Elsevier

Signal Processing

Volume 131, February 2017, Pages 412-421
Signal Processing

Iterative RANSAC based adaptive birth intensity estimation in GM-PHD filter for multi-target tracking

https://doi.org/10.1016/j.sigpro.2016.09.001Get rights and content

Highlights

  • A multi-target tracking algorithm combining PHD filter with adaptive detection of newborn targets is developed.

  • A novel birth intensity estimation approach is proposed to accurately and robustly determine the intensity of new targets.

  • A measurement classifying approach is proposed to remove errors from the measurement uncertainties.

  • A spatio-temporal filtering based on I-RANSAC is proposed to further eliminate errors of birth intensity from clutter.

  • The proposed tracker can improve number and state estimation of targets in complicated scenarios.

Abstract

This paper investigates a novel multi-target tracking algorithm for jointly estimating the number of multiple targets and their states from noisy measurements in the presence of data association uncertainty, target birth, clutter and missed detections. Probability hypothesis density (PHD) filter is a popular multi-target Bayes filter. But the standard PHD filter assumes that the target birth intensity is known or homogeneous, which usually results in inefficiency or false tracks in a cluttered scene. To solve this weakness, an iterative random sample consensus (I-RANSAC) algorithm with a sliding window is proposed to incrementally estimate the target birth intensity from uncertain measurements at each scan in time. More importantly, I-RANSAC is combined with PHD filter, which involves applying the PHD filter to eliminate clutter and noise, as well as to discriminate between survival and birth target originated measurements. Then birth targets originated measurements are employed to update the birth intensity by the I-RANSAC as the input of PHD filter. Experimental results prove that the proposed algorithm can improve number and state estimation of targets even in scenarios with intersections, occlusions, and birth targets born at arbitrary positions.

Introduction

Multi-target tracking algorithms have generated a great deal of interest in fields like smart surveillance [1], [2], [3], [4], automated guidance of robotics [5], [6], as well as biology [7] etc. Multi-target tracking (MTT) aims to on-line estimate target information of interest (e.g., target number, position, velocity and size) from uncertain measurements collected by sensors, such as cameras, radar, sonar, and microscopy. Since a target can generate multiple measurements detected or not detected by the sensor, and spurious measurements (clutter), measurements collected by a sensor are uncertain. Moreover, multiple targets can appear, disappear and intersect anywhere and anytime in the surveillance view, which lead to unknown target number and uncertain association of targets with measurements. Therefore, in general, due to clutter, detection uncertainty, target number variation, as well as unknown data association of targets with measurements, tracking a variable number targets is still a challenging issue to be addressed.

Traditional approaches to cope with unknown data association, clutter, noise, and missed detections in multi-target state estimation are data association techniques, such as multiple hypotheses tracking (MHT) and joint probability data filter (JPDAF). MHT [8] resolves them by the deferred decision logic, where all measurement-track hypotheses are enumerated and propagated by Kalman filter and the subsequent data in a sliding window. Also, JPDA [9] is another data association method, which eliminates data association uncertainty and missed detections by the association probabilities of the given measurements to various targets in validation gate. Compared with MHT, JPDA can not effectively account for target birth and target death. Moreover, both MHT and JPDA, due to the combinatorial computation of association between targets and measurements, may suffer a heavy computational load.

Alternatively, avoiding the association computation in traditional multi-target filters, the finite set statistics (FISST) [10] provides a theoretically optimal solution to multi-target tracking via Bayesian recursion, where the states and measurements of multiple targets at each scan time are modeled by a random finite set (RFS) respectively. Under RFS framework, jointly estimating the number of multiple targets and their states from noisy measurements is formulated by optimal multi-target Bayes filter in the presence of clutter, association uncertainty and varying number of targets. Multi-target filters under RFS, such as probability hypothesis density (PHD) filter [10], [11], [12], the cardinalized PHD (CPHD) [13], [14] filter and multi-Bernoulli filter [15], [16], [17], [18], have achieved many advances and developments in theoretical researches and applications. To deal with the computation complexity of the multi-target Bayes filter, PHD and CPHD propagate moments and cardinality distributions [10], [11], [12], [13], [14], whilst multi-target multi-Bernoulli (MeMBer) recursion propagates the multi-target posterior density [15]. To decrease the bias in cardinality estimation of Mahler's MeMBer [15], the cardinality-balanced MeMBer was proposed by propagating a set of multi-Bernoulli parameters of the posterior multi-target RFS [16]. The labeled MeMBer was also developed to output target tracks with an unbiased posterior cardinality by exploiting the conjugate prior form for labeled RFS [17]. In addition, Gaussian mixture and particle implementations of MeMBer have been developed [15]. These RFS based filters have been successfully applied to estimate expected states of multiple point targets (e.g., radar tracking) [3], [10], [11], [12], [13], [14], [15], [16], [17], and extended targets (e.g., image based tracking) [1], [2], [4], [5], [7], [18], [19], [20], [21], [22].

