Computational complexity analysis for multiple hypothesis tracking

This paper presents a detailed analysis of the computational complexity of multiple hypothesis tracking (MHT). The result shows that the computational complexity of MHT is dominated by the number of hypotheses. Track merging and pruning are also analyzed. The results of this paper provide a new efficient tool for selecting parameters for an MHT tracker and predicting its complexity.

In this paper, an algorithm for tracking multiple maneuvering targets by Multiple Hypothesis Tracking (MHT) with nonlinear non-Gaussian Kalman filter is investigated. The main challenges in multiple maneuvering targets tracking are the nonlinearity and non -Gaussianity problems. The Multiple Hypothesis Tracking (MHT) is used to detect the multiple targets in maneuverable and non-maneuverable modes. The computational requirements increase exponentially with number of tracks, the backscan depth and this can be reduced by careful design and tuning of MHT. The 1-backscan MHT algorithm is a good compromise between the two conflicting requirements of good tracking performance and limitation of computation time. The nonlinear non-Gaussian Kalman filter is used to track the target with high maneuver rate. The nonlinear non-Gaussian Kalman filter is implemented in MHT to give less probability of missing the target. The 1-backscan MHT with nonlinear non-Gaussian Kalman filter is free from computational burden by using simple probability concepts. This method of tracking also shows the reduction in the overshoot of root mean square error (RMSE).

Hypothesis formation is a major computational burden for any multiple hypotheses tracking (MHT) method. In particular, a track-oriented MHT method defines compatible tracks to be tracks not sharing common observations and then re-forms hypotheses from compatible tracks after each new scan of data is received. The Cheap Joint Probabilistic Data Association (CJPDA) method provides an efficient means for computing approximate hypothesis probabilities. This paper presents a method of extending CJPDA calculations in order to eliminate low probability track branches in a track-oriented MHT method. The method is tested using IRST data. This approach reduces the number of tracks in a cluster and the resultant computations required for hypothesis formation. It is also suggested that the use of CJPDA methods can reduce assignment matrix sizes and resultant computations for the hypothesis-oriented (Reid’s algorithm) MHT implementation.

To date, Wald sequential probability ratio test (WSPRT) has been widely applied to track management of multiple hypothesis tracking (MHT). But in a real situation, if the false alarm spatial density is much larger than the new target spatial density, the original track score will be very close to the deletion threshold of the WSPRT. Consequently, all tracks, including target tracks, may easily be deleted, which means that the tracking performance is sensitive to the tracking environment. Meanwhile, if a target exists for a long time, its track will have a high score, which will make the track survive for a long time even after the target has disappeared. In this paper, to consider the relationship between the hypotheses of the test, we adopt the Shiryayev SPRT (SSPRT) for track management in MHT. By introducing a hypothesis transition probability, the original track score can increase faster, which solves the first problem. In addition, by setting an independent SSPRT for track deletion, the track score can decrease faster, which solves the second problem. The simulation results show that the proposed SSPRT-based MHT can achieve better tracking performance than MHT based on the WSPRT under a high false alarm spatial density.

Interacting multiple model (IMM) filtering and multiple hypothesis tracking (MHT) represent the most accurate methods currently available for tracking multiple maneuvering targets in cluttered environments. Although these methods are complex, modern computational capabilities make their combined implementation feasible for modern tracking systems. This paper discusses alternative approaches for developing a combined IMM/MHT tracking system and describes specific implementations that have been developed for radar and IRST applications. Simulation results for both radar and IRST systems are presented. Track maintenance and accuracy performance for the IMM/MHT system is compared with that obtained from an MHT tracker using a conventional filtering approach. Results indicate that the improvements in data association derived from the use of IMM filtering with MHT may be comparable to the well known IMM improvements in track accuracy. The addition of multiple filter models to MHT data association has the potential to significantly increase computational requirements. Thus, several compromises, described in this paper, have been developed in order to assure computational feasibility. Preliminary estimates of computational requirements are given in order to demonstrate implementation feasibility.© (1997) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

Multiple Object Tracking (MOT) has attracted increasing attention due to its academic and commercial potential. However, it still remains challenging due to factors like data association ambiguity and abrupt appearance changes. To address these issues, we extended the multiple hypothesis tracking (MHT) by incorporating the appearance features which extracted from faster region convolutional neural network (Faster-RCNN). Additionally, a principal component analysis method was introduced to update discriminative appearance features. Thus, the data association ambiguity can be reduced surprisingly by exploiting Faster-RCNN, which means fewer hypothesis for MHT. Meanwhile, the issue of abrupt appearance changes can be addressed by modeling discriminative appearance feature based-on MHT. Many experiments on MOT benchmark show competitive performance of the proposed approach in comparison with other state-of-art tracking methods.

