Consensus Maximization Research Articles

Transformation Decoupling Strategy Based on Screw Theory for Deterministic Point Cloud Registration With Gravity Prior.

Point cloud registration is challenging in the presence of heavy outlier correspondences. This paper focuses on addressing the robust correspondence-based registration problem with gravity prior that often arises in practice. The gravity directions are typically obtained by inertial measurement units (IMUs) and can reduce the degree of freedom (DOF) of rotation from 3 to 1. We propose a novel transformation decoupling strategy by leveraging the screw theory. This strategy decomposes the original 4-DOF problem into three sub-problems with 1-DOF, 2-DOF, and 1-DOF, respectively, enhancing computation efficiency. Specifically, the first 1-DOF represents the translation along the rotation axis, and we propose an interval stabbing-based method to solve it. The second 2-DOF represents the pole which is an auxiliary variable in screw theory, and we utilize a branch-and-bound method to solve it. The last 1-DOF represents the rotation angle, and we propose a global voting method for its estimation. The proposed method solves three consensus maximization sub-problems sequentially, leading to efficient and deterministic registration. In particular, it can even handle the correspondence-free registration problem due to its significant robustness. Extensive experiments on both synthetic and real-world datasets demonstrate that our method is more efficient and robust than state-of-the-art methods, even when dealing with outlier rates exceeding 99%.

Consensus-oriented linguistic multi-criteria group sorting method incorporating dynamic trust management

Multi-criteria group sorting (MCGS) concerns the multi-person process of evaluating alternatives and assigning them to predetermined ordered categories under certain criteria. Identifying class thresholds and coordinating conflicting opinions are two primary challenges within this process. Taking into account the 2-tuple linguistic preferences of decision-makers (DMs), we propose a consensus-oriented sorting method that incorporates dynamic trust management for linguistic MCGS. The main contributions and innovations are as follows. (a) A group consensus maximization model is constructed to optimize class thresholds and initial individual sorting results. (b) Integrating familiarity-based trust and similarity-based trust, the dynamic comprehensive trust among DMs is established. On this basis, a feedback mechanism is designed, in which the bi-objective programming is utilized to generate adjustment recommendations. (c) The final consensual group sorting result is obtained by maximizing the similarity of group views. (d) The feasibility of the proposed method is demonstrated using a case of sorting fresh agricultural products. Using sensitivity analysis and comparative analysis, the proposed method is verified to be rational and effective. A comparison based on real datasets and a qualitative comparison further demonstrate the validity and characteristics of the proposed method.

Accelerating Globally Optimal Consensus Maximization in Geometric Vision.

Branch-and-bound-based consensus maximization stands out due to its important ability of retrieving the globally optimal solution to outlier-affected geometric problems. However, while the discovery of such solutions caries high scientific value, its application in practical scenarios is often prohibited by its computational complexity growing exponentially as a function of the dimensionality of the problem at hand. In this work, we convey a novel, general technique that allows us to branch over an n-1 dimensional space for an n-dimensional problem. The remaining degree of freedom can be solved globally optimally within each bound calculation by applying the efficient interval stabbing technique. While each individual bound derivation is harder to compute owing to the additional need for solving a sorting problem, the reduced number of intervals and tighter bounds in practice lead to a significant reduction in the overall number of required iterations. Besides an abstract introduction of the approach, we present applications to four fundamental geometric computer vision problems: camera resectioning, relative camera pose estimation, point set registration, and rotation and focal length estimation. Through our exhaustive tests, we demonstrate significant speed-up factors at times exceeding two orders of magnitude, thereby increasing the viability of globally optimal consensus maximizers in online application scenarios.

