We study algorithms for matching user tracks, consisting of time-ordered location points, to paths in the road network. Previous work has focused on the scenario where the location data is linearly ordered and consists of fairly dense and regular samples. In this work, we consider the , where the location data comes from different trips on the same route, each with very sparse samples. This captures the realistic scenario where users repeatedly travel on regular routes and samples are sparsely collected, either due to energy consumption constraints or because samples are only collected when the user actively uses a service. In the multi-track problem, the total set of combined locations is only partially ordered, rather than globally ordered as required by previous map-matching algorithms. We propose two methods, the iterative projection scheme and the graph Laplacian scheme, to solve the multi-track problem by using a single-track map-matching subroutine. We also propose a boosting technique which may be applied to either approach to improve the accuracy of the estimated paths. In addition, in order to deal with variable sampling rates in single-track map matching, we propose a method based on a particular regularized cost function that can be adapted for different sampling rates and measurement errors. We evaluate the effectiveness of our techniques for reconstructing tracks under several different configurations of sampling error and sampling rate.
Map matching has become an increasingly important problem over the past few years due to the proliferation of GPS tracking devices and track-based applications. A number of algorithms have been proposed to address this problem @cite_18 @cite_12 @cite_10 @cite_11 @cite_4 . A class of these works contain statistical methods which are based on Bayesian estimators. The authors in @cite_12 @cite_18 use the fact that the actual positions of the user on a path form a Markov chain. Given the location measurements, a hidden Markov model is defined with the actual positions on the path as the hidden states. The measurement probabilities in the model are determined based on the location measurement noise distribution (normal distribution with mean zero and variance @math ); the transition probabilities are determined based on the spatial geometric and topological restrictions along with the temporal speed constraints of the trajectories. The matched path is the one with maximum posterior probability.
@cite_18 @cite_4 @cite_10 @cite_12 @cite_11
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Map-matching is the process of aligning a sequence of observed user positions with the road network on a digital map. It is a fundamental pre-processing step for many applications, such as moving object management, traffic flow analysis, and driving directions. In practice there exists huge amount of low-sampling-rate (e.g., one point every 2--5 minutes) GPS trajectories. Unfortunately, most current map-matching approaches only deal with high-sampling-rate (typically one point every 10--30s) GPS data, and become less effective for low-sampling-rate points as the uncertainty in data increases. In this paper, we propose a novel global map-matching algorithm called ST-Matching for low-sampling-rate GPS trajectories. ST-Matching considers (1) the spatial geometric and topological structures of the road network and (2) the temporal speed constraints of the trajectories. Based on spatio-temporal analysis, a candidate graph is constructed from which the best matching path sequence is identified. We compare ST-Matching with the incremental algorithm and Average-Frechet-Distance (AFD) based global map-matching algorithm. The experiments are performed both on synthetic and real dataset. The results show that our ST-matching algorithm significantly outperform incremental algorithm in terms of matching accuracy for low-sampling trajectories. Meanwhile, when compared with AFD-based global algorithm, ST-Matching also improves accuracy as well as running time. In order to track moving objects in long range against occlusion, interruption, and background clutter, this paper proposes a unified approach for global trajectory analysis. Instead of the traditional frame-by-frame tracking, our method recovers target trajectories based on a short sequence of video frames, e.g., 15 frames. We initially calculate a foreground map at each frame obtained from a state-of-the-art background model. An attribute graph is then extracted from the foreground map, where the graph vertices are image primitives represented by the composite features. With this graph representation, we pose trajectory analysis as a joint task of spatial graph partitioning and temporal graph matching. The task can be formulated by maximizing a posteriori under the Bayesian framework, in which we integrate the spatio-temporal contexts and the appearance models. The probabilistic inference is achieved by a data-driven Markov chain Monte Carlo algorithm. Given a period of observed frames, the algorithm simulates an ergodic and aperiodic Markov chain, and it visits a sequence of solution states in the joint space of spatial graph partitioning and temporal graph matching. In the experiments, our method is tested on several challenging videos from the public datasets of visual surveillance, and it outperforms the state-of-the-art methods. Matching a raw GPS trajectory to roads on a digital map is often referred to as the Map Matching problem. However, the occurrence of the low-sampling-rate trajectories (e.g. one point per 2 minutes) has brought lots of challenges to existing map matching algorithms. To address this problem, we propose an Interactive Voting-based Map Matching (IVMM) algorithm based on the following three insights: 1) The position context