In multi-target tracking, Multiple Hypothesis Tracking (MHT) can effectively solve the data association problem. However, traditional MHT can not make full use of motion information. In this work, we combine MHT with Interactive Multiple Model (IMM) estimator and feature fusion. New algorithm greatly improves the tracking performance due to the fact that IMM estimator provides better estimation and feature information enhances the accuracy of data association. The new algorithm is tested by tracking tropical fish in fish container. Experimental result shows that this algorithm can significantly reduce tracking lost rate and restrain the noises with higher computational effectiveness when compares with traditional MHT.

In this paper, we present a novel 2-D laser-based global localization approach for mobile robots, which is composed of geometrical relationship construction, a new structural unit encoding scheme (SUES), and an extended multiple hypothesis tracking (MHT) algorithm. Different from existing methods, we construct a 3-D "directional endpoint" feature encapsulating both the endpoint and the direction of a line segment; on this basis, a novel and efficient online structural unit encoding scheme (SUES) is proposed to describe the geometric relationship between the two directional endpoint features with some robustness to dynamic disturbances. Note that SUES presented in this paper is different from the bag-of-words scheme in two aspects: 1) SUES quantizes the geometrical relationship without offline training for vocabulary and 2) SUES is independent of the quality of the vocabulary. By factoring the global localization problem into a discrete pose estimation problem, the MHT is extended on the basis of SUES and odometry information to gradually restore the global robot pose. Different from the classical MHT framework, the extended MHT takes the independent observation results as the a priori, while the likelihood term is composed of consecutive candidate poses and the odometry information. Evaluations are carried out by using both publicly available data sets and self-recorded data sets. Comparative experimental results with respect to the adaptive Monte Carlo localization are presented to show the superior performance of the proposed approach in terms of success ratio and efficiency.

A distributed two-tier near optimal algorithm is proposed for target tracking in sensor networks. Tier one is a multiple hypothesis tracking (MHT) algorithm where the Viterbi algorithm is used. In this tier, only binary data is used to obtain a rough region around the target. Tier two improves the accuracy of the MHT decision by localized maximum likelihood. This reduces the computational complexity and the communication costs between sensors over the global maximum likelihood approach. It also results in higher sensor power efficiency, hence longer service time of the tracking network. This two-tier system is a distributed near optimal tracking algorithm. The localized maximum likelihood tracking can tolerate errors made by the Viterbi algorithm in tier one, hence the overall algorithm is robust.

This paper discusses several theoretical issues related to the score function for the measurement-to-track association/assignment decision in the track oriented version of the multiple hypothesis tracker (MHT). This score function is the likelihood ratio: the ratio of the pdf of a measurement having originated from a track, to the pdf of this measurement having a different origin. The likelihood ratio score is derived rigorously starting from the fully Bayesian (hypothesis oriented) MHT, which is shown to be amenable under some (reasonable) assumptions to the track oriented MHT. The latter can be implemented efficiently using multidimensional assignment. The main feature of a likelihood ratio is the fact that it is a (physically) dimensionless quantity and, consequently, can be used for the association of different numbers of measurements and/or measurements of different dimension. The explicit forms of the likelihood ratio are discussed both for the commonly used Kalman tracking filter, as well as for the interacting multiple model estimator. The issues of measurements of different dimension and different coordinate systems are also discussed.

In this work, we adapt a method based on multiple hypothesis tracking (MHT) that has been shown to give state-of-the-art vessel segmentation results in interactive settings, for the purpose of extracting trees. Regularly spaced tubular templates are fit to image data forming local hypotheses. These local hypotheses are then used to construct the MHT tree, which is then traversed to make segmentation decisions. Some critical parameters in the method, we base ours on, are scale-dependent and have an adverse effect when tracking structures of varying dimensions. We propose to use statistical ranking of local hypotheses in constructing the MHT tree which yields a probabilistic interpretation of scores across scales and helps alleviate the scale dependence of MHT parameters. This enables our method to track trees starting from a single seed point. The proposed method is evaluated on chest computed tomography data to extract airway trees and coronary arteries and compared to relevant baselines. In both cases, we show that our method performs significantly better than the Original MHT method in semiautomatic setting. The statistical ranking of local hypotheses introduced allows the MHT method to be used in noninteractive settings yielding competitive results for segmenting tree structures.

