according to the learning rate of the long-term background, the pixel values corresponding to static objects will be learned by this model too, so that, following the hypotheses in Table 1, those pixels will be hypothesized from this time on as scene background. Moreover, if any of those objects get removed from the scene after their pixel values have been learned by the long-term background, the potential background may be detected as a static object.
In order to handle those situations, we propose in this paper a system that, based on the foreground masks obtained by the subtraction of two background models learning at two different rates, hypothesizes on the pixel classification according to the last pixel classification. This system is formulated as a finite-state machine where the hypotheses depend on the state of a pixel at a given time, and the conditions are the results obtained from background subtraction.
As background model,we use two improved Gaussian mixture models as described in  initialized with identical parameters except for the learning rate, a short-term background model , and a long-term background model . Actually, we could use any parametrical multimodal background model (see , e.g.) that do not alter the parameters of the distribution that represents the background when a foreground object hides it.
The background model presented in  is very similar to the well-known mixture of Gaussians model proposed in . In a nutshell, each pixel is modelled as a mixture of a maximum number of Gaussians. Each Gaussian distribution is characterized by an estimated mixing weight , a mean value, and a variance. The Gaussian distributions are sorted attending to their mixing weight. For every new frame, each pixel is compared with the distributions describing it. If there exists a distribution that explains this pixel value, the parameters of the distribution are updated according to a learning rate as expressed in . If not, a new one is generated with mean value equal to the pixel value and weight and variance set to some fixed initialization value. The first distributions are chosen as the background model, where
with being a measure of the minimum portion of the data that should be considered as background. After each update, the components that are not supported by the data, that is, these with negative weights, are suppressed and the weights of the remaining components are normalized in a way that they add up to one.
3. Static Objects Detection
As we show in Section 2, a dual background model is not enough to detect static objects for an arbitrarily long period of time. Consider a pixel being part of the background model (the pixel is thus classified as background) and the same pixel at the next time step being occluded by a foreground object. The value of both foreground masks and at will be 1. If the foreground object stays static, it will be learned by the short-term background model at first (let us assume at , and ) and afterwards by the long-term background (let us assume at , and ). This process can be graphically described as shown in Figure 1.
If we further observe the behavior of the background model of this pixel in time, we can transfer the meaning of obtaining a given result from background subtraction after a given history into pixel classification hypothesis (states) and establish which transitions are allowed from each state and what are the inputs needed to cause these transitions. In this way, we can define the state transitions of a finite-state machine, which can be used to hypothesize on the pixel classification.
As we will see in the following subsections, there are some states that require additional information in order to determine what is the next state for a given input. In these cases it is necessary to know if any of the background models gives a description of the actual scene background and, in affirmative case, which of them. Therefore, we keep a copy of the last background value observed at every pixel position. This value will be used, for example, to distinguish when a static object is being removed or when it is being occluded by another object. In this sense, the finite-state machine (FSM) presented in the following can be considered as an extended finite-state machine (EFSM), which is an FSM extended with input and output parameters, context variables, operations and predicates defined over context variables and input parameters . An EFSM can be viewed as a compressed notation of an FSM, since it is possible to unfold it into a pure FSM, assuming that all the domains are finite , which is the case in the state machine presented here. In fact, we make use of context variables in a very limited number of transitions. Therefore, for clarity in the presentation, we prefer to introduce the state-machine as an FSM at first and then remark where the EFSM features are exploited.
In the following subsection we present the FSM in its general form. Section 3.2 outlines how the results of the FSM can be used by higher layers in a computer vision system. Section 3.3 presents how the FSM can be further enhanced in terms of robustness and efficiency.
3.1. A Finite-State Machine for Hypothesizing on the Pixel Classification
A finite-state machine describes the dynamic behavior of a discrete system as a set of input symbols, a set of possible states, transitions between those states, which are originated by the inputs, a set of output symbols, and sometimes actions that must be performed when entering, leaving or staying in a given state. A given state is determined by past states and inputs of the system. Thus, an FSM can be considered to record information about the past of the system it describes. Therefore, by defining a state machine whose states are the hypothesis on the pixels and whose inputs are the values obtained from background subtraction, we can record information about the pixel history and thus hypothesize on the classification of a pixel given a background subtraction result depending on the state where it was before.