of a GPS point as well as the topological information of road networks, 2) the mutual influence between GPS points (i.e., the matching result of a point references the positions of its neighbors; in turn, when matching its neighbors, the position of this point will also be referenced), and 3) the strength of the mutual influence weighted by the distance between GPS points (i.e., the farther distance is the weaker influence exists). In this approach, we do not only consider the spatial and temporal information of a GPS trajectory but also devise a voting-based strategy to model the weighted mutual influences between GPS points. We evaluate our IVMM algorithm based on a user labeled real trajectory dataset. As a result, the IVMM algorithm outperforms the related method (ST-Matching algorithm). Evaluation of tracking algorithms in the absence of ground truth is a challenging problem. There exist a variety of approaches for this problem, ranging from formal model validation techniques to heuristics that look for mismatches between track properties and the observed data. However, few of these methods scale up to the task of visual tracking, where the models are usually nonlinear and complex and typically lie in a high-dimensional space. Further, scenarios that cause track failures and or poor tracking performance are also quite diverse for the visual tracking problem. In this paper, we propose an online performance evaluation strategy for tracking systems based on particle filters using a time-reversed Markov chain. The key intuition of our proposed methodology relies on the time-reversible nature of physical motion exhibited by most objects, which in turn should be possessed by a good tracker. In the presence of tracking failures due to occlusion, low SNR, or modeling errors, this reversible nature of the tracker is violated. We use this property for detection of track failures. To evaluate the performance of the tracker at time instant t, we use the posterior of the tracking algorithm to initialize a time-reversed Markov chain. We compute the posterior density of track parameters at the starting time t = 0 by filtering back in time to the initial time instant. The distance between the posterior density of the time-reversed chain (at t = 0) and the prior density used to initialize the tracking algorithm forms the decision statistic for evaluation. It is observed that when the data are generated by the underlying models, the decision statistic takes a low value. We provide a thorough experimental analysis of the evaluation methodology. Specifically, we demonstrate the effectiveness of our approach for tackling common challenges such as occlusion, pose, and illumination changes and provide the Receiver Operating Characteristic (ROC) curves. Finally, we also show the applicability of the core ideas of the paper to other tracking algorithms such as the Kanade-Lucas-Tomasi (KLT) feature tracker and the mean-shift tracker. We present a new method for the robust detection and matching of multiple planes in pairs of images. Such planes can serve as stable landmarks for vision-based urban navigation. Our approach starts from SIFT matches and generates multiple local homography hypotheses using the recent J-linkage technique by Toldo and Fusiello, a robust randomized multi-model estimation algorithm. These hypotheses are then globally merged, spatially analyzed, robustly fitted, and checked for stability. When tested on more than 30,000 image pairs taken from panoramic views of a college campus, our method yields no false positives and recovers 72 of the matchable building walls identified by a human, despite significant occlusions and viewpoint changes. In this paper, we propose a citywide and real-time model for estimating the travel time of any path (represented as a sequence of connected road segments) in real time in a city, based on the GPS trajectories of vehicles received in current time slots and over a period of history as well as map data sources. Though this is a strategically important task in many traffic monitoring and routing systems, the problem has not been well solved yet given the following three challenges. The first is the data sparsity problem, i.e., many road segments may not be traveled by any GPS-equipped vehicles in present time slot. In most cases, we cannot find a trajectory exactly traversing a query path either. Second, for the fragment of a path with trajectories, they are multiple ways of using (or combining) the trajectories to estimate the corresponding travel time. Finding an optimal combination is a challenging problem, subject to a tradeoff between the length of a path and the number of trajectories traversing the path (i.e., support). Third, we need to instantly answer users' queries which may occur in any part of a given city. This calls for an efficient, scalable and effective solution that can enable a citywide and real-time travel time estimation. To address these challenges, we model different drivers' travel times on different road segments in different time slots with a three dimension tensor. Combined with geospatial, temporal and historical contexts learned from trajectories and map data, we fill in the tensor's missing values through a context-aware tensor decomposition approach. We then devise and prove an object function to model the aforementioned tradeoff, with which we find the most optimal concatenation of trajectories for an estimate through a dynamic programming solution. In addition, we propose using frequent trajectory patterns (mined from historical trajectories) to scale down the candidates of concatenation and a suffix-tree-based index to manage the trajectories received in the present time slot. We evaluate our method based on extensive experiments, using GPS