Loopy Belief Propagation Algorithm Research Articles

Large-Scale and Efficient Texture Mapping Algorithm via Loopy Belief Propagation

Texture mapping as a fundamental task in 3D modeling has been well established for well-acquired aerial assets under consistent illumination, yet it remains a challenge when it is scaled to large datasets with images under varying views and illuminations. A well-performed texture mapping algorithm must be able to efficiently select views, fuse and map textures from these views to mesh models, at the same time, achieve consistent radiometry over the entire model. Existing approaches achieve efficiency either by limiting the number of images to one view per face, or simplifying global inferences to only achieve local color consistency. In this paper, we break this tie by proposing a novel and efficient texture mapping framework that allows the use of multiple views of texture per face, at the same time to achieve global color consistency. The proposed method leverages a loopy belief propagation algorithm to perform an efficient and global-level probabilistic inferences to rank candidate views per face, which enables face-level multi-view texture fusion and blending. The texture fusion algorithm, being non-parametric, brings another advantage over typical parametric post color correction methods, due to its improved robustness to non-linear illumination differences. The experiments on three different types of datasets (i.e. satellite dataset, unmanned-aerial vehicle dataset and close-range dataset) show that the proposed method has produced visually pleasant and texturally consistent results in all scenarios, with an added advantage of consuming less running time as compared to the state of the art methods, especially for large-scale dataset such as satellite-derived models.

Efficient approximations of the multi-sensor labelled multi-Bernoulli filter

In this paper, we propose two efficient, approximate formulations of the multi-sensor labelled multi-Bernoulli (LMB) filter, which both allow the sensors’ measurement updates to be computed in parallel. Our first filter is based on the direct mathematical manipulation of the multi-sensor, multi-object Bayes filter’s posterior distribution. Unfortunately, it requires the division of probability distributions and its extension beyond linear Gaussian applications is not obvious. Our second filter approximates the multi-sensor, multi-object Bayes filter’s posterior distribution using the geometric average of each sensor’s measurement-updated distribution. This filter can be used under non-linear conditions; however, it is not as accurate as our first filter. In both cases, we approximate the LMB filter’s measurement update using an existing loopy belief propagation algorithm. Both filters have a constant complexity in the number of sensors, and linear complexity in both number of measurements and objects. This is an improvement on an iterated-corrector LMB (IC-LMB) filter, which has linear complexity in the number of sensors. The proposed filters are of interest when tracking many objects using several sensors, where filter run-time is more important than filter accuracy. Simulations indicate that the filters’ loss of accuracy compared to the IC-LMB filter is not significant.

Social event planning using hybrid pairwise Markov random fields

Event-based social networks (EBSNs) have become increasingly popular, which provide online social event management platforms for event organizers to publish and share social events (e.g., outdoor activities). In EBSNs, a major challenge for a social event organizer is how to plan a social event to attract the maximum number of attendance. To organize an event, three essential elements are required, namely, what (i.e., event content), where (i.e., event location), and when (i.e., event time). In this paper, we focus on the social event planning problem, which selects a location and time to hold a social event for the organizer with the given event content, to maximize the total number of participants. The solution of the social event planning problem could support decision-making for social event organizers. For simplicity, we denote a location and time pair as an item in this paper. To solve the social event planning problem, we present a hybrid pairwise Markov random field (H-PMRF) model which takes latent preferences of users, latent attributes of items, similarities between users and similarities between items into consideration. In particular, we construct an undirected graph where each node represents a user's decision on a specific item and each edge represents the relationship between the nodes, define the node potentials and edge potentials which model the dependency relationships between nodes, and give a joint probability distribution over the graph. Further, we adopt the Loopy Belief Propagation algorithm to compute the posterior probability distribution of each node in H-PMRF and select the location and time to hold the event which could attract the maximum number of participants. We collect real-world data set from DoubanEvent website and conduct extensive experiments on it. Experimental results show that the proposed model outperforms several baselines.

