This paper presents the Bayes Fisher information measures, defined by the expected Fisher information under a distribution for the parameter, for the arithmetic, geometric, and generalized mixtures of two probability density functions. The Fisher information of the arithmetic mixture about the mixing parameter is related to chi-square divergence, Shannon entropy, and the Jensen-Shannon divergence. The Bayes Fisher measures of the three mixture models are related to the Kullback-Leibler, Jeffreys, Jensen-Shannon, Rényi, and Tsallis divergences. These measures indicate that the farther away are the components from each other, the more informative are data about the mixing parameter. We also unify three different relative entropy derivations of the geometric mixture scattered in statistics and physics literatures. Extensions of two of the formulations to the minimization of Tsallis divergence give the generalized mixture as the solution.

We consider a network consisting of n components and assume that the network has two states up and down. We further suppose that the network is subject to shocks that appear according to a counting process and that each shock may lead to the component failures. Under some assumptions on the shock occurrences, we present a new variant of the notion of signature which we call t-signature. Then, t-signature-based mixture representations for the reliability function of the network are obtained. Several stochastic properties of the network lifetime are investigated. In particular, under the assumption that the number of failures at each shock follows a binomial distribution and the process of shocks is nonhomogeneous Poisson process, explicit form of the network reliability is derived and its aging properties are explored. Several examples are also provided.

We consider a coherent system consisting of n components where the component lifetimes are assumed to be random variables following a probabilistically exchangeable joint distribution function, where the probability distribution does not change with any permutation of the components. We study stochastic properties of the residual lifetime of live components of the system, under different conditions. The number of failed components of the system are explored, under the assumption that the system is operating at time t. We also study the probability that the ith component failure in the system causes the system failure, given that the system is operating at time t. The results of the paper extend some of the existing results in the literature.

The concept of D-spectrum is a useful tool to investigate the reliability and stochastic properties of networks. In this paper, we consider a network consisting of n components (links or nodes), and assume that the network has two states: up, and down. We study the D-spectrum-based reliability of the network under the assumption that the components are subject to failure according to a counting process. Mixture representation of the reliability of the network lifetime is given in terms of the reliability functions of arrival times. It is shown that, when the D-spectra of two networks are stochastically ordered, then under some conditions the lifetimes of two networks are also stochastically ordered. Under the special case when the process of the failure of the components is a nonhomogeneous Poisson process, we arrive at a mixture representation for the reliability function of the network lifetime, and explore several stochastic and aging properties of the network lifetime under different scenarios. The failure rate of the network lifetime and its asymptotic behavior is investigated. D-spectrum based representation theorems are also given on the basis of the stochastic precedence concept.

The concept of the signature of a coherent system is useful to study the stochastic and aging properties of the system. Let X1m, X2:n, ⋯ Xn:ndenote the ordered lifetimes of the components of a coherent system consisting of n i.i.d components. If T denotes the lifetime of the system, then the signature vector of the system is defined to be a probability vectors = (s1, s2, ⋯, sn) such that si= P(T = Xi:n), i = 1, 2, ⋯,n. Here we consider a coherent system with sig- nature of the form s = (s1, s2, ⋯ Si, 0 ... , 0), where sk>; 0, k = 1,2, ⋯, i. Under the condition that the system is working at time t, we propose a time dependent measure to calculate the probability of residual life of live components of the system, i.e., Xk:n, k = i + 1 ⋯, n. Several stochastic and aging properties of the proposed measure are explored.

The concept of `signature' is a useful tool to study the stochastic and aging properties of coherent systems. We consider a coherent system, and assume that there is some partial information about the failure status of the system lifetime. We study various properties of the conditional signature.

The paper presents a probabilistic Bayesian framework for object tracking using a combination of a corner-based model and coefficients of Undecimated wavelet packet transform (UWPT) inside a patch around each corner. This combination uses the UWPT coefficients patch helps to enrich the global representation of the object shape model by local descriptors. The goal is to maximize the posterior of the object global position. To this end, a voting mechanism is used based on the coherency among the model corners. The role of the local wavelet-based descriptors is to filter out some irrelevant observation before the voting process. Experimental results indicate good performances of the algorithm in crowd scenes and partial occlusions.

We consider a coherent structure consisting ofncomponents having the property that if it is known that at mostrcomponents (rn) have failed, the system is still operating with probability 1. Some examples of the systems having this property are (n-k+ 1)-out-of-n, some parallel-series, and some series-parallel structures. Depending on the structure, and the number of active components of the coherent systems at timet, the mean residual life function of the system is studied, by several authors. This paper investigates more properties of the mean residual life function of the coherent systems sharing the described property. We will show that, when the components of the system have increasing failure rate, the mean residual life function of the system is decreasing in time. Several examples, and illustrative graphs are also provided.