An FSM can be defined as a 5-tuple () , where
is the input alphabet (a finite set of input symbols),
is a finite set of states,
is the output alphabet (a finite set of output symbols),
is the next-state function, a mapping of into , and
is the output function, a mapping of onto .
to be the possible combinations of the results obtained from background subtraction. By defining the pair , the input alphabet reduces to ;
to be the set of states a pixel can go through as described below;
to be either a set of numbers indicating the hypothesis on the pixel classification , with being the cardinality of , or a boolean output with the value 0 for pixels not belonging to a static object and 1 for pixels belonging to a static object. Choosing the output alphabet depends on whether the hypotheses of the machine are to be further interpreted or not;
to be a next-state function as depicted in Figure 2.
to be the output function. This can be either a multivalued function with output values corresponding to the state of a pixel at a given time, or a boolean function with output 0 for pixels not belonging to a static object and 1 for pixels belonging to a static object.
Additionally, we keep a copy of the last background value observed at every pixel position.
In the following, we list the states of the state machine, their hypothetical meaning, the condition that must be met to enter them, or to stay in them and a brief description of their meaning:
(BG), background, . The pixel belongs to the scene background,
(MP), moving pixel, . The pixel belongs to a moving object. This state can be reached as well by pixels belonging to the background scene being affected by spurious noise not characterized by the background model,
(PAP), partially absorbed pixel, . The pixel belongs to an object that has already been absorbed by but not by . In the following, we refer to these objects as short-term static objects,
(UBG), uncovered background, . The pixel belongs to a background region that was occluded by a short-term static object,
(AP), absorbed pixel, . The pixel belongs to an object that has already been absorbed by and . In the following, we refer to these objects as long-term static objects,
(NI), new indetermination, . The pixel cannot be classified as background neither by nor by . It is not possible to ascertain if the pixel corresponds to a moving object occluding a long-term static object or if a long-term static object was removed. We do not take any decision at this moment. If the pixel belongs to a moving object occluding a long-term static object, the state machine will jump back to AP when the moving object moves out. If not, the "new" color will be learned by and the state machine will jump to AI, where a decision will be taken,
(AI), absorbed indetermination, . The pixel is classified as background by but not by . Given the history of the pixel it is not possible to ascertain if any of the background models gives a description of the actual scene background. To solve this uncertainty, the current pixel value is compared to the last known background value at this pixel position. We discuss below how to obtain and update the last known background value,
(ULKBG), uncovered last known background, . The pixel is classified as background by but not by and identified as belonging to the scene background,
(OULKBG), occluded uncovered last known background, . The pixel is classified as background by but not by , and is known to contain a representation of the scene background. This state can be reached when a long-term static object has been removed, the actual scene background has been learned again by and an object whose appearance is very similar to the removed long-term static object occludes the background,
(PAPAP), partially absorbed pixel over absorbed pixel, . The pixel is classified as background by but not by and could not be identified as belonging to the scene background. Therefore, it is classified as a pixel belonging to a short-term static object occluding a long-term static object,
(UAP), uncovered absorbed pixel, . The pixel is classified as background by but not by , and could not be interpreted to contain a representation of the actual scene background. This state can be reached when a short-term static object was occluding a long-term static object and the short-term static object gets removed.
Observe that we need additional information in order to determine the transitions from state 6. This is due to the fact that it is not possible to ascertain if any of the background models gives a good description of the actual scene background. To illustrate this, let us consider two cases: a long-term static object getting removed and a long-term static object getting occluded by a short-term static object. In both cases, when the long-term static object is visible and classify it as background (state 4, ). Afterwards, when the long-term static object gets removed or occluded, a "new" color is observed. The "new" color persists at this pixel position, and it gets first learned by (state 6, ), causing an uncertainty, since it is impossible to distinguish if the "new" color corresponds to the scene background or to a short-term static object occluding the long-term static object. To solve this uncertainty, we compare the current pixel value with the last known background value at this pixel position. In this state the FSM is actually behaving as an EFSM, and the copy of the last background value observed at this position is a context variable. Since this is the unique state where the FSM explicitly makes use of extended features, we decided to remark that aside in order to keep the description of the state machine as simple as possible.
The last known background value is initialized for each pixel after the initialization phase of the background models. How to initialize a background model is out of the scope of this paper. In Section 2, we give references on papers dealing with this topic. This value is subsequently updated for every pixel position when a transition from BG (state 1) is triggered as follows:
where denotes the last known background value.
The output function of the FSM can have two forms:
a boolean function with output 0 for nonstatic pixels and 1 for static pixels. In this case, it has to be decided which subset of designates a static pixel. There are many possibilities, depending on the desired responsiveness of the system. The lower and higher responsiveness are achieved by and , respectively;
A multivalued function with output values corresponding to the state where the pixel is at a given time.