trajectories generated by more than 32,000 taxis over a period of two months. The results demonstrate the effectiveness, efficiency and scalability of our method beyond baseline approaches. We address the fundamental problem of goal-directed path planning in an uncertain environment represented as a probability (of occupancy) map. Most methods generally use a threshold to reduce the grayscale map to a binary map before applying off-the-shelf techniques to find the best path. This raises the somewhat ill-posed question, what is the right (optimal) value to threshold the map? We instead suggest a persistent homology approach to the problem-a topological approach in which we seek the homology class of trajectories that is most persistent for the given probability map. In other words, we want the class of trajectories that is free of obstacles over the largest range of threshold values. In order to make this problem tractable, we use homology in ℤ 2 coefficients (instead of the standard ℤ coefficients), and describe how graph search-based algorithms can be used to find trajectories in different homology classes. Our simulation results demonstrate the efficiency and practical applicability of the algorithm proposed in this paper.paper. Map matching determines which road a vehicle is on based on inaccurate measured locations, such as GPS points. Simple algorithms, such as nearest road matching, fail often. We introduce a new algorithm that finds a sequence of road segments which simultaneously match the measured locations and which are traversable in the time intervals associated with the measurements. The time constraint, implemented with a hidden Markov model, greatly reduces the errors made by nearest road matching. We trained and tested the new algorithm on data taken from a large pool of real drivers. Learning and then recognizing a route, whether travelled during the day or at night, in clear or inclement weather, and in summer or winter is a challenging task for state of the art algorithms in computer vision and robotics. In this paper, we present a new approach to visual navigation under changing conditions dubbed SeqSLAM. Instead of calculating the single location most likely given a current image, our approach calculates the best candidate matching location within every local navigation sequence. Localization is then achieved by recognizing coherent sequences of these “local best matches”. This approach removes the need for global matching performance by the vision front-end - instead it must only pick the best match within any short sequence of images. The approach is applicable over environment changes that render traditional feature-based techniques ineffective. Using two car-mounted camera datasets we demonstrate the effectiveness of the algorithm and compare it to one of the most successful feature-based SLAM algorithms, FAB-MAP. The perceptual change in the datasets is extreme; repeated traverses through environments during the day and then in the middle of the night, at times separated by months or years and in opposite seasons, and in clear weather and extremely heavy rain. While the feature-based method fails, the sequence-based algorithm is able to match trajectory segments at 100 precision with recall rates of up to 60 . A terrain-based underwater navigation using sonar bathymetric profiles is presented. It deals with matching high-resolution local depth maps against a large on-board reference map. The matching algorithm locates the local depth map within the a priori known larger map to determine the absolute position and heading of the vehicle. Two separate approaches for this problem are presented. The first uses a contour-based representation of depth maps. Contours are extracted from both local and reference maps. Invariant attributes under rigid plane transformation are associated with each contour point, so that the problem is reduced to a point-based matching algorithm: given two point sets, find correspondences and estimate transformation between the two sets. We shall particularly focus on the formalism of partial differential equations, which is used to smooth depth maps in a morphologically invariant way and to obtain anisotropic contours. The second approach is also based on a correspondence algorithm. Here, ... The increasing availability of GPS-embedded mobile devices has given rise to a new spectrum of location-based services, which have accumulated a huge collection of location trajectories. In practice, a large portion of these trajectories are of low-sampling-rate. For instance, the time interval between consecutive GPS points of some trajectories can be several minutes or even hours. With such a low sampling rate, most details of their movement are lost, which makes them difficult to process effectively. In this work, we investigate how to reduce the uncertainty in such kind of trajectories. Specifically, given a low-sampling-rate trajectory, we aim to infer its possible routes. The methodology adopted in our work is to take full advantage of the rich information extracted from the historical trajectories. We propose a systematic solution, History based Route Inference System (HRIS), which covers a series of novel algorithms that can derive the travel pattern from historical data and incorporate it into the route inference process. To validate the effectiveness of the system, we apply our solution to the map-matching problem which is an important application scenario of this work, and conduct extensive experiments on a real taxi trajectory dataset. The experiment results demonstrate that HRIS can achieve higher accuracy than the existing map-matching algorithms for low-sampling-rate trajectories. This paper describes a process for automatically inferring maps from large collections of