Theory of evidence for face detection and tracking

This paper deals with face detection and tracking by computer vision for multimedia applications. Contrary to current techniques that are based on huge learning databases and complex algorithms to get generic face models (e.g., active appearance models), the proposed method handles simple contextual knowledge representative of the application background thanks to a quick supervised initialization. The transferable belief model is used to counteract the incompleteness of the prior model due first to a lack of exhaustiveness of the learning stage and secondly to the subjectivity of the task of face segmentation. The algorithm contains two main steps: detection and tracking. In the detection phase, an evidential face model is estimated by merging basic beliefs elaborated from Viola and Jones face detector and from a skin colour detector, for the assignment of mass functions. These functions are computed as the merging of sources in a specific nonlinear colour space. In order to deal with colour information dependence in the fusion process, the Den?ux cautious rule is used. The pignistic probabilities stemming from the face model guarantee the compatibility between the belief framework and the probabilistic framework. They are the entries of a bootstrap particle filter which yields face tracking at video rate. We show that the proper tuning of the evidential model parameters improves the tracking performance in real-time. Quantitative evaluation of the proposed method gives a detection rate reaching 80%, comparable to what can be found in the literature. However the proposed method requires only a weak initialization.     

Belief functions combination without the assumption of independence of the information sources

This paper considers the problem of combining belief functions obtained from not necessarily independent sources of information. It introduces two combination rules for the situation in which no assumption is made about the dependence of the information sources. These two rules are based on cautious combinations of plausibility and commonality functions, respectively. The paper studies the properties of these rules and their connection with Dempster’s rules of conditioning and combination and the minimum rule of possibility theory.     

The conjunctive combination of interval-valued belief structures from dependent sources

To combine belief functions from reliable dependent sources, Denoeux proposed an operator called the cautious conjunctive rule. In this paper, the conjunctive combination of interval-valued belief structures (IBSs) from reliable dependent sources is investigated. Nonlinear optimization problems based on the cautious rule are constructed and solved to generate an unnormalized and a normalized cautious combination of two IBSs. In a similar manner, optimization problems used to combine multiple IBSs are also constructed. Furthermore, to deal with some situations in which the relative weights of IBSs must be considered, optimization problems considering relative weights are constructed to implement the unnormalized and normalized weighted cautious combination of IBSs. To verify the validity and usefulness of the conjunctive combination of IBSs, a trustworthiness evaluation problem of hospital information systems, which is employed in many hospitals of the Anhui province in China, is solved based on the normalized weighted cautious combination of IBSs.     

An aggregation framework based on coherent lower previsions: Application to Zadeh’s paradox and sensor networks

The problem of aggregating two or more sources of information containing knowledge about a common domain is considered. We propose an aggregation framework for the case where the available information is modelled by coherent lower previsions, corresponding to convex sets of probability mass functions. The consistency between aggregated beliefs and sources of information is discussed. A closed formula, which specializes our rule to a particular class of models, is also derived. Two applications consisting in a possible explanation of Zadeh’s paradox and an algorithm for estimation fusion in sensor networks are finally reported.     

On the inexactness level of robust Levenberg–Marquardt methods

Recently, the Levenberg–Marquardt (LM) method has been used for solving systems of nonlinear equations with nonisolated solutions. Under certain conditions it converges Q-quadratically to a solution. The same rate has been obtained for inexact versions of the LM method. In this article the LM method will be called robust, if the magnitude of the regularization parameter occurring in its sub-problems is as large as possible without decreasing the convergence rate. For robust LM methods the article shows that the level of inexactness in the sub-problems can be increased significantly. As an application, the local convergence of a projected robust LM method is analysed.     

