I Introduction
Human Body Pose Estimation (HBPE) is a longlasting challenge in computer vision. The capability to detect and reconstruct the human motion is indeed of paramount importance in many applications, ranging from human movement analysis to humanrobot cooperation. However, despite the high relevance of the topic, the challenge is still far from being effectively and fully addressed. This is mainly due to the complexity of tracking in realtime the movements of a highly articulated, selfoccluding, threedimensional, variable system as the human body is. Furthermore, the goal becomes even more challenging when the requirement is to track multiple subjects in realtime without the aid of any bodymounted external device or marker.
One of the most promising technologies to face this challenge exploits the use of several distributed RGBD cameras acting as nodes of an extensive heterogeneous network. The common goal of the approaches relying on this technology is to obtain temporally stable 3D reconstructions of multiple subjects’ motion by employing the information coming from the different nodes of the network.
The work presented in this paper addresses this problem by means of a trackingbydetection approach enhanced with solutions tailored to guarantee temporal and physical consistency to the tracked motion. The system exploits the feed of multiple RGBD cameras placed in the scene: each detection node
uses a combination of a convolutional neural network together with a depth inference algorithm to obtain the singleview 3D pose estimation of all the subjects in the scene. Finally, the singleview poses are fused by the
central processing node to obtain the final multiview 3D track of each subject’s motion. A fundamental characteristic of the developed methodology is the capability to fuse each node’s detections requiring the network nodes neither to be hard synchronized nor to have the same data production rate. Indeed, every time a new singleview detection is made available by one detection node, the central processing node uses it to update the multiview track ensuring, by construction, the timing consistency.In this paper we propose, in addition to our previous work OpenPTrack^{1}^{1}1www.github.com/openptrack/open_ptrack_v2 [1], an improved version of the Kalman filter to augment its capability to ensure temporal consistency. To this end, we developed an adaptation mechanism, similar to the one presented in [2]
, to effectively identify and filter out misleading detections acting as outliers and producing noise and errors on the final 3D tracked motions. Furthermore, we placed in cascade to this enhanced Kalman filter an optimization mechanism, based on an hierarchical model of the human body, in charge of ensuring the physical consistency of the limb lengths.
In details, with respect to our previous work [3], this paper introduces four novel elements: (i) a new implementation of the Kalman filter considering in its state all the joint positions and velocities of the skeleton model (Sec. IIIB
), (ii) a joint confidence feedback to adjust the variance of the measurement noise process of the Kalman filter according to the confidence level associated to each singleview detection (Sec.
IIIC), (iii) an adaptive scheme to further adjust the variance of the measurement noise process of the Kalman filter when possible outlier detections are found (Sec.
IIID), (iv) a limbbased optimization mechanism, based on a hierarchical human body model, to ensure the physical consistency of the limb lengths (Sec. IIIE).The accuracy and realtime performances of the developed system have been evaluated on a newly collected dataset. The dataset includes both static and dynamic movements of up to two healthy subjects recorded simultaneously by our 4 RGBD camera network and by a stateoftheart markerbased motion capture system used as ground truth. The rest of the paper is organized as follows: Sec. II analyses the related works and compares them with the proposed approach; Sec. III describes the developed methodology, Sec. IV reports the results of the performance evaluation, and Sec. V draws the final remarks and considerations.
Ii Related Works
A broad range of scientific, industrial, and consumer systems rely on the estimation of the human body pose [4]. Indeed, this information is needed in several applications, such as action recognition [5, 6], people reidentification [7], and humancomputer interaction [8]. Applications in the humanrobot interaction field require the robot to closely operate with humans: awareness of the human motion is therefore crucial, both for assisted living [9, 10] and for industrial scenarios [11]. Another class of applications that has strongly boosted the research work is video surveillance [12, 13], including actions and behaviors recognition of people and crowds to detect abnormalities. Finally, HBPE can be seen as the main building block for motion capture, i.e. the process of digital reconstructing and analysing people movements.
The capability of providing the body pose estimates at the same time that the actions are performed is indeed a central requirement for the large majority of the aforementioned applications. In recent years, many research efforts have been spent on obtaining, in realtime, fast and reliable pose estimates [14, 15], supported by the availability of increasingly powerful computing hardware and sensors, like the first and second generations of Microsoft Kinect (Microsoft Corporation, USA).