opportunistically collected GPS traces. In this type of dataset, there is often a great disparity in terms of coverage. For example, a freeway may be represented by thousands of trips, whereas a residential road may only have a handful of observations. Additionally, while modern GPS receivers typically produce high-quality location estimates, errors over 100 meters are not uncommon, especially near tall buildings or under dense tree coverage. Combined, GPS trace disparity and error present a formidable challenge for the current state of the art in map inference. By tuning the parameters of existing algorithms, a user may choose to remove spurious roads created by GPS noise, or admit less-frequently traveled roads, but not both. In this paper, we present an extensible map inference pipeline, designed to mitigate GPS error, admit less-frequently traveled roads, and scale to large datasets. We demonstrate and compare the performance of our proposed pipeline against existing methods, both qualitatively and quantitatively, using a real-world dataset that includes both high disparity and noise. Our results show significant improvements over the current state of the art. In this paper we present a prototype system for image based localization in urban environments. Given a database of views of city street scenes tagged by GPS locations, the system computes the GPS location of a novel query view. We first use a wide-baseline matching technique based on SIFT features to select the closest views in the database. Often due to a large change of viewpoint and presence of repetitive structures, a large percentage of matches (> 50 ) are not correct correspondences. The subsequent motion estimation between the query view and the reference view, is then handled by a novel and efficient robust estimation technique capable of dealing with large percentage of outliers. This stage is also accompanied by a model selection step among the fundamental matrix and the homography. Once the motion between the closest reference views is estimated, the location of the query view is then obtained by triangulation of translation directions. Approximate solutions for cases when triangulation cannot be obtained reliably are also described. The presented system is tested on the dataset used in ICCV 2005 Computer Vision Contest and is shown to have higher accuracy than previous reported results. GPS-enabled devices are now ubiquitous, from airplanes and cars to smartphones and wearable technology. This has resulted in a wealth of data about the movements of individuals and populations, which can be analyzed for useful information to aid in city and traffic planning, disaster preparedness and so on. However, the places that people go can disclose extremely sensitive information about them, and thus their use needs to be filtered through privacy preserving mechanisms. This turns out to be a highly challenging task: raw trajectories are highly detailed, and typically no pair is alike. Previous attempts fail either to provide adequate privacy protection, or to remain sufficiently faithful to the original behavior. This paper presents DPT, a system to synthesize mobility data based on raw GPS trajectories of individuals while ensuring strong privacy protection in the form of e-differential privacy. DPT makes a number of novel modeling and algorithmic contributions including (i) discretization of raw trajectories using hierarchical reference systems (at multiple resolutions) to capture individual movements at differing speeds, (ii) adaptive mechanisms to select a small set of reference systems and construct prefix tree counts privately, and (iii) use of direction-weighted sampling for improved utility. While there have been prior attempts to solve the subproblems required to generate synthetic trajectories, to the best of our knowledge, ours is the first system that provides an end-to-end solution. We show the efficacy of our synthetic trajectory generation system using an extensive empirical evaluation. We consider the problem of constructing street networks from geo-referenced trajectory data: Given a set of trajectories in the plane, compute a street network that represents all trajectories in the set. We present a simple and practical incremental algorithm that is based on partial matching of the trajectories to the graph. We use minimumlink paths to reduce the complexity of the reconstructed graph. We provide quality guarantees and experimental results based on both real and synthetic data. For the partial matching we introduce a new variant of partial Frechet distance. Location is a key context ingredient and many existing pervasive applications rely on the current locations of their users. However, with the ability to predict the future location and movement behavior of a user, the usability of these applications can be greatly improved. In this paper, we propose an approach to predict both the intended destination and the future route of a person. Rather than predicting the destination and future route separately, we have focused on making prediction in an integrated way by exploiting personal movement data (i.e. trajectories) collected by GPS. Since trajectories contain daily whereabouts information of a person, the proposed approach first detects the significant places where the person may depart from or go to using a clustering-based algorithm called FBM (Forward-Backward Matching), then abstracts the trajectories based on a space partitioning method, and finally extracts movement patterns from the abstracted trajectories using an extended CRPM (Continuous Route Pattern Mining) algorithm. Extracted movement patterns are organized in terms of origin-destination couples. The prediction is made based on a pattern tree built from these movement patterns. With