Robustly stable pole-placement based adaptive control of continuous linear systems with multiestimation

This paper deals with the pole-placement type robust adaptive control of continuous linear systems in the presence of bounded noise and a common class of unmodeled dynamics with the use of multiple estimation schemes working in parallel. The multiestimation scheme consisting of the above set of various single estimation schemes is a tool used to minimize the plant identification error by building an estimate which is a convex combination of the estimates at all time. The weighting functions of the individual estimates are provided at each time by a suboptimization scheme for a quadratic loss function of a possibly filtered tracking error and/or control input. The robust stability of the overall adaptive scheme is ensured by an adaptation relative dead zone which takes into account the contribution of the unmodeled dynamics and bounded noise. The basic results are derived for two different estimation strategies which have either a shared regressor with the plant or individual regressors for the input contribution and its relevant time-derivatives. In this second case, the plant input is obtained through a similar convex combination rule as the one used for the estimators in the first approach. An extension of the basic strategies is also pointed out including a combined use of the suboptimization scheme with a supervisor of past measures for the on-line calculation of the estimator weights in the convex combination.     

A skin detection approach based on the Dempster–Shafer theory of evidence

Skin detection is an important step for a wide range of research related to computer vision and image processing and several methods have already been proposed to solve this problem. However, most of these methods suffer from accuracy and reliability problems when they are applied to a variety of images obtained under different conditions. Performance degrades further when fewer training data are available. Besides these issues, some methods require long training times and a significant amount of parameter tuning. Furthermore, most state-of-the-art methods incorporate one or more thresholds, and it is difficult to determine accurate threshold settings to obtain desirable performance. These problems arise mostly because the available training data for skin detection are imprecise and incomplete, which leads to uncertainty in classification. This requires a robust fusion framework to combine available information sources with some degree of certainty. This paper addresses these issues by proposing a fusion-based method termed Dempster–Shafer-based Skin Detection (DSSD). This method uses six prominent skin detection criteria as sources of information (SoI), quantifies their reliabilities (confidences), and then combines their confidences based on the Dempster–Shafer Theory (DST) of evidence. We use the DST as it offers a powerful and flexible framework for representing and handling uncertainties in available information and thus helps to overcome the limitations of the current state-of-the-art methods. We have verified this method on a large dataset containing a variety of images, and achieved a 90.17% correct detection rate (CDR). We also demonstrate how DSSD can be used when very little training data are available, achieving a CDR as high as 87.47% while the best result achieved by a Bayesian classifier is only 68.81% on the same dataset. Finally, a generalized DSSD (GDSSD) is proposed achieving 91.12% CDR.     

Relevance and truthfulness in information correction and fusion

A general approach to information correction and fusion for belief functions is proposed, where not only may the information items be irrelevant, but sources may lie as well. We introduce a new correction scheme, which takes into account uncertain metaknowledge on the source’s relevance and truthfulness and that generalizes Shafer’s discounting operation. We then show how to reinterpret all connectives of Boolean logic in terms of source behavior assumptions with respect to relevance and truthfulness. We are led to generalize the unnormalized Dempster’s rule to all Boolean connectives, while taking into account the uncertainties pertaining to assumptions concerning the behavior of sources. Eventually, we further extend this approach to an even more general setting, where source behavior assumptions do not have to be restricted to relevance and truthfulness. We also establish the commutativity property between correction and fusion processes, when the behaviors of the sources are independent.     

ON THE STABILITY OF FUSION FRAMES （FRAMES OF SUBSPACES）

A frame is an orthonormal basis-like collection of vectors in a Hilbert space, but need not be a basis or orthonormal. A fusion frame (frame of subspaces) is a frame-like collection of subspaces in a Hilbert space, thereby constructing a frame for the whole space by joining sequences of frames for subspaces. Moreover the notion of fusion frames provide a framework for applications and providing efficient and robust information processing algorithms.In this paper we study the conditions under which removing an element from a fusion frame, again we obtain another fusion frame. We give another proof of [5, Corollary 3.3(iii)] with extra information about the bounds.     