Data-Driven Approach for Analyzing Spatiotemporal Price Elasticities of EV Public Charging Demands Based on Conditional Random Fields

With the increase of electric vehicle (EV) sales, the pricing strategies of public charging stations have significant impacts on their revenues and the spatiotemporal distribution of charging loads. In this paper, we quantify three kinds of price elasticity of charging demands based on the historical charging data of multiple public charging stations with different pricing schemes. The relationship between the volume-weighted average price (VWAP) and the corresponding total charging demand within a zone is studied, which does not require changing the charging prices to estimate elasticity. To evaluate the shifting of charging demands in different periods and zones, a conditional random field (CRF) model is built, which depicts the spatiotemporal correlations of charging demands. In this model, the VWAPs and the total charging demands are taken as observed variables and hidden variables, respectively. The loopy belief propagation algorithm is used to infer the loopy graph approximately, and the learning algorithm with forgetting factors is used to estimate the unknown parameters of the CRF model. The price elasticities are derived from CRF, and the elasticity matrices of charging demands are obtained. Computational results based on historical charging data verify the validity of the proposed model and method.

A CRF-Based Framework for Tracklet Inactivation in Online Multi-Object Tracking

Online multi-object tracking (MOT) is an active research topic in the domain of computer vision. Although many previously proposed algorithms have exhibited decent results, the issue of tracklet inactivation has not been sufficiently studied. Simple strategies such as using a fixed threshold on classification scores are adopted, yielding undesirable tracking mistakes and limiting the overall performance. In this paper, a conditional random field (CRF) based framework is put forward to tackle the tracklet inactivation issue in online MOT problems. A discrete CRF which exploits the intra-frame relationship between tracking hypotheses is developed to improve the robustness of tracklet inactivation. Separate sets of feature functions are designed for the unary and binary terms in the CRF, which take into account various tracking challenges in practical scenarios. To handle the problem of varying CRF nodes in the MOT context, two strategies named as hypothesis filtering and dummy nodes are employed. In the proposed framework, the inference stage is conducted by using the loopy belief propagation algorithm, and the CRF parameters are determined by utilizing the maximum likelihood estimation method followed by slight manual adjustment. Experimental results show that the tracker combined with the CRF-based framework outperforms the baseline on the MOT16 and MOT17 benchmarks. The extensibility of the proposed framework is further validated by an extensive experiment.

Ground Segmentation Algorithm for Sloped Terrain and Sparse LiDAR Point Cloud

Distinguishing obstacles from ground is an essential step for common perception tasks such as object detection-and-tracking or occupancy grid maps. Typical approaches rely on plane fitting or local geometric features, but their performance is reduced in situations with sloped terrain or sparse data. Some works address these issues using Markov Random Fields and Belief Propagation, but these rely on local geometric features uniquely. This article presents a strategy for ground segmentation in LiDAR point clouds composed by two main steps: (i) First, an initial classification is performed dividing the points in small groups and analyzing geometric features between them. (ii) Then, this initial classification is used to model the surrounding ground height as a Markov Random Field, which is solved using the Loopy Belief Propagation algorithm. Points are finally classified comparing their height with the estimated ground height map. On one hand, using an initial estimation to model the Markov Random Field provides a better description of the scene than local geometric features commonly used alone. On the other hand, using a graph-based approach with message passing achieves better results than simpler filtering or enhancement techniques, since data propagation compensates sparse distributions of LiDAR point clouds. Experiments are conducted with two different sources of information: nuScenes’s public dataset and an autonomous vehicle prototype. The estimation results are analyzed with respect to other methods, showing a good performance in a variety of situations.

Approximate multi-object filter with known SNR information for an optical sensor system.

In the image plane of an optical sensor, the amplitude information (AI) is very reliable for distinguishing returns generated by actual targets or coming from clutter generators. However, the majority of recently derived multi-object filters based on Mahler's finite set statistics (FISST) theory have ignored utilizing this information. This paper proposes an approximate multi-object filter with additive AI applied for optical sensor systems. The algorithm is operated on an image plane generated by the optical sensor, which has been pre-processed. After each prediction step, we sample multiple particles to approximate the prior multi-object density. Moreover, at the update step, we employ the amplitude feature likelihood for situations where the signal-to-noise ratio (SNR) information of targets is known. The loopy belief propagation (LBP) method with sequentially updated initialization messages is designed to solve the data association problem involved in the update step of the multi-object particle filter. We analyze the convergence performance of the LBP algorithm with additive AI and sequentially updated initialization messages; an ad hoc method for improving the performance of the AI-aided LBP is designed.