the real personal movement data of 14 participants, we conducted a number of experiments to evaluate the performance of our system. The results show that our approach can achieve approximately 80 and 60 accuracy in destination prediction and 1-step prediction, respectively, and result in an average deviation of approximately 60 m in continuous future route prediction. Finally, based on the proposed approach, we implemented a prototype running on mobile phones, which can extract patterns from a user's historical movement data and predict the destination and future route. We present a novel probabilistic approach for fitting a statistical model to an image. A 3D Morphable Model (3DMM) of faces is interpreted as a generative (Top-Down) Bayesian model. Random Forests are used as noisy detectors (Bottom-Up) for the face and facial landmark positions. The Top-Down and Bottom-Up parts are then combined using a Data-Driven Markov Chain Monte Carlo Method (DDMCMC). As core of the integration, we use the Metropolis-Hastings algorithm which has two main advantages. First, the algorithm can handle unreliable detections and therefore does not need the detectors to take an early and possible wrong hard decision before fitting. Second, it is open for integration of various cues to guide the fitting process. Based on the proposed approach, we implemented a completely automatic, pose and illumination invariant face recognition application. We are able to train and test the building blocks of our application on different databases. The system is evaluated on the Multi-PIE database and reaches state of the art performance. We introduce an approach to feature-based object recognition, using maximum a posteriori (MAP) estimation under a Markov random field (MRF) model. This approach provides an efficienct solution for a wide class of priors that explicitly model dependencies between individual features of an object. These priors capture phenomena such as the fact that unmatched features due to partial occlusion are generally spatially correlated rather than independent. The main focus of this paper is a special case of the framework that yields a particularly efficient approximation method. We call this special case spatially coherent matching (SCM), as it reflects the spatial correlation among neighboring features of an object. The SCM method operates directly on the image feature map, rather than relying on the graph-based methods used in the general framework. We present some Monte Carlo experiments showing that SCM yields substantial improvements over Hausdorff matching for cluttered scenes and partially occluded objects. This paper discusses the role played by signal detection algorithms in the mobile robot map building problem. Typical mapping techniques make the assumption that the internal signal detection, which is required to produce an (r, rho) point estimate, is ideal. That is, the probability of detecting the signal is unity, and the probabilities of a false alarm or missed detection are zero. In the case of grid mapping, this allows for the occupancy probability to be distributed under the constraint of a unity summation amongst affected cells. In the case of SLAM, this allows for a feature's (x,y) coordinates to be modeled with (Gaussian) probability density functions. This paper shows that typical signal detection algorithms contain all the necessary measurement models to exactly calculate the map occupancy estimates. Furthermore, once restrictive signal assumptions are relaxed, its shown that evidence theory and not Bayesian theory should be used in the combination and updating of the map estimates. The ideas presented in this paper are demonstrated in the field robotics domain using a millimeter wave radar sensor. Target presence and absence beliefs are derived directly from signal likelihood ratios as opposed to a priori assigned constants as is typical for mapping algorithms. Results obtained from outdoor sensing experiments, show the improvement of this new model, given targets of fluctuating radar cross section (RCS) The pervasiveness of mobile devices and location based services is leading to an increasing volume of mobility data.This side eect provides the opportunity for innovative methods that analyse the behaviors of movements. In this paper we propose WhereNext, which is a method aimed at predicting with a certain level of accuracy the next location of a moving object. The prediction uses previously extracted movement patterns named Trajectory Patterns, which are a concise representation of behaviors of moving objects as sequences of regions frequently visited with a typical travel time. A decision tree, named T-pattern Tree, is built and evaluated with a formal training and test process. The tree is learned from the Trajectory Patterns that hold a certain area and it may be used as a predictor of the next location of a new trajectory finding the best matching path in the tree. Three dierent best matching methods to classify a new moving object are proposed and their impact on the quality of prediction is studied extensively. Using Trajectory Patterns as predictive rules has the following implications: (I) the learning depends on the movement of all available objects in a certain area instead of on the individual history of an object; (II) the prediction tree intrinsically contains the spatio-temporal properties that have emerged from the data and this allows us to define matching methods that striclty depend on the properties of such movements. In addition, we propose a set of other measures, that evaluate a priori the predictive power of a set of Trajectory Patterns. This measures were tuned on a real life case study. Finally, an exhaustive set of experiments and results on the real dataset are presented.