At the moment, we use a subset of to classify groups of pixels as static objects, but we used the second form in order to provide some examples of the classification states obtained. Furthermore, the results obtained by using a multivalued function can be used to feed up a second-layer grouping pixels by means of their hypotheses and build objects.
3.2. Grouping Pixels into Objects
The state of each pixel at a given time provides a rich information that can be further processed to refine the hypothesis. Pixels can be spatially combined depending on their states and their connectivity. At the moment, we take those pixels in the states 4 and 5 and those that have been in the states 2 or 9 for more than a given time threshold and group them attending to their connectivity. Those groups of pixels bigger than a fixed size are then classified as static objects.
3.3. Robustness and Efficiency Issues
The FSM introduced in Section 3.1 provides a reliable tool to hypothesize on the meaning of the results obtained from a dual background subtraction. However, there are some state-input sequences where an additional computation must be done in order to decide on the next state, namely when the state machine arrives at the state AI (6). A state-input sequence entering the state AI is AP-(1,1) → NI-(1,0) → AI, which corresponds to a pixel of a long-term static object being removed or getting occluded by a short-term static object. In this situation it is necessary to disambiguate the results obtained from background subtraction.
There are three more state-input sequences entering the state AI, where this extra computation can be eventually avoided. These are MP-(0,1) → OULKBG-(1,1) → AI, UBG-(1,1) → AI, and PAP-(1,1) → AI. In fact, these sequences enter the state AI because they can derive in a state input where a disambiguation is necessary, given the pixel history. Therefore, if we define known sequences starting at the first state-input pair of the three sequences mentioned above, we can avoid reaching AI for these known sequences. In order to do that, we added five more states to the FSM:
(OULKBGII), occluded uncovered last known background ii, ,
(UBGII), uncovered background ii, ,
(MPII), moving pixel ii, ,
(PAPII), partially absorbed pixel ii, ,
(MPIII), moving pixel iii, .
These states are specializations of the states they inherit their name from and have the sense of avoiding to enter the state AI in these situations where the meaning of the state-input sequence is non ambiguous. Therefore, we call them known sequences. Their meaning can be inferred out of the transitions shown in Figure 3 and of the state they specialize. In this fashion some additional specialized states can be defined.
Figure 3 also shows six additional conditions on six transitions marked as an orange point on the respective transition arrows. The reason why we introduce these conditions here is that the tuple at time step does not really make sense if being in the state where the transitions are conditioned. Thus, we hypothesized that it was obtained because of noise and "stay" at the current state. If the tuple in the next time step is equal to , then the conditioned transition is done. In practice, these additional conditions are implemented as replica states with identical transitions as the state being replicated except for the transition being conditioned, which is only done in the corresponding replica state (the replicated state transitions to the replica state). We do not represent these replica states in the next-state function graph for clarity.
Introducing additional states enhances the robustness of the state machine, since there are less input sequences deriving in state AI. Thus, there are less pixels that have to be checked with an eventually old version of the scene background (the last known background value is updated when a transition leaving the state BG is). Furthermore, because of avoiding this additional computation, we gain in efficiency. Replica states also contribute to enhance the performance of the system, since they filter out noisy inputs.
4. Experimental Results
In this section, we present results obtained with the proposed system and with a dual background-based system that does not use an FSM (pixels are classified by using the hypotheses shown in Table 1 and an evidence value in a similar way as proposed in ), which we use as reference system. To abbreviate, we will refer to those systems as DBG+FSM and DBG+T, respectively.
To test the systems, we used three public datasets: i-LIDS, PETS2006 and CAVIAR. The sequences AB-Easy, AB-Medium and AB-Hard from the i-LIDS dataset show a scene in an underground station. In PETS2006, there are several scenes from different camera views of a closed space; we took the scene S1-T1-C-3. CAVIAR covers many different events for scene interpretation of interest in a video surveillance application (people fighting, people/groups meeting, walking together and splitting up, or people leaving bags behind…), taken from a high camera view; from this dataset we took the scene LeftBag. The scenes from i-LIDS became our major attention, since they show one of the challenges that we tackle on this paper, namely a static object being for a long time in the scene and then being removed. However, the scenes AB-Medium and AB-Hard present the handicap that the static scene cannot be learned before the static objects come into the scene, which is a requirement for both systems (DBG+T and DBG+FSM); therefore, we added 10 frames showing the empty scene at the beginning of each scene, respectively, in order to train the background models. In PETS2006, static objects are not removed, and thus, even if the static objects have to be detected, they do not pose the problem of detecting when a static object has been removed. In the CAVIAR scene LeftBag, static objects are removed that early, that every background model can be tuned not to absorb them without risking the responsiveness of the background model. Thus, we do not consider these two last sets of scenes very challenging for the task of static objects detection. We nevertheless chose these three datasets, since they are the most commonly used in the computer vision community for the presentation of systems for the detection of static objects.