The focus of this paper is multi-target filtering algorithm based on PHD filter. PHD filter is an approximation solution to the optimal multi-target Bayes filter based on RFS. Greatly alleviating the computational complexity, PHD filter propagates the intensity (referred to as PHD) instead of multi-target posterior [10], [11], [12]. The PHD recursion can be implemented by either the analytic solution (i.e., Gaussian mixture PHD, GM-PHD) [11] or the sequential Monte Carlo (SMC) method (i.e., particle PHD) [12]. Despite PHD filter can remove clutter and noise from measurements via Bayesian recursion, PHD filter based trackers remain a challenging task due to target birth and detection uncertainty, such as missed detections and detection of extended (group) targets. As well known, new targets can appear or disappear at arbitrary positions at any time step in real world scenarios. In other words, unknown spatial and temporal distributions of new targets usually arise in the state space. Also, extended targets potentially generate more than one measurement at each time step, where target merging and splitting events may randomly increase birth targets around an extended target [19], [20], [21], [22]. However, the standard PHD filter assumes that the birth intensity is a known priori or homogenous in the field of view, which is not in accordance with the real tracking scenarios. The inappropriate assumptions may result in inefficiency such as large computation load, human interactions, high false alarm rate and a long delay of track initialization (i.e., deferred confirmation of birth targets).

An intrinsic problem in tracking a varying number of targets or extended targets is the unknown distribution of newborn targets. Instead of approximating intensity of targets over the entire state space, most existing solutions explore the spatial relation between the output states at previous time step and the input measurements at the current time [23], [24], [25]. Ristic et al. [23] designed a newborn target intensity in the region of the state space with high likelihood values. In a similar vein in [25], instead of Gaussian mixture approximation over the entire state space, a uniform density given state estimates at previous time step was designed as birth density to improve the efficiency. However, all of the above methods assume that birth targets appear in the vicinity of the position estimates of a tracker, thus not covering new targets appearing from arbitrary positions, which shows a significant limitation.

Another way to birth intensity estimation is to discriminate between newborn targets originated measurements and measurements of survival targets and clutter. Zhou et al. [26] determined measurements of new targets according to the entropy distribution and coverage rate of state estimates and measurements in two consecutive images, then established spatial intensity of new births. However, this method only explored the spatial distribution of measurements at the current time, thus suffering from uncertain observations such as clutters and missing detections. Alternatively, assuming the birth intensity depends on the state estimates, Maggio et al. [27] modeled the birth intensity and recursively learned possible positions of new targets in terms of the output state estimates of a tracker and human defining context information. Besides, Wang et al. [28] confirmed positions of birth targets and birth intensity from the future multiple frames of measurements by sequential probability ratio test (SPRT) . Compared with spatial filtering in [26], algorithms in [27], [28], smooth the input measurements both in space and time, thus providing a more stable solution. But due to combinatorial computation on the entire measurement sets, [28] suffers a heavy computational load. In addition, [27] requires additional human intersection to get context information on birth events, which will degrade the effects of birth intensity estimation.

In this paper, a novel adaptive birth intensity estimation algorithm is proposed for PHD filter, by which a robust multi-target tracking algorithm is provided (Fig. 1). To estimate birth intensity in terms of spatio-temporal information, an iterative random sample consensus(I-RANSAC) algorithm is proposed to smooth the input measurements in a sliding window. I-RANSAC operates on multi-scan measurements and permits a deferred confirmation of the birth target positions using the future measurements. To eliminate biased errors due to only using the measurement set, the output states of PHD filter is employed to discriminate between the survival and the new birth targets originated measurements. Moreover, in conjunction with I-RANSAC, the improved PHD filter is a feedback system, which is able to adaptively update the birth target intensity and estimate reliable state and number of targets at each time step. This paper presents the Gaussian mixture implementation of the resulting multi-target tracker and demonstrates the capability of the proposed tracker.

The rest of this paper is outlined as follows. Section 2 presents the PHD filter and its Gaussian mixture implementation. A discussion on birth intensity estimation for PHD filter is also covered in Section 2. Section 3 firstly presents the mathematical formulation of birth intensity estimation for GM-PHD filter. Then the proposed I-RANSAC based birth intensity estimation and its implementation is described in details. Section 4 analyzes experiments on a scenario for point target tracking and a real visual surveillance dataset with extended targets. Finally, some conclusions are discussed in Section 5.

Section snippets

Multi-target tracking algorithm under RFS

Estimating the number and states of multiple targets always remains challenges due to target birth, target death, and uncertain detections such as clutter, missed detections and uncertain origin. Multi-target Bayes filter under RFS framework has been a popular systematic approach to multi-target tracking. Under the RFS framework, states of multiple targets Xk at time k is represented as a RFS,Xk={xk(1),,xk(M(k))}where M(k) is a random variable defining the number of targets at time k. Sensors

Problem formulation

As analyzed in Section 2, the standard PHD filter will lose tracks of targets or yield more false alarms, when the new target intensity is unknown or homogeneous over the field of view. From analysis in Section 1, measurement based methods [26], [27], [28] are reasonable solutions to birth intensity estimation, for measurements contain most of observable information of targets. Also, this paper attempts to adaptively estimate birth intensity from the measurement set.

However, due to detection

Experimental results

The proposed I-RANSAC based algorithm provides a useful solution to generate birth target intensity, which can be in conjunction with PHD filter for an improved tracker as in Fig. 1. To demonstrate the performance improvements on dealing with newborn targets, two different complex scenarios are used to evaluation, namely, point target tracking scenario with birth targets appearing from unknown positions, and an extended target tracking scenario with birth targets induced by occlusions.

Conclusions

This paper presents a robust GM-PHD filtering algorithm with adaptive birth intensity estimation. In this tracker, the output states of PHD filter is used to discriminate between the potential measurements of the survival and the new birth targets for birth intensity updating. In order to cope with unknown distribution of newborn targets, I-RANSAC with a sliding window is proposed to adaptively smooth the potential birth target measurements in time and space. The proposed I-RANSAC with a

Acknowledgments

This paper is jointly supported by the National Natural Science Foundation of China (61305016) and Fundamental Research Funds for the Central Universities (Grant No. JUSRP1059).

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