Loopy belief propagation based data association for extended target tracking

The data association problem of multiple extended target tracking is very challenging because each target may generate multiple measurements. Recently, the belief propagation based multiple target tracking algorithms with high efficiency have been a research focus. Different from the belief propagation based Extended Target tracking based on Belief Propagation (ET-BP) algorithm proposed in our previous work, a new graphical model formulation of data association for multiple extended target tracking is proposed in this paper. The proposed formulation can be solved by the Loopy Belief Propagation (LBP) algorithm. Furthermore, the simplified measurement set in the ET-BP algorithm is modified to improve tracking accuracy. Finally, experiment results show that the proposed algorithm has better performance than the ET-BP and joint probabilistic data association based on the simplified measurement set algorithms in terms of accuracy and efficiency. Additionally, the convergence of the proposed algorithm is verified in the simulations.

Simultaneous Tracking and Separation of Multiple Sources Using Factor Graph Model

In this article, we present an algorithm for direction of arrival (DOA) tracking and separation of multiple speakers with a microphone array using the factor graph statistical model. In our model, the speakers can be located in one of a predefined set of candidate DOAs, and each time-frequency (TF) bin can be associated with a single speaker. Accordingly, by attributing a statistical model to both the DOAs and the associations, as well as to the microphone array observations given these variables, we show that the conditional probability of these variables given the microphone array observations can be modeled as a factor graph. Using the loopy belief propagation (LBP) algorithm, we derive a novel inference scheme which simultaneously estimates both the DOAs and the associations. These estimates are used in turn for separating the sources, by directing a beamformer towards the estimated DOAs, and then applying a TF masking according to the estimated associations. A comprehensive experimental study demonstrates the benefits of the proposed algorithm in both simulated data and real-life measurements recorded in our laboratory.

Marginal Inference in Continuous Markov Random Fields Using Mixtures

Exact marginal inference in continuous graphical models is computationally challenging outside of a few special cases. Existing work on approximate inference has focused on approximately computing the messages as part of the loopy belief propagation algorithm either via sampling methods or moment matching relaxations. In this work, we present an alternative family of approximations that, instead of approximating the messages, approximates the beliefs in the continuous Bethe free energy using mixture distributions. We show that these types of approximations can be combined with numerical quadrature to yield algorithms with both theoretical guarantees on the quality of the approximation and significantly better practical performance in a variety of applications that are challenging for current state-of-the-art methods.

A Framework for Clustered and Skewed Sparse Signal Recovery

A novel framework, clustered-skew normal mixture-belief propagation, is developed to solve the reconstruction of undersampled clustered signals, where the magnitudes of signal coefficients in each cluster are distributed asymmetrically w.r.t the cluster mean. To address the skewness feature, a finite skew-normal density mixture is utilized to model the prior distribution, where the marginal posterior of the signal is inferred by an efficient approximate message-passing-based algorithm. An expectation-maximization-based algorithm is developed to estimate the mixture density. The clustered property is then modeled by the Potts model, and a loopy belief propagation algorithm is designed to promote the spatial feature. Experimental results show that our technique is highly effective and efficient in exploiting both the clustered feature and asymmetrical feature of the signals and outperforms many sophisticated techniques.

Comparison of optimization algorithms for interferometric synthetic aperture radar phase unwrapping based on identical Markov random fields

Phase unwrapping (PU) is one of the key processes in measuring the elevation or deformation of the Earth’s surface from its interferometric synthetic aperture radar (InSAR) data. PU problems may be formulated as maximum a posteriori estimation estimations of Markov random field (MRF). The key issue of this formulation is energy minimization. Iterated conditional mode (ICM), graph cuts (GC), loopy belief propagation (LBP), and sequential tree-reweighted message passing (TRW-S) have been proposed for the energy minimization. Unfortunately, they differ in the formulation of the MRF model for PU, which raises the question of how they compare against each other on the same MRF model for PU. We address this by investigating the four optimization algorithms and comparing them on an identical MRF model, which gives researchers some guidance as to which optimization method is best suited for solving the PU problem. Experiments using simulated and real-data illustrate that the GC algorithm is clearly the winner among the four algorithms in all cases. The ICM algorithm, although very rapid, performs much worse than the other three especially in the terrain with violent changes or discontinuities. The two message-passing algorithms—LBP and TRW-S—perform completely differently. The LBP algorithm performs surprisingly poorly on solving phase discontinuities issue, whereas the TRW-S algorithm does quite well (second only to the GC algorithm).