The availability of such technologies enabled researchers to develop costefficient solutions to realtime human pose and motion tracking [1, 16, 17]. To this end, many markerless skeleton detection algorithms were developed [18, 19]. However, the employment of a single sensor limits the reliability of the estimates, due to the fact that they are generally affected by occlusions and fieldofview limitations. A common solution seems to be connecting several cameras to form a common network [3, 20]. One of the biggest challenges when exploiting a multiplecamera network consists in the methodology used to merge information from different sensors. Several approaches have been developed to obtain accurate skeleton data in a multiview environment. The authors in [21] used a multipleKinect setup for posture and gesture recognition. They acquired singleview skeletons from each camera and then computed joint coordinates differences. A similar approach has been used for walking posture assessment in [22]. In [23], authors used a distributed RGBD camera network to feed an informationweighted consensus filter based human pose estimator for activities recognition. In this approach, each sensory node provides a measurement of the target human joint, which is used to update the state of the estimator [24]. The main limitations of this system, however, are that it only works offline and is compatible to the tracking of just one subject at a time. A different method is presented in [25], where a fully connected pairwise conditional random field is used. However, these approaches rely only on RGB images, thus not exploiting the depth information provided by each camera.
The work proposed in this paper exploits both RGB and depth data from each camera of the asynchronous network. Furthermore, it implements (i) an improved implementation of the multiview fusion Kalman filter, (ii) an outlier detection scheme, (iii) a joint confidence adaptation scheme, and (iv) a limbbased optimization step.
Iii System Overview
The body pose estimation system relies on the feed of a camera network composed of asynchronous RGBD sensors, thus on sequences of RGB images and depth maps from the different sensors of the network. Neither assumptions on the number of sensor nor on the availability of external aiding tools are made by the system. The only prerequisite is the extrinsic calibration of the camera network^{2}^{2}2In this work, we exploited a stateoftheart opensource approach to compute the extrinsic calibration of the network. See [26] for further information.. This calibration procedure firstly defines a common global reference frame and then computes the matrix expressing the relative transformation between the local frame of the th camera and the global frame .
The system can be considered as composed by two parts: (i) the singleview detector and (ii) the multiview fusion algorithm. The first part (i) is the same for each detection node of the network (i.e. the computer in charge of acquiring and processing the data coming only from the camera connected to it). The multiview fusion algorithm (ii), instead, is executed only by the central processing node which collects and fuses together the estimates provided by the detection nodes.
Although a variety of different solutions to estimate 3D body poses from a single RGBD sensor exists, in this work we used the one described in [3] which extends the singleview approach described in [14]. Despite our work not being constrained by the specific runtime singleview detection approach, the rationale behind our choice stands in its general applicability since its performances are independent from both the number of people to be tracked and the movements they perform.
Iiia Singleview detections identification
The singleview estimates coming from each detection node of the network are fused together by the central processing node. At the generic time , it keeps in memory a set of tracks , where the generic
is defined as the vector of the joint positions of the
th skeleton at time , expressed in the global reference frame. Formally, , where is the number of joints included in the skeleton.Let us call the generic set of skeletons detected by the th detection node in its local reference frame . Formally, we have , where each is composed of the position of the joints of the skeleton. Whenever the central processing node receives a new from the th detection node, it applies the rigid transformation to express every skeleton in the global reference frame:
(1) 
For the ease of reading, in the following the apex will be neglected since every quantity has been already expressed in the global reference frame. Furthermore, also the subscript will be removed from the notation since, if not explicitly stated, we will consider just the generic th detection node.
The following step performed by the central processing node is data association. The objective is to match each skeleton detected in the current view with its corresponding track, i.e. with its state computed at the previous computation time step. If the algorithm fails to find a matching track for one or more of the detected skeletons within the available ones, it generates a new track for each of them, meaning that persons never seen before walked into the scene.