Fast and deterministic (3+1)DOF point set registration with gravity prior

Point set registration is the technology used to estimate the spatial transformation between two LiDAR scans, which is challenging in the presence of outlier correspondences and noise. Our focus is on 4 degrees of freedom (DOF) point set registration, in which 1DOF rotation and 3DOF translation need to be estimated. It is commonly found in practical scenarios, such as arbitrarily mobile robots equipped with an inertial measurement unit (IMU), terrestrial LiDAR scanners, or planar moving vehicles in urban environments. Recently, many solutions have leveraged branch and bound (BnB) in global and deterministic approaches to solve the registration problem with performance guarantees. However, BnB-based methods are usually time-consuming since their convergence speed is exponential to the dimensionality of the solution domain, and existing methods estimate these 4DOF simultaneously. Our key idea is to speed up BnB-based methods by decoupling the joint pose into separate translation and rotation with the aid of known gravity directions. This effectively reduces the search domain to 3DOF+1DOF, thereby enhancing algorithm efficiency. Specifically, we propose a novel BnB-based consensus maximization method for a fast 3DOF translation search and derive the specific lower and upper bound functions. We then propose an efficient global voting method for estimating the rotation with 1DOF. To demonstrate the superiority of our proposed method, we conduct extensive experiments on both synthetic and real-world datasets. The experimental results show that (1) our proposed method is more robust against outliers and noise than several existing methods and far faster than the existing BnB-based 4DOF method by almost an order of magnitude, (2) our proposed method is robust against the biases in gravity directions, such that the general error of the IMU is acceptable, and (3) thanks to its significant robustness, our proposed method can solve the challenging problem of simultaneous pose and correspondence registration (SPCR). Moreover, the proposed approach is also more robust and accurate than several SPCR benchmark methods. Code is available at https://github.com/Xinyi-tum/Fast-and-Deterministic-Registration.

DANIEL: A fast and robust consensus maximization method for point cloud registration with high outlier ratios

Correspondence-based point cloud registration is a cornerstone in computer vision, robotics, autonomous navigation and remote sensing, which seeks to estimate the best rigid transformation between two point clouds from the point correspondences established over 3D keypoints. Owing to limited robustness and accuracy, current 3D keypoint matching techniques are rather prone to yield outliers, probably in large numbers, thus making robust estimation (outlier rejection) for the registration problem very important. Unfortunately, previously proposed robust registration methods often suffer from high computation cost or insufficient robustness when encountering high (or even extreme) outlier ratios, hardly ideal enough for practical use. In this paper, we present a novel, time-efficient consensus maximization solver, named Double-layered sAmpliNg with consensus maximization based on stratIfied Element-wise compatibiLity (DANIEL), for robust point cloud registration. DANIEL is smartly designed with two layers of random sampling operation, in order to find the inlier subset with the lowest computational cost possible. Specifically, we (i) apply the rigidity constraint to prune raw outliers in the first layer of one-point sampling, (ii) introduce a series of stratified element-wise compatibility tests to conduct rapid compatibility checking between minimal models so as to realize more efficient consensus maximization in the second layer of two-point sampling, and (iii) employ probabilistic termination conditions to ensure the timely return of the final inlier set. By conducting a series of experiments on multiple real datasets, we demonstrate that the proposed solver DANIEL (i) is robust against over 99% of outliers, (ii) is also significantly faster than previous state-of-the-art robust algorithms, and (iii) is fairly practical for use in real-world applications such as object localization and scan matching problems.

VODRAC: Efficient and robust correspondence-based point cloud registration with extreme outlier ratios

Point set registration (PSR) from correspondences is a basic problem in the area of computer vision, robotics and remote sensing. Nevertheless, because of the limited accuracy of current correspondence building and feature matching technologies, PSR is frequently afflicted by the problem of outliers. In this work, we put forward VODRAC (VOting-based Double-point RAndom sampling with Compatibility weighting), a fast, highly robust and practically effective solution for the PSR problem as well as its real-world applications. To realize this, our first contribution is to integrate the scale-invariant constraint with a double-point random sampling framework to achieve the rapid seeking of inlier candidates and the rough rejection of outliers in the meantime. The second contribution is that we introduce the concept of weight matrix for PSR which is to use the robust loss function for weight computation between pairwise correspondences and also propose a time-efficient way to embed the construction of this matrix into the operation of the algorithm without requiring additional computational time. Moreover, we employ the correspondence voting technique to accelerate the consensus maximization (convergence) of the algorithm, as our third contribution. Through comprehensive experiments over multiple actual datasets, we demonstrate that VODRAC is fast, accurate, and highly robust against up to 99% of outliers (e.g. solving PSR within 2 s when there exist 99% outliers among 1000 correspondences), outperforming existing state-of-the-art (SOTA) robust algorithms.