Early detection of vessel delays using combined historical and real-time information

In ocean transportation, detecting vessel delays in advance or in real time is important for fourth-party logistics (4PL) in order to fulfill the expectations of customers and to help customers reduce delay costs. However, the early detection of vessel delays faces the challenges of numerous uncertainties, including weather conditions, port congestion, booking issues, and route selection. Recently, 4PLs have adopted advanced tracking technologies such as satellite-based automatic identification systems (S-AISs) that produce a vast amount of real-time vessel tracking information, thus providing new opportunities to enhance the early detection of vessel delays. This paper proposes a data-driven method for the early detection of vessel delays: in our new framework of refined case-based reasoning (CBR), real-time S-AIS vessel tracking data are utilized in combination with historical shipping data. The proposed method also provides a process of analyzing the causes of delays by matching the tracking patterns of real-time shipments with those of historical shipping data. Real data examples from a logistics company demonstrate the effectiveness of the proposed method.     

Application of Adapted-Bubbles to the Helmholtz Equation with Large Wavenumbers in 2D

An adapted-bubbles approach which is a modification of the residual-free bubbles (RFB) method, is proposed for the Helmholtz problem in 2D. A new two-level finite element method is introduced for the approximations of the bubble functions. Unlike the other equations such as the advection-diffusion equation, RFB method when applied to the Helmholtz equation, does not depend on another stabilized method to obtain approximations to the solutions of the sub-problems. Adapted-bubbles (AB) are obtained by a simple modification of the sub-problems. This modification increases the accuracy of the numerical solution impressively. We provide numerical experiments with the AB method up to $ch = 5$ where $c$ is the wavenumber and $h$ is the mesh size. Numerical tests show that the AB method is better by far than higher order methods available in the literature.     

The reduction and fusion of fuzzy covering systems based on the evidence theory

This paper studies reduction of a fuzzy covering and fusion of multi-fuzzy covering systems based on the evidence theory and rough set theory. A novel pair of belief and plausibility functions is defined by employing a method of non-classical probability model and the approximation operators of a fuzzy covering. Then we study the reduction of a fuzzy covering based on the functions we presented. In the case of multiple information sources, we present a method of information fusion for multi-fuzzy covering systems, by which objects can be well classified in a fuzzy covering decision system. Finally, by using the method of maximum flow, we discuss under what conditions, fuzzy covering approximation operators can be induced by a fuzzy belief structure.     

Fusing multiple Bayesian knowledge sources

We address the problem of information fusion in uncertain environments. Imagine there are multiple experts building probabilistic models of the same situation and we wish to aggregate the information they provide. There are several problems we may run into by naively merging the information from each. For example, the experts may disagree on the probability of a certain event or they may disagree on the direction of causality between two events (e.g., one thinks A causes B while another thinks B causes A). They may even disagree on the entire structure of dependencies among a set of variables in a probabilistic network. In our proposed solution to this problem, we represent the probabilistic models as Bayesian Knowledge Bases (BKBs) and propose an algorithm called Bayesian knowledge fusion that allows the fusion of multiple BKBs into a single BKB that retains the information from all input sources. This allows for easy aggregation and de-aggregation of information from multiple expert sources and facilitates multi-expert decision making by providing a framework in which all opinions can be preserved and reasoned over.     

Dempster's rule of combination

The theory of belief functions is a generalization of probability theory; a belief function is a set function more general than a probability measure but whose values can still be interpreted as degrees of belief. Dempster's rule of combination is a rule for combining two or more belief functions; when the belief functions combined are based on distinct or “independent” sources of evidence, the rule corresponds intuitively to the pooling of evidence. As a special case, the rule yields a rule of conditioning which generalizes the usual rule for conditioning probability measures. The rule of combination was studied extensively, but only in the case of finite sets of possibilities, in the author's monograph A Mathematical Theory of Evidence. The present paper describes the rule for general, possibly infinite, sets of possibilities. We show that the rule preserves the regularity conditions of continuity and condensability, and we investigate the two distinct generalizations of probabilistic independence which the rule suggests.     