The problem can be mathematically formulated as an assignment problem. To efficiently solve it, we define the cost of the association of track to skeleton and we look for the pair skeletontrack which leads to the minimum total cost [27, 28]. We need therefore to compute, at each time , the assignment cost matrix , where its generic element represents the cost of associating the th skeleton to the th track. For each generic th track among the already available ones, let we call the Kalman filter in charge of tracking the position and velocity of its centroid. We first compute , the Kalman filter prediction for the th track at time computed without adding any new detection. We then compute, for each skeleton detected at time , as the state of at time under the assumption of associating the th skeleton to the th track. The likelihood vector is therefore computed as:
(2) 
Finally, we compute the cost of the th trackskeleton pair as the Mahalanobis distance between and the covariance matrix of the Kalman filter . Therefore, each element of the cost matrix uses the Mahalanobis distance, where the covariance matrix of the Kalman filter weights the squared norm of the distance vector:
(3) 
At this point, providing the soconstructed matrix to the Hungarian algorithm [27], also known as Munkres algorithm [28], we solve the assignment problem finding the optimal pairing between tracks and detections. However, since that algorithm does not directly implement a constraint on the maximum distance between tracks and detections, a threshold
is introduced to reduce the probability of wrong associations. Given a skeleton, if its distance from all the tracks is higher than
, than it does not match any of them, meaning that it corresponds to a new person on the scene and, therefore, a new track for him needs to be created.IiiB Multiview skeletal fusion
Once the singleview detections identification is completed, the tracks are given as input to the proposed processing pipeline (Fig. 1). The whole algorithm is based on the association of each track with a dimensional Kalman filter, where is the number of joints. From this point on, for ease of reading, just one track is considered since all the tracks are treated as separate entities and processed following exactly the same pipeline.
The state of the Kalman filter at time is constructed by juxtaposition, for each th joint, of its 3D position and velocity . Formally:
(4) 
The prediction phase of the Kalman filter is driven by the following constant velocity evolution model:
(5) 
where is the transition matrix that implements the constant velocity prediction for each component. In other words, at time step , the velocity part of the state is predicted to be equal to the previous one (), while the position part evolves as , where is the sampling period. We use , because is the maximum framerate of our sensor. In case of heavy occlusions, a normal situation in multipersons scenarios, it is likely that the time interval between two consecutive detections of the same full skeleton can be approximated to an integer multiple of . Therefore, letting the time interval between two consecutive detections be , the prediction step is computed times.
is the noise coupling matrix that describes how the elements of the Gaussian white noise vector
affect the system.The observations at time are represented by the 3D joint positions of the identified skeleton in the global reference frame. Therefore, the measurement model is:
(6) 
where
(7) 
The meaning of is straightforward, and the measurement noise vector is defined as Gaussian white noise .
Once defined the structure of the Kalman filters, we need to find the values of the noise variances. In the presented work, we estimated the measurement noise variance offline from a prerecorded static sequence available in our dataset. We therefore computed the value of
by averaging, through all the joints, the standard deviation of the joint positions in all the detections of the sequence. As the careful reader may notice, this is an approximation, given that this value might be variable in different spots of the scene due to a nonperfectly uniform calibration of the camera network.
The process noise variance, on the other hand, cannot be computed using the same offline procedure since it is dependent from the movements performed by the people in the scene. Therefore, a manual tuning of the process noise variance has been performed.
IiiC Joint confidence feedback
The basic concept of Bayesian filtering is the inclusion of apriori information in the estimation process. Starting from this consideration, we preprocess the detections coming from each singleview detection node to gain insights to be included in the system state. The singleview detector returns, for each th joint of each detection, its 3D position and the associated confidence level . In order to include this information in our estimation procedure, we implement an adaptive scheme that determines, at time step , the measurement noise variance of , i.e. in relation to :
(8) 
In order to reduce the tracking errors coming from highly uncertain detections, we use a threshold of to filter them out. Therefore, if , the joint detection is rejected and substituted with the Kalman filter prediction at time ().
IiiD Outlier filtering
One of the most important advantages of camera networks is the possibility to overcome occlusions and inconsistencies typical of the singleview detections which generally lead to huge spikes in joint position estimates. To filter out the socalled outliers, we introduce an adaptive scheme that updates the measurement reliability, based on the recent history of the tracked joint, to prevent too rapid changes in its position. We consider the Euclidean distance between consecutive positions of the same joint. Once a threshold is determined, the new measurement is considered unreliable if the distance value from the previous state is above the threshold. In our algorithm we use, for each th joint, a slow timevarying threshold that takes into account the information from the joint history. The idea is to consider the consecutive distances between the previous samples of the joint position , where . The threshold at time is therefore computed as:
(9) 
where . ^{3}^{3}3In our experiments, we found adequate values for and to be respectively and . In this way, the jointspecific threshold is potentially capable of slowly adapting to the changes in joint speed.