As background model, we used two Gaussian mixture models with shadow detection. A comprehensive description of the model can be found in . We set up both background models with identical parameters except for the learning rate. The learning rate of the short-term model is 10 times the learning rate of the long-term model . We consciously chose a relatively large value for to force to learn the static objects in the scene and thus being able to prove the correct operation of the proposed system both when static objects are learned by and when they get removed from the scene. It is important thus to remark that the goal of the experiments presented here is to evidence what problems double background-based systems face on the detection of long-term static objects and how the proposed approach solves them. Therefore, we had to cope with objects getting very fast classified as static. In practice, can be drastically reduced. The rest of the parameters were chosen as follows:
, which means that only the first component of the background model is taken as background,
where is the initialization value for the variance of a new distribution, and is the threshold value for a pixel to be considered to match a given distribution. These are the most commonly used values in papers reporting the use of Gaussian mixture models for the task of background subtraction.
The masks obtained from background subtraction were taken without any kind of postprocessing as input for the FSM. We let the background models learn for a period of 10 frames and, assuming that at this time the short-term background already has a model of the scene background, start the state machine.
The FSM was implemented as a lookup table and is thus very low demanding in terms of computation time. Only at state AI extra computations are needed. At this step, we use a voting system to decide the next state for a given input, by comparing the pixel against the last value seen for background at this pixel and impose the condition of obtaining a candidate state at least five times. For this comparison, we used a context variable. We do not define this comparison as an input of the state machine, since it is only needed for pixels being in this state. Therefore, we save the computational cost of computing a third foreground mask based on this background model.
Pixel classification was made taking the pixels whose FSMs were in the states AP and NI, or in the states PAP and PAPAP for a time longer than 800 frames and building connected components. To build connected components we used the CvBlobsLib, available at http://sourceforge.net/projects/cvblobslib/, which implements the algorithm in . Groups of pixels bigger than 200 pixels were classified as static objects. Time and size thresholds were changed for the LeftBag sequence, according to the geometry and challenge of the scene. While in the PETS and iLIDS sequences a rucksack can be bounded with a pixels box, a rucksack of the approximately same size takes because of the frame size a box of only pixels in the CAVIAR sequences. Moreover, the LeftBag sequence of CAVIAR poses the challenge of detecting static objects being in the scene for 385 frames, what would make no sense in a subway station (iLIDS sequences), since almost each waiting person would trigger an alarm.
Table 2 presents some results obtained with the proposed system and with DBG-T. True detections indicate that an abandoned object was detected. False detections indicate that an abandoned object was detected where, in fact, there was not an abandoned object (but, for example, a person). Missed detections indicate that an abandoned object was not detected. Lost detections indicate correctly detected static objects that were not detected anymore after a given time because of being absorbed by the long-term background model. We detected successfully all static objects. While we report some false detections in the AB-Medium and AB-Hard sequences, these detections do correspond in every case to static objects (persons staying static for a long time); we rated them as false detections, since they do not correspond to abandoned objects.
We detected successfully all static objects. The false detections in the AB-Medium and AB-Hard sequences correspond in every case to persons staying static for a long time. These detections can be ignored by incorporating an object classifier in order to discard people staying static for a long time (this classification step will be incorporated in future work). Furthermore, notice that we set a learning rate for larger than needed in order to prove the correct operation of the FSM, which is also partially the cause of static objects being detected that fast.
Figures 4, 5 and 6 show some examples obtained for the i-LIDS sequences. Pixels are colored according to the colors of the states shown in Figure 2. Pixels belonging to moving objects are painted in green, pixels belonging to short-term static objects in yellow, and so on. The second frame of each sequence shows how time can be used to mark short-term static objects as static. The third frames show how long-term static objects (in red) are still being detected (these objects get lost by a DBG-T system if not additionally using some kind of selective updating scheme for the long-term background model). In the AB-Medium and AB-Hard sequences it is also shown the robustness of the proposed system against occlusions in crowded scenes. The fourth frames show the starting of the disambiguation process when long-term static objects get removed. The fifth frames show how the static object detection stops when the scene background is again identified as such.