For operations in the Arctic, drift ice can be a major hazard. To be able to mitigate this, it is essential to know the position of viable threats. Many sensors can be employed, such as satellite Synthetic Aperture Radar (SAR), marine radar, air surveillance et cetera. At the core of the fusion of this sensor data is a Multi-Target Tracking (MTT) problem. This problem is studied in this paper through the implementation and application of the Multiple Hypothesis Tracking (MHT) algorithm. A major limiting factor in the application of multi-target tracking is scalability. A common method of handling the scaling is clustering, which separates the MHT filter into smaller independent parts. However, with growing scale, the association of sensor data to the “right” cluster can become resource intensive in itself. A method is explored, based on rectangular lower probability bounds, to efficiently index the clusters and compartmentalize the measurement update of the MHT. The method uses the bounding box of the lower probability bound of tracks and reports respectively, to perform an intersection lookup against the sensor field-of-view, efficiently selecting clusters of relevance. The method, as well as the MHT algorithm, has been implemented and published online under an open-source license. In this report, the implementation is described and tested on simulated data for statistics. Further, it is tested against data extracted from the polarimetric classification of ice using satellite imagery of the Arctic. Results show that computational speed improvements can be achieved, in comparison to the linear complexity of a naive search, but that comparable performance can be obtained using standard database lookups.

Tracking body parts of multiple people in a video sequence is very useful for face/gesture recognition systems as well as human computer interaction (HCI) interfaces. This paper describes a framework for tracking multiple objects (e.g., hands and faces of multiple people) in a video stream. We use a probabilistic model to fuse the color and motion information to localize the body parts and employ a multiple hypothesis tracking (MHT) algorithm to track these features simultaneously. The MHT algorithm is capable of tracking multiple objects with limited occlusions and is suitable for resolving any data association uncertainty. We incorporated a path coherence function along with MHT to reduce the negative effects of spurious measurements that produce unconvincing tracks and needless computations. The performance of the framework has been validated using experiments on synthetic and real sequence of images.

Panoramic sweeps produced by a scanning range sensor often defy interpretation using conventional line-of-sight models, particularly when the environment contains curved, specularly reflective surfaces. Combining multiple scans from different vantage points provides geometric constraints necessary to solve this problem, but not without introducing new difficulties. Existing multiple scan implementations, for the most part, ignore the data correspondence issue. The multiple hypothesis tracking (MHT) algorithm explicitly deals with data correspondence. Given canonical observations extracted from raw scans, the MHT applies multiple behavior models to explain their evolution from one scan to the next. This technique identifies different topological features in the world to which it assigns the corresponding measurements. We apply the algorithm to real sonar scans generated specifically for this investigation. The experiments consist of interrogating a variety of two-dimensional prismatic objects, standing on end in a 1.2-m-deep freshwater tank, from multiple vantage points using a 1.25 MHz profiling sonar system. The results reflect the validity of the algorithm under the initial assumptions and its gradual performance degradation when these assumptions fail to characterize the environment adequately. We close with recommendations that detail extending the approach to handle more natural underwater settings.

The crucial problem in multiple target tracking is the hit-to-track data association. A hit is a received signal from a target or background clutter which provides positional information. If an incorrect hit is associated with a track, that track could diverge and prematurely terminate or cause other tracks to also diverge. Most methods for hit-to-track data association fall into two categories: Multiple Hypothesis Tracking (MHT) and Joint Probabilistic Data Association (JPDA). Versions of MHT use all or some reasonable hits to update a track and delay the decision on which hit was correct. JPDA uses a weighted sum of the reasonable hits to update a track. These weights are the probability that the hit originated from the target in track. The computational load for the joint probabilities increase exponentially as the number of targets increases and therefore, is not an attractive algorithm when expecting to track many targets. This paper reviews the JPDA filter and two simple approximations of the joint probabilities which increase linearly in computational load as the number of targets increase. Then a new class of near optimal JPDA algorithms is introduced which run in polynomial time. The power of the polynomial is an input to the algorithm. This algorithm bridges the gap in computational load and accuracy between the very fast simple approximations and the efficient optimal algorithms.© (1993) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.