If the new detection distance for the th joint is larger than the just computed threshold , the detection is not directly rejected, but the corresponding measurement noise variance, after the joint confidence adaptation, is updated as follow:
(10) 
A possible limitation of this approach might be that correct detections describing a very fast motion of a joint could be detected as outliers. To overcome this limitation we introduced the parameter , which represents the maximum number of consecutive outliers a track can accept. In this way, even if consecutive measurements are detected as outliers, the next one is considered reliable and used to update the track. In practice we chose , based on the idea that, being in a network, if one detection node is experiencing an occlusion leading to an outlier, hopefully the next detection will come from another detection node not experiencing the same occlusion.
IiiE Skeleton consistency
A typical problem in skeletal tracking from images is the segment length variability. Indeed, the distance between two adjacent joints might vary depending on their relative position estimated from images taken from different viewing angles. To overcome this limitation, we introduce an algorithm which aims at keeping the segment lengths constant during the whole tracking process. While the Kalman filter presented in the previous sections focuses on ensuring temporal coherence, this section aims at discussing the algorithm introduced to guarantee the physical consistency of the tracked skeletons.
At each time step , the physical consistency algorithm takes as input the system state , and the hierarchical model of the human body (Fig. 2).
Head and chest joints have been excluded from the optimization for two reasons. On the one hand, we obtained more stable results computing the chest as the central point between shoulders and hips. On the other hand, the head has been removed since out of interest for this preliminary assessment. However, the developed implementation of the algorithm already supports the inclusion of those two joints. At the time (dependency omitted for the ease of reading), for each th link of the filtered skeleton track (, with number of links of the skeleton model), we compute the energy of its length error:
(11) 
where and are the 3D coordinates of, respectively, the child and parent joints of the th link. While is the output of the current link length optimization, is the output of the length optimization of the previous link of the hierarchical model. Initial values for are set equal to the estimates of the Kalman filter .
We initialize for each link using the average of the limb lengths measured in the first few frames in which the entire skeleton is completely tracked. Then, after the optimization, the estimated lengths are updated using the just computed joint coordinates to slowly compensate possible inaccurate link lengths initializations. In order to avoid jitters in the final estimates due to local minima computed by the minimization of the energy defined as in Eq. 11, we add a second term which accounts for link orientation errors. Therefore, we redefin as:
(12) 
where:
(13) 
The unitary vectors and describe, respectively, the orientation of the th link during the optimization process and the original link orientation estimated by the Kalman filter. To solve this energy minimization problem we use the LevenbergMarquardt algorithm implemented in the Ceres Solver library^{4}^{4}4http://www.ceressolver.org.
Iv Experiments and Results
In order to highlight the efficacy of the proposed approach, given the lack of publicly available RGBD cameranetwork datasets, a new one has been recorded. We are currently working to make our dataset public. To record the dataset, we asked different subjects to perform free movements in the scene. We recorded data from a camera network composed by 4 Kinect v2 cameras and, at the same time, the output of a commercial motion capture system (BTS SMARTDX, BTS Bioengineering Corp., USA). Each subject was instrumented with a set of passive reflective markers attached to the skin following the BTS standard marker placing protocol.
The 4 Kinects were placed at the four corners of the considered motion area, while the 12 SMARTDX cameras were equally spaced along the perimeter. Both the Kinects and the SMARTDX cameras were placed at a height of approximately 2.5 m. Noteworthy, the two systems acquire data at different frequencies: 30 fps for the Kinect sensor network, and 50 fps for the SMARTDX cameras. A time synchronization mechanism for relating each Kinect data point with the corresponding reference was therefore set up.
After completing the calibration procedures of both the systems, we recorded three static sequences (15 seconds each) and six dynamic sequences (approx. 60 seconds each). Each dynamic sequence is characterized by different motion characteristics (i.e. fast or slow movements) performed by a different number of subjects (one or two). While the static sequences have been used for tuning systems parameters, the dynamic ones have been used to assess the accuracy of the proposed approach against the goldstandard results provided by the BTS system.
Fig. 3 shows an example of the virtual scene where the four identified skeletons (the subject ID is presented as the number over the skeleton) replicating the real subject movements.