The processing time needed can slightly vary depending on the scene complexity and on the configuration of the underlying background model. A very complex background scene requires more components and thus more computation time. Moreover, when long-term static objects get absorbed by the long-term background and afterwards get removed, an indetermination state has to be solved. Beyond that, the more static objects there are, the more the blobs generation costs. To give an idea, what the computational times are, we report in Table 3 the average frame processing time in miliseconds and in frames per second for the i-LIDS sequences AB-Easy, AB-Medium, AB-Hard and an average over the PETS2006 dataset, running in an Intel Core2 Extreme CPU X9650 at 3.00 GHz without threading. Since each pixel is considered individually, the processing described here can be easily implemented in a parallel architecture, gaining considerably in speed. In the i-LIDS sequences we only analyzed the platform (that means, 339.028 pixels out of 414.720). The frames of the PETS2006 dataset were taken as they are (that means a total amount of 414.720 pixels per frame). We show processing times for the update of a double background system (DBG), for the DBG-T system, and for the proposed system (DBG-FSM).
It is apparent that the proposed method outperforms the DBG-T system in terms of detection accuracy while having similar processing demands. Table 3 shows that the computational time needed for the update of the state machine is very low compared to the time needed for the update of the background model. The processing time of the proposed system was always lower when using a state machine with the enhancements proposed in Section 3.3, but the most important advantage of using specialized states is that the state machine of many pixels does not go to states in which an indetermination has to be solved, as shown in Figure 7. The times reported show that the system can run in real time in surveillance scenarios.
4.1. System Limitations and Merits
The system presented here aims to detect static objects in a video sequence that do not belong to the scene background. As such, the actual scene background must be known when the state machine starts working, which is a realistic requirement for real-life applications. Furthermore, we do not use any kind of object models in order to distinguish, for instance, persons waiting in a bank from other kind of static objects. Neither tracking information was used to trigger "drop-off" alarms in a similar fashion as Guler and Farrow do in , which could be coupled with our system in form of a parallel layer in order to bring a kind of semantic for scene interpretation. Static objects would still be detected with no need of tracking information, while a higher layer could fuse incoming information from several cues in order to make a semantic scene interpretation. As pointed out, the system presented here is restricted to the detection of static objects which do not belong to the scene background.
As shown in Figure 2, the condition for the FSM to stay at the state AP at a given pixel is that , which is the same condition as the one to stay at BG. That means that if a piece of the scene background was wrongly classified as static object, an operator could interactively correct this mistake with no need for the system to correct any of the background models, since those are updated regularly in a blind fashion. This could happen, for example, if a static object has occluded the background that long, that the last known background is not similar anymore to the scene background when the object is removed because of a lighting change. This is a huge advantage of our system in comparison to other systems based on selectively updating the background model, not only because we avoid wrong update decisions but also because the system provides the possibility of incorporating interactive corrections with no need of modifying the background model. Thus, the background model remains as a pure statistical information.
The same applies for static objects that an operator can be considered noninteresting, which is a common issue in open spaces, where waste containers and other static objects are moved in the scene but do not represent a dangerous situation. Static object detection approaches based on selective updating of the background model do not offer a principled way of incorporating such items into the background model. Since our background model is updated in a blind fashion, these objects do get incorporated into the background model. Only the state of the FSM has to be changed. This kind of interaction can be defined as well with other layers in a complex computer vision system.
A further extension of the system can be to use information of neighboring pixels to discard some detected static objects. Based on the observation that the inner pixels of slightly moving objects are learned by and faster than the outer pixels (especially by uniform colored objects), it can be differentiated between static objects and slightly moving objects by grouping neighboring pixels. This can be implemented as a second layer which results can even be feedback as an additional input in order to help solving some indeterminations at state AI. Figure 8 shows a detected static object that can be discarded following this criterion.
In this paper we presented a robust system for the detection of static objects in crowded scenes without the need of any tracking information. By transferring the meaning of obtaining a given result from background subtraction after a given history into transitions in a finite-state machine, we obtain a rich information that we use for the pixel classification. The state machine can be implemented as a lookup table with negligible computational cost, it can be easily extended to accept more inputs and can also be coupled with parallel layers in order to extract semantic information in video sequences. In fact, the proposed method outperforms the reference system in terms of detection accuracy while having similar processing demands. Due to the condition imposed for a pixel to remain classified as static in a long-term basis, the system can be interactively corrected by an operator without need for the system to modify anything in the background models, what alleviates the system from persistent false classification originated by incorrect update decisions in contrast to selective updating-based systems. The system was successfully validated with several public datasets.
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