多源验前信息下的Bayes信息融合方法

本文以指数分布寿命型电子产品为例,讨论了多源验前信息情况下如何对产品失效率进行融合估计的问题。首先,介绍了寿命试验数据的信息融合方法,并以此为例,说明了取伽玛分布为指数分布寿命型产品失效率的先验分布的合理性。然后,在产品具有多源验前信息源的情况下,给出了一种方便实用的Bayes信息融合方法,充分融合各验前信息,得到产品失效率的验前分布及后验分布。最后给出了数值实例。     

极大熵方法与二次规划子问题的显式解

本文对混合约束极大极小问题的目标函数与约束分别用熵函数来逼近,讨论了逼近问题的二次规划子问题的搜索方向的显式形式,并给出了极大极小问题和多目标规划的二次规划予问题的显式解。将所得结果用于相应的算法中,可提高算法的有效性。     

On the fundamental convergence in the (C) mean in problems of information fusion

The Choquet integral can be regarded as one of aggregation operators being used in information fusion. In this study, we offer an interpretation of sequences of measurable functions and the Choquet integral in the framework of information fusion. Based on an efficiency measure space, we also define a new concept of a fundamental convergence in the (C) mean of sequences of measurable functions and discuss its theoretical underpinnings along with related interpretation issues as well as deliver some new results. Furthermore, an application of this concept is discussed in the context of information fusion. More specifically, based on the theoretical investigations, this idea is applied to the determination of a measurable function being used in the Choquet integral.     

Information theory and alternate-hypothesis tests

Lindley's concept of the information in an experiment is used to study alternate-hypothesis statistical tests. A test is considered to be a combination of a sampling rule and a decision rule which is based on the samples taken. Two information functions are formed: the information about the unknown parameter contained in the samples taken and the information contained in the decision to which these samples lead. The former quantity is at least as great as the latter, with equality if, and only if, the test is an SPRT (sequential probability ratio test) neglecting the excess over the boundary.If the average information contained in the samples taken in one alternate-hypothesis test is greater than the average information contained in the samples taken in another, then the first test has greater expected length. It is also shown that an SPRT neglecting excess is the unique alternate-hypothesis test that utilizes all the information contained in the samples taken. These results provide a proof of the standard result concerning the optimal character of the SPRT neglecting excess.The major purpose of this paper is to develop an information-theoretic analysis of alternate-hypothesis tests. By means of this approach, new results on the SPRT and alternate-hypothesis tests in general are obtained.     

Boosting video tracking performance by means of Tabu Search in intelligent visual surveillance systems

In this paper, we present a fast and efficient technique for the data association problem applied to visual tracking systems. Visual tracking process is formulated as a combinatorial hypotheses search with a heuristic evaluation function taking into account structural and specific information such as distance, shape, color, etc.     

Based on interval type-2 fuzzy-neural network direct adaptive sliding mode control for SISO nonlinear systems

In this paper, a novel direct adaptive interval type-2 fuzzy-neural tracking control equipped with sliding mode and Lyapunov synthesis approach is proposed to handle the training data corrupted by noise or rule uncertainties for nonlinear SISO nonlinear systems involving external disturbances. By employing adaptive fuzzy-neural control theory, the update laws will be derived for approximating the uncertain nonlinear dynamical system. In the meantime, the sliding mode control method and the Lyapunov stability criterion are incorporated into the adaptive fuzzy-neural control scheme such that the derived controller is robust with respect to unmodeled dynamics, external disturbance and approximation errors. In comparison with conventional methods, the advocated approach not only guarantees closed-loop stability but also the output tracking error of the overall system will converge to zero asymptotically without prior knowledge on the upper bound of the lumped uncertainty. Furthermore, chattering effect of the control input will be substantially reduced by the proposed technique. To illustrate the performance of the proposed method, finally simulation example will be given.