The evaluation was conducted using as overall metrics the average and standard deviation of the joints displacement tracking errors among all the joints. In particular, after the interpolation step, for each
th joint, we compare the estimated 3D position and the corresponding ground truth, respectively named and . Then, given the sequences of time samples and , where and, the two evaluation metrics are defined as:
(14)  
For all the six sequences, we computed the same performance metrics (average joint displacement error and standard deviation) on the estimates provided by other stateoftheart approaches using as input exactly the same data from all the four available Kinects. The other comparison methods have been: (i) OpenPose [14] enriched with the data association and depth inference algorithms, (ii) moving average filtering (MAF), a common baseline approach already described in other similar stateoftheart works such as [3, 19], and (iii) the standard version of OpenPTrack [3]. The obtained results are reported in Table I.
Sequence and  OpenPose [14]  MAF  OpenPTrack [3]  Proposed 

Subject  Solution  
Seq. 1  
Seq. 2  
Seq. 3  
Seq. 4  
Seq. 5, Sbj. 1  
Seq. 5, Sbj. 2  
Seq. 6, Sbj. 1  
Seq. 6, Sbj. 2 
The results clearly show how the proposed multisubject kinematics tracking approach outperforms, in terms of joint displacement errors, the other considered stateoftheart systems. Moreover, it is worth noticing that in the fifth and sixth sequences the two subjects on the scene were tracked at the same time, demonstrating the absence of accuracy drops in multiuser applications of our system.
As an additional evaluation metric for the proposed system, we investigated the consistence of the estimates quality when the network is composed by a lower number of cameras. To do that we selected, for every available sequence, data coming just from two, three, or four detection nodes.
Fig. 4 shows how the estimation quality increases with the number of cameras installed in the network.
Furthermore, it is important to observe that such performances were obtained while producing the body pose estimates in realtime (tested on an Intel Core i74770 CPU and Nvidia GeForce GTX 1060 GPU powered desktop). In a typical iteration, the average computational time (approx. ) is distributed among the different major processes as follow:

for the adaptive scheme with the outlier detection, the iterative computation of the outlier thresholds, and the iterative estimate of the limb lengths;

– for the limb lengths optimization;

– for the update step of the Kalman filter;

for other computational activities.
Tracked  Worst case comp. time  Worst case fps  Experimental fps 

persons  (theoretical)  
1  
2  
3  –  
4  
5  –  
6  – 
Table II reports how the theoretical output frame rate scales with the number of subjects to be tracked by our system. In case of up to two subjects the actual tracking output frame rate is however lower than the theoretical one due to the input data frequency constraint; indeed, the Kinect cameras are capable of providing data at maximum at ^{5}^{5}5Due to the lack of constraints in cameras synchronization placed by our system, however, it is feasible to achieve slightly higher data input frame rates.. In case of three or more persons, instead, the most restrictive limit becomes the computational time, with an actual tracking frame rate which scales proportionally to the number of subjects to track. Setting a limit for considering an application as realtime to be equal to , it is shown that for cases of up to 5 persons in the scene our approach satisfies this constraint.
V Conclusions
In this work we proposed, discussed, and evaluated an innovative markerless approach to accurately estimate and the track human motion in realtime through a calibrated network of RGBD cameras. The proposed methodology demonstrated to be reliable and accurate in tracking multiple persons at the same time, without requiring the subjects to perform initial calibration activities or to wear any marker. The developed system requires neither a specific number of cameras in the network, nor all the cameras to be of the same manufacturer; moreover, it does not require the cameras to be synchronized. These three valuable features enable users to build their own heterogeneous network following their specific needs and possibilities.
Starting from the noisy singleframe singleview detections, our algorithm ensures temporal and physical consistency during the whole tracking period. As demonstrated by the obtained results, it reduces the joint displacement tracking error, with respect to the current stateoftheart approaches used as reference for the comparison. Moreover, the proposed approach is not only reliable and effective, but also efficient, enabling to track in realtime up to 5 subjects at the same time. This is indeed a crucial capability, since it is a major requirement for the large majority of the applications in the humanrobot interaction field.
Acknowledgment
Authors would like to thank Dr. Zimi Sawacha and the Magick team for their help in collecting and processing the ground truth references for our database with their markerbased motion capture system.
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