A three-stage grey evaluation method for assessing the performance of interdisciplinary organizations

PurposeThis study constructs a three-stage evaluation model for interdisciplinary organizations to solve their ranking problems effectively.Design/methodology/approachA three-stage interdisciplinary organization evaluation model abounds the key problems of “who will evaluate the projects?” and “how to evaluate the projects?”. In the first stage, the authors build a consensus maximization model to identify the selected experts based on the interval grey number because of the uncertainty in assessment. In the second stage, considering the reliability of the experts, the authors calculate the reliability of the experts based on historical data. Meanwhile, considering the gradual changes of the experts, the dynamic weighting method is obtained based on the clustering method. In the third stage, considering decision-makers regret psychological behavior, the authors construct a cross-organizational performance evaluation model based on consensus expectations.FindingsFirst, for selecting the experts responsible for assessing interdisciplinary organizations, the consensus-reaching method can effectively avoid cognitive bias. Second, during the assessment, the authors obtained more reasonable results by considering the psychological changes of experts based on regret theory. Third, based on the results, the cross-organization of colleges focused on the achievements of talent training, cross effects, and system construction.Practical implicationsOur study could help organizations establish a suitable assessment mechanism and promote interdisciplinary development.Originality/valueFirst, considering the importance of selecting the experts, the authors use the consensus-reaching process for expert selection. This method could guarantee most experts' preferences. Then, the authors propose a two-stage dynamic weighting method, including a pre-determined and adjusted process. The dynamic method can better perform the preferences of experts. Third, the authors studied the assessment in interdiscipline. In addition, based on the framework and considering the features of the interdiscipline, the authors use the grey number to perform the uncertain preferences of the experts using regret theory.

TriVoC: Efficient Voting-Based Consensus Maximization for Robust Point Cloud Registration With Extreme Outlier Ratios

Correspondence-based point cloud registration is a cornerstone in robotics perception and computer vision, which seeks to estimate the best rigid transformation aligning two point clouds from the putative correspondences. However, due to the limited robustness of 3D keypoint matching approaches, outliers, probably in large numbers, are prone to exist among the correspondences, which makes robust registration methods imperative. Unfortunately, existing robust methods have their own limitations (e.g. high computational cost or limited robustness) when facing high or extreme outlier ratios, probably unsuitable for practical use. In this letter, we present a novel, fast, deterministic and guaranteed robust solver, named TriVoC (Triple-layered Voting with Consensus maximization), for the robust registration problem. We decompose the selecting of the minimal 3-point sets into 3 consecutive layers, and in each layer we design an efficient voting and correspondence sorting framework on the basis of the pairwise equal-length constraint. In this manner, the 3-point sets can be selected independently from the reduced correspondence sets according to the sorted sequence, which can significantly lower the computational cost and meanwhile provide a strong guarantee to achieve the largest consensus set (as the final inlier set) as long as a probabilistic termination condition is fulfilled. Varied experiments show that our solver TriVoC is robust against up to 99% outliers, highly accurate, time-efficient even with extreme outlier ratios, and also practical for real-world applications, showing performance superior to other state-of-the-art competitors.

Practical, Fast and Robust Point Cloud Registration for Scene Stitching and Object Localization

3D point cloud registration ranks among the most fundamental problems in remote sensing, photogrammetry, robotics and geometric computer vision. Due to the limited accuracy of 3D feature matching techniques, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">outliers</i> may exist, sometimes even in very large numbers, among the correspondences. Since existing robust solvers may encounter high computational cost or restricted robustness, we propose a novel, fast and highly robust solution, named VOCRA (VOting with Cost function and Rotating Averaging), for the point cloud registration problem with extreme outlier rates. Our first contribution is to employ the Tukey’s Biweight robust cost to introduce a new voting and correspondence sorting technique, which proves to be rather effective in distinguishing true inliers from outliers even with extreme (99%) outlier rates. Our second contribution consists in designing a time-efficient consensus maximization paradigm based on robust rotation averaging, serving to seek inlier candidates among the correspondences. Finally, we apply Graduated Non-Convexity with Tukey’s Biweight (GNC-TB) to estimate the correct transformation with the inlier candidates obtained, which is then used to find the complete inlier set. Both standard benchmarking and realistic experiments with application to two real-data problems are conducted, and we show that our solver VOCRA is robust against over 99% outliers (exceeding traditional GNC by nearly 10% and RANSAC by nearly 4%) and more time-efficient than the state-of-the-art competitors.