Multiple human 3D pose estimation from multiview images

Multiple human 3D pose estimation is a challenging task. It is mainly because of large variations in the scale and pose of humans, fast motions, multiple persons in the scene, and arbitrary number of visible body parts due to occlusion or truncation. Some of these ambiguities can be resolved by using multiview images. This is due to the fact that more evidences of body parts would be available in multiple views. In this work, a novel method for multiple human 3D pose estimation using evidences in multiview images is proposed. The proposed method utilizes a fully connected pairwise conditional random field that contains two types of pairwise terms. The first pairwise term encodes the spatial dependencies among human body joints based on an articulated human body configuration. The second pairwise term is based on the output of a 2D deep part detector. An approximate inference is then performed using the loopy belief propagation algorithm. The proposed method is evaluated on the Campus, Shelf, Utrecht Multi-Person Motion benchmark, Human3.6M, KTH Football II, and MPII Cooking datasets. Experimental results indicate that the proposed method achieves substantial improvements over the existing state-of-the-art methods in terms of the probability of correct pose and the mean per joint position error performance measures.

Implementation of Knowledge-Based Expert System Using Probabilistic Network Models

The latest development in machine learning techniques has enabled the development of intelligent tools which can identify anomalies in the system in real time. These intelligent tools become expert systems when they combine the algorithmic result of root cause analysis with the domain knowledge. Truth maintenance, fuzzy logic, ontology classification are just a few out of many techniques used in building these systems. Logic is embedded in the code in most of the traditional computer program, which makes it difficult for domain experts to retrieve the underlying rule set and make any changes. These system bridge the gap by making information explicit rather than implicit. In this paper, we present a new approach for developing an expert system using decision tree analysis with probabilistic network models such as Bayes-network. The proposed model facilitate the process of correlation between belief probability with the unseen data by use of logical flowcharting, loopy belief propagation algorithm, and decision trees analysis. The performance of the model will be measured by evaluation and cross validation techniques.

Opinioned Post Detection in Sina Weibo

Sina Weibo has become an important data resource for opinion mining. However, this data resource is polluted with un-opinionated posts. Detecting posts containing opinions in Sina Weibo faces two challenges. One is the short text in Sina Weibo that leads to insufficient textual features. The other challenge is the absence of ground-truth data for training models. In this paper, we propose a weakly supervised framework named graph-based opinioned post detector (GOPD) to detect the opinioned posts in Sina Weibo . GOPD utilizes three types of user interactions, which include reposting , responding , and referring , to construct the opinioned similarity graph (OSG) that describes the opinioned similarity between posts. On the OSG, opinioned post detection is formulated as a classification problem. The pairwise Markov random field model and the loopy belief propagation algorithm are employed to solve the problem. GOPD is evaluated on the manually labeled real-world datasets. Results show that the GOPD efficiently detects opinioned posts and transfers cross topics.

Approximate Message Passing for Structured Affine Rank Minimization Problem

The topic of the rank minimization problem with affine constraints has been well studied in recent years. However, in many applications the data can exhibit other structures beyond simply being low rank. For example, images and videos present complex spatio-temporal structures, which are largely ignored by current affine rank minimization (ARM) methods. In this paper, we propose a novel approximate message passing (AMP)-based approach that is capable of capturing additional structures in the matrix entries, and can be implemented in a wide range of applications with little or no modification. Using probabilistic low-rank factorization, we derive our generalized AMP-based algorithm as an approximation of the loopy belief propagation algorithm. In addition, we apply a rank selection strategy and an expectation-maximization estimation strategy that adaptively obtain the optimal value of the algorithmic parameters. Then, we discuss the specializations of our proposed algorithm to the applications of structured ARM problems, such as compressive hyperspectral imaging and compressive video surveillance. Simulation results with both synthetic and real data demonstrate that the proposed algorithm yields the state-of-the-art reconstruction performance while maintaining competitive computational complexity.

Change Detection Based on a Multifeature Probabilistic Ensemble Conditional Random Field Model for High Spatial Resolution Remote Sensing Imagery

In this letter, a multifeature probabilistic ensemble conditional random field (MFPECRF) model is proposed to perform the task of change detection for high spatial resolution (HSR) remote sensing imagery. MFPECRF not only considers the spectral feature of single pixels but also the interaction between neighborhood pixels and the structural property of the ground objects in HSR imagery to give a higher detection accuracy than the traditional random field methods, which only utilize spectral and label information. In the unary potential, the spectral and morphological features of the difference image are combined using a probabilistic ensemble strategy, and the pairwise potential considers the contextual information of the observed field. The parameters of MFPECRF are estimated using a piecewise strategy, and the final result is obtained by the use of the loopy belief propagation algorithm. The experimental results of two groups of HSR multispectral images confirm the potential of the proposed method in improving the detection accuracy for HSR imagery.