In this paper, we propose a new algorithm for occlusion handling for object tracking in the crowded video scenes. The algorithm exploits the properties of undecimated wavelet packet transform (UWPT) coefficients and texture analysis to track arbitrary objects. The algorithm is initialized by the user through specifying a region around the object of interest at the reference frame. Then, coefficients of the UWPT of the region construct a Feature Vector (FV) for every pixel in that region. Optimal search for the best match is then performed by using the generated FVs inside an adaptive search window. Adaptation of the search window is achieved by inter- frame texture analysis to find the direction and speed of the object motion. This temporal texture analysis also assists in tracking of the object under partial or short-term full occlusion. Experimental results show a good performance for occlusion handling for object tracking in crowded scenes, in particular crowds on stairs in airports or train stations.

The paper presents a new corner-model based learning method able to track non-rigid objects in the presence of occlusion. A voting mechanism followed by a probability density analysis of the voting space histogram is used to estimate new position of the target. The model is updated at any frame. The problem rises in the occlusion events where the occluder corners affect the model and the tracker may follow the occluder. The key point of the method toward success is automatically deciding on the corners to classify them into two classes, good and malicious corners. Good corners are used to update the model in a conservative way removing the corners that are voting to the highly voted wrong positions due to the occluder. This leads to a continuous model learning during occlusion. Experimental results show a successful tracking along with a more precise estimation of shape and motion during occlusion

This paper presents a corner based voting method for estimating the object shift in video image frames. Information about the corners distribution around a reference point is used to represent the object shape and then to find the most probable target position in the next frame. Tracking is done through using a voting space obtained by matching corners information. A motion vector for the reference point is nonlinearly estimated with three different strategies by using the global information of the matched corners. The results show a comparison between three considered strategies for estimating the object shift.

In the last years, the Particle Filter algorithm has been extensively proposed and employed for handling the problem of visual tracking of multiple moving objects under different assumptions. This wide usage is due to the capability of performing a recursive multiple hypothesis state estimation for non-linear non-Gaussian motion and observation models. In this paper a method, based on the Particle Filter framework, is proposed for multiple objects tracking, exploiting a target representation consisting of position and shape described as a fixed dimensionality vector composed by a fixed number of grouped target corners. However, usually, application domains of visual tracking algorithms are characterized by non-rigid objects and high occlusions rate entailing new corners to appear and others to disappear at each frame. In order to cope with this problem, a voting method (i.e. the Generalized Hough Transform) is employed to estimate the likelihood function to weight different propagated particles (i.e. multiple corners configurations describing shapes) by means of the corners extracted from the currently observed image. This method, in addition to the high dimensionality of the state representation, depicts the two main particularities of the presented Particle Filter. The proposed algorithm has been tested in a real-world domain and experiments indicate good results in tracking both rigid and non-rigid objects.

This paper presents a method based on skin colormodel face detection and human body proportion constraints to estimate the number and position of people entering the monitored scene as a compact group. This helps to split the group into individual persons and solve a common lack in traditional background subtraction based detection and tracking methods: despite common systems, this algorithm can recognize the number and position of the people in a single change detection blob. The hypotheses are: standing subjects, face visibility from the point of view of the camera, a calibrated map to estimate objects' distance from the sensor and to estimate expected people's height on the image plane. These estimations allow dynamic thresholding of several shape parameters and lead to very interesting results.

This paper presents a shape prediction algorithm in a noisy video sequence based on pixel representation in the undecimated wavelet domain. In our algorithm for tracking of user-defined shapes in a noisy sequence of images, the amplitude of coefficients in the best basis tree expansion of the undecimated wavelet packet transform are used as feature vectors (FVs). FVs robustness against noise has been achieved through inherent denoising and edge component separation in the best basis selection algorithm. The algorithm uses these FVs to track the pixels of small square blocks located at the vicinity of the object boundary. Searching for the best-matched block has been performed using conventional block matching algorithm in the wavelet domain. Our experimental results show that the algorithm is robust to noise in case of object's shape translation, rotation and/or scaling and can be used to track both rigid and non-rigid shapes in image sequences

In the study of the reliability of technical systems, k-out-of-n systems play an important role. In the present paper, we consider a k-out-of-n system consisting of n identical components with independent lifetimes having a common distribution function F. Under the condition that, at time t, all the components of the system are working, we propose a new definition for the mean residual life (MRL) function of the system, and obtain several properties of that system.