Globally Optimal Consensus Maximization for Relative Pose Estimation With Known Gravity Direction

Relative pose estimation is a core task in robotic vision, and it is the basis of many high-level applications (e.g., visual odometry). In this letter, we focus on a quite common case in which the gravity direction is known in advance with the help of IMUs. Commonly, incorrect feature matches (a.k.a. outliers) are unavoidable, and they will impair the accuracy significantly. RANSAC is the de facto standard to suppress the outliers and obtain a robust solution. However, RANSAC is a non-deterministic algorithm, which means it produces a reasonable result only with a certain probability, and it cannot guarantee the global optimality to meet the safety demand in many life-critical applications. Therefore, we propose a globally optimal algorithm for relative pose estimation with known gravity direction. Specifically, the proposed method employs the branch-and-bound algorithm to solve a consensus maximization problem, and thus it is able to obtain the global solution with a provable guarantee. To verify the feasibility of our proposed method, both synthetic and real-data experiments are conducted. The experimental results support the global optimality of the proposed method and show that the method performs more robustly than existing methods.

Practical globally optimal consensus maximization by Branch-and-bound based on interval arithmetic

Consensus maximization is widely used in robust model fitting, and it is usually solved by RANSAC-type methods in practice. However, these methods cannot guarantee global optimality and sometimes return the wrong solutions. A series of Branch-and-bound (BnB) based globally optimal methods have been proposed, most of which involve deriving a complex bound. Interval arithmetic was utilized to derive simple bounds for BnB in solving geometric matching problems in 2003. However, this idea was somewhat forgotten in the community because it seems natural that the simple interval arithmetic based bounds might be worse than those elaborate bounds. Recently, some new globally optimal algorithms without using BnB were developed for consensus maximization, but they can only work with a small number of data points and low outlier ratios. In this work, we draw the idea of simple bounds by interval arithmetic back on the map and demonstrate its practicability by making substantial extensions. Concretely, we give detailed derivation of solving robust model fitting problems with both linear and quasi-convex residuals and propose practical methods to use them under Unit-Norm constraint and in a high-dimensional problem. Extensive experiments show that the proposed method can handle practical problems with large number of data points and high outlier ratios. It outperforms state-of-the-art global, RANSAC-type, and deterministic methods in terms of both accuracy and efficiency in low-dimensional problems. The source code is publicly available.22https://github.com/YiruWangYuri/Demo-for-GoIA.

Deterministic Approximate Methods for Maximum Consensus Robust Fitting.

Maximum consensus estimation plays a critically important role in several robust fitting problems in computer vision. Currently, the most prevalent algorithms for consensus maximization draw from the class of randomized hypothesize-and-verify algorithms, which are cheap but can usually deliver only rough approximate solutions. On the other extreme, there are exact algorithms which are exhaustive search in nature and can be costly for practical-sized inputs. This paper fills the gap between the two extremes by proposing deterministic algorithms to approximately optimize the maximum consensus criterion. Our work begins by reformulating consensus maximization with linear complementarity constraints. Then, we develop two novel algorithms: one based on non-smooth penalty method with a Frank-Wolfe style optimization scheme, the other based on the Alternating Direction Method of Multipliers (ADMM). Both algorithms solve convex subproblems to efficiently perform the optimization. We demonstrate the capability of our algorithms to greatly improve a rough initial estimate, such as those obtained using least squares or a randomized algorithm. Compared to the exact algorithms, our approach is much more practical on realistic input sizes. Further, our approach is naturally applicable to estimation problems with geometric residuals. Matlab code and demo program for our methods can be downloaded from https://goo.gl/FQcxpi.

Politeness Language Analysis in Teenagers Reviewed from Sociolinguistics

This study aims to find out and describe data on language politeness among teenagers in Kuala Simpang city, Aceh Tamiang district in terms of sociolinguistics. The appropriate research approach uses in this study is qualitative research. The type of research is field research. The data of this study is the conversation of teenagers of Bukit Tempurung Village, Kuala Simpang City. Data sources are a number of teenagers in Bukit Tempurung Village, Kuala Simpang City. Data collected by recording techniques during social activities, then in manuscripts in the form of conversation. The results showe that there are 6 languages politeness maxims used by teenagers during social activities. Maksim is in the form of wisdom maxims of four (4) data, generosity maxims as much as seven (7) data, award maxims of two (2) data, simplicity maxim of one (1) data, consensus maximization of fourteen (14) data, and the implicit maxim of one (1) data. Based on the research data, the most dominant maxim is the agreement maxim

Ensemble Teaching for Hybrid Label Propagation.