Cooperative Spectrum Sensing in the Presence of Correlated and Malicious Cognitive Radios

While cooperative spectrum sensing improves sensing reliability when secondary users (SUs) have independent measurements, these gains are limited in the presence of correlated or malicious SUs. In this paper, we propose algorithms to improve spectrum sensing performance when the system contains both honest and malicious SUs all of whom may be experiencing correlated fading channels. We show that, when the SUs’ reports at each time slot are independent and identically distributed, it is impossible to distinguish between malicious collaboration, i.e., collusion, and correlations caused by the environment. Thus, the optimal test statistic for cooperative spectrum sensing depends on the correlations in the SU reports but not on the source of these correlations. We propose two algorithms: one to identify SUs whose reports are correlated and another to infer the spectrum occupancy by using the learned structure of correlations. Groups of SUs whose reports are correlated are identified by learning the structure of the underlying Bayesian network model. This structure is implemented as a factor graph to infer the spectrum occupancy using a loopy belief propagation algorithm. We derive an upper bound of the error probability of the proposed structure learning algorithm and prove convergence of our loopy belief propagation algorithm.

Pilot study of dynamic Bayesian networks approach for fault diagnostics and accident progression prediction in HTR-PM

The first high-temperature-reactor pebble-bed demonstration module (HTR-PM) is under construction currently in China. At the same time, development of a system that is used to support nuclear emergency response is in progress. The supporting system is expected to complete two tasks. The first one is diagnostics of the fault in the reactor based on abnormal sensor measurements obtained. The second one is prognostic of the accident progression based on sensor measurements obtained and operator actions. Both tasks will provide valuable guidance for emergency staff to take appropriate protective actions. Traditional method for the two tasks relies heavily on expert judgment, and has been proven to be inappropriate in some cases, such as Three Mile Island accident. To better perform the two tasks, dynamic Bayesian networks (DBN) is introduced in this paper and a pilot study based on the approach is carried out. DBN is advantageous in representing complex dynamic systems and taking full consideration of evidences obtained to perform diagnostics and prognostics. Pearl's loopy belief propagation (LBP) algorithm is recommended for diagnostics and prognostics in DBN. The DBN model of HTR-PM is created based on detailed system analysis and accident progression analysis. A small break loss of coolant accident (SBLOCA) is selected to illustrate the application of the DBN model of HTR-PM in fault diagnostics (FD) and accident progression prognostics (APP). Several advantages of DBN approach compared with other techniques are discussed. The pilot study lays the foundation for developing the nuclear emergency response supporting system (NERSS) for HTR-PM.

Crop feature extraction from images with probabilistic superpixel Markov random field

In the process of agriculture automation, mechanization and intelligentialization, image segmentation for crop extraction plays a crucial role. However, the performance of crop segmentation is closely related to the quality of the captured image, which is easily affected by the variability, randomness, and complexity of the natural illumination. The previously proposed crop extraction approaches produce inaccurate segmentation under natural illumination when highlight occurs. And specularity removal techniques are still hard to improve the crop extraction performance, because of the flaw of their assumption and the high requirement of the experimental configuration. In this paper, we propose a novel crop extraction method resistant to the strong illumination by using probabilistic superpixel Markov random field. Our method is based on the assumption that color changes gradually between highlight areas and its neighboring non-highlight areas and the same holds true for the other regions. This priori knowledge is embedded into the MRF–MAP framework by modeling the local and mutual evidences of nodes. Besides, superpixel and Fisher linear discriminant are utilized to construct the probabilistic superpixel patches. Loopy belief propagation algorithm is adopted in the optimization step. And the label for the crop segmentation is provided in the final iteration result. We also compare our method to the other state-of-the-art approaches. The results demonstrate that our method is resistant to the strong illumination and can be applied to generic species. Moreover, our approach is also capable of extracting the crop from the shadow regions. Statistics from comparative experiments manifest that our crop segmentation method yields the highest mean value of 92.29% with the lowest standard deviation of 4.65%, which can meet the requirement of practical uses in our agriculture automatic vision system.