Label propagation aims to iteratively diffuse the label information from labeled examples to unlabeled examples over a similarity graph. Current label propagation algorithms cannot consistently yield satisfactory performance due to two reasons: one is the instability of single propagation method in dealing with various practical data, and the other one is the improper propagation sequence ignoring the labeling difficulties of different examples. To remedy above defects, this paper proposes a novel propagation algorithm called hybrid diffusion under ensemble teaching (HyDEnT). Specifically, HyDEnT integrates multiple propagation methods as base "learners" to fully exploit their individual wisdom, which helps HyDEnT to be stable and obtain consistent encouraging results. More importantly, HyDEnT conducts propagation under the guidance of an ensemble of "teachers". That is to say, in every propagation round the simplest curriculum examples are wisely designated by a teaching algorithm, so that their labels can be reliably and accurately decided by the learners. To optimally choose these simplest examples, every teacher in the ensemble should comprehensively consider the examples' difficulties from its own viewpoint, as well as the common knowledge shared by all the teachers. This is accomplished by a designed optimization problem, which can be efficiently solved via the block coordinate descent method. Thanks to the efforts of the teachers, all the unlabeled examples are logically propagated from simple to difficult, leading to better propagation quality of HyDEnT than the existing methods. Experiments on six popular datasets reveal that HyDEnT achieves the highest classification accuracy when compared with six state-of-the-art propagation methodologies such as harmonic functions, Fick's law assisted propagation, linear neighborhood propagation, semisupervised ensemble learning, bipartite graph-based consensus maximization, and teaching-to-learn and learning-to-teach.

SigmaKB

The interest in integrating web-scale knowledge bases (KBs) has intensified in the last several years. Research has focused on knowledge base completion between two KBs with complementary information, lacking any notion of uncertainty or method of handling conflicting information. We present S igma KB, a knowledge base system that utilizes Consensus Maximization Fusion and user feedback to integrate and improve the query results of a total of 71 KBs. This paper presents the architecture and demonstration details.

A Graph-Based Consensus Maximization Approach for Combining Multiple Supervised and Unsupervised Models

Ensemble learning has emerged as a powerful method for combining multiple models. Well-known methods, such as bagging, boosting, and model averaging, have been shown to improve accuracy and robustness over single models. However, due to the high costs of manual labeling, it is hard to obtain sufficient and reliable labeled data for effective training. Meanwhile, lots of unlabeled data exist in these sources, and we can readily obtain multiple unsupervised models. Although unsupervised models do not directly generate a class label prediction for each object, they provide useful constraints on the joint predictions for a set of related objects. Therefore, incorporating these unsupervised models into the ensemble of supervised models can lead to better prediction performance. In this paper, we study ensemble learning with outputs from multiple supervised and unsupervised models, a topic where little work has been done. We propose to consolidate a classification solution by maximizing the consensus among both supervised predictions and unsupervised constraints. We cast this ensemble task as an optimization problem on a bipartite graph, where the objective function favors the smoothness of the predictions over the graph, but penalizes the deviations from the initial labeling provided by the supervised models. We solve this problem through iterative propagation of probability estimates among neighboring nodes and prove the optimality of the solution. The proposed method can be interpreted as conducting a constrained embedding in a transformed space, or a ranking on the graph. Experimental results on different applications with heterogeneous data sources demonstrate the benefits of the proposed method over existing alternatives. (More information, data, and code are available at http://www.cse.buffalo.edu/~jing/integrate.htm.)

Attribute weights determination models for consensus maximization in multiple attribute group decision-making

Multiple attribute group decision making (MAGDM) is an important research field of decision science. A critical aspect of MAGDM is to determine the weights of attributes. In this paper, we study the MAGDM problem in which the attributes are given in real numbers or interval numbers, and the information about attribute weights is completely unknown or partially known. We first get the group opinion by fusing all individual opinion with each decision-makers' importance and introduce the deviation variable of each individual opinion and the group opinion. Then, we develop a quadratic programming model by means of minimizing the sum of all the deviation values, and a simple and straightforward formula for determining attribute weights can be derived from solving the developed models. We also establish a generalized model for solving MAGDM problems with partial weight information on attributes. In addition, we establish some similar models for MAGDM with interval attribute values. At last, we apply our models to a practical problem of a military unit purchasing new artillery weapons.