For appropriate orthonormal wavelet basis {ψjke}j∈Zk∈Zde∈{0,1}d, constants p and γ, if Iγdenotes the Riesz fractional integral operator of order γ and (ηjke)j∈Zk∈Zde∈{0,1}d a sequence of independent identically distributed symmetric p-stable random variables, we investigate the convergence of the series ΣjkeηjkeIγψjke. Similar results are also studied for modified fractional integral operators. Finally, some geometric properties related to self similarity are studied.

Some general conditions for multichannel sampling are established for wide sense stationary sequences with spectral density. First, necessary and sufficient conditions are given for these processes so that they are linearly determined by the samples obtained from a multichannel sampling scheme. Some results are studied for stationary sequences and then applied to the problem of sampling, not necessarily band limited, wide sense stationary processes. Conditions are also given for the existence of a frame sequence of the samples. In the case of frames, the condition that the spectral measure is absolutely continuous is proved to be necessary.

A motion texture is an instantaneous motion map extracted from a dynamic texture. We observe that such motion maps exhibit values of two types: a discrete component at zero (absence of motion) and continuous motion values. We thus develop a mixed-state Markov random field model to represent motion textures. The core of our approach is to show that motion information is powerful enough to classify and segment dynamic textures if it is properly modeled regarding its specific nature and the local interactions involved. A parsimonious set of 11 parameters constitutes the descriptive feature of a motion texture. The motivation of the proposed formulation runs toward the analysis of dynamic video contents, and we tackle two related problems. First, we present a method for recognition and classification of motion textures, by means of the Kullback--Leibler distance between mixed-state statistical models. Second, we define a two-frame motion texture maximum a posteriori (MAP)-based segmentation method applicable to motion textures with deforming boundaries. We also investigate a new issue, the space-time dynamic texture segmentation, by combining the spatial segmentation and the recognition methods. Numerous experimental results are reported for those three problems which demonstrate the efficiency and accuracy of the proposed two-frame approach.

We characterize random signals which can be linearly determined by their samples. This problem is related to the question of the representation of random variables by means of a countable Riesz basis. We study different representations for processes which are linearly determined by a countable Riesz basis. This concerns the representation of continuous time processes by means of discrete samples.

In this paper, we study the question of the representation of random variables by means of frames or Riesz basis generated by stationary sequences. This concerns the representation of continuous time wide sense stationary random processes by means of discrete samples.

In this paper we study the question of the representation of random variables by means of frames or Riesz basis generated by stationary sequences. This concerns to the possible representation of continuous time processes by means of discrete samples.

Dynamic textures are time-varying visual patterns that exhibit certain spatio-temporal stationarity properties and are displayed mostly by natural scene elements. In this paper, we present new statistical models for the characterization of motion in this type of sequences. First we observe that motion measurements present values of two types: a discrete component at zero expressing the absence of motion and a continuous distribution for the rest of the motion values. Thus, we define random variables with mixed-states and propose to model a sequence of motion maps as a Markov chain, where the transition densities are mixed-state probability densities. Based on this approach, we propose a method for dynamic texture segmentation in real sequences showing the efficiency of the proposal in dynamic content analysis applications.

The aim of this work is to model the apparent motion in image sequences depicting natural dynamic scenes. We adopt the mixed-state Markov Random Fields (MRF) models recently introduced to represent so-called motion textures. The approach consists in describing the spatial distribution of some motion measurements which exhibit mixed-state nature: a discrete component related to the absence of motion and a continuous part for measurements different from zero. We propose several significative extensions to this model. We define an original motion texture segmentation method which does not assume conditional independence of the observations for each texture and normalizing factors are properly handled. Results on real examples demonstrate the accuracy and efficiency of our method.

This paper studies the almost sure almost every where convergence of random series of the form Sigmai=1infinaifiLebesgue spaces LP(X, Sigma, mu), where the ai's are centered random variables, and the fi's constitute an unconditional basic sequence.

In this paper, a new conditional formulation of classical filtering methods is proposed. This formulation is dedicated to image sequence-based tracking. These conditional filters allow solving systems whose measurements and state equation are estimated from the image data. In particular, the model that is considered for point tracking combines a state equation relying on the optical flow constraint and measurements provided by a matching technique. Based on this, two point trackers are derived. The first one is a linear tracker well suited to image sequences exhibiting global-dominant motion. This filter is determined through the use of a new estimator, called the conditional linear minimum variance estimator. The second one is a nonlinear tracker, implemented from a conditional particle filter. It allows tracking of points whose motion may be only locally described. These conditional trackers significantly improve results in some general situations. In particular, they allow for dealing with noisy sequences, abrupt changes of trajectories, occlusions, and cluttered background.

We provide an almost-sure convergent expansion of a process with power law of fractional order by means of some known theorems from harmonic analysis and rather simple probability theory results.

We construct an a.s. convergent expansion of a /spl prop/1/|/spl omega/|/sup /spl beta// spectral behavior process.

The time between failures is a very useful measurement to analyze reliability models for time-dependent systems. In many cases, the failure-generation process is assumed to be stationary, even though the process changes its statistics as time elapses. This paper presents a new estimation procedure for the probabilities of failures; it is based on estimating time-between-failures. The main characteristics of this procedure are that no probability distribution function is assumed for the failure process, and that the failure process is not assumed to be stationary. The model classifies the failures in Q different types, and estimates the probability of each type of failure s-independently from the others. This method does not use histogram techniques to estimate the probabilities of occurrence of each failure-type; rather it estimates the probabilities directly from the values of the time-instants at which the failures occur. The method assumes quasistationarity only in the interval of time between the last 2 occurrences of the same failure-type. An inherent characteristic of this method is that it assigns different sizes for the time-windows used to estimate the probabilities of each failure-type. For the failure-types with low probability, the estimator uses wide windows, while for those with high probability the estimator uses narrow windows. As an example, the model is applied to software reliability data.

Neural networks and image processing algorithms typically use very large amounts of data and usually this data is processed iteratively. Hence, the issue of cache memories for enhancing the processing speed is important. A particularly important model that fits these applications is the simple loop model. Here, the exact solution for the cache memory simple loop model under random replacement is given using an urn model and the theory of Markov chains. The probability distribution is obtained as a quotient of Stirling Numbers of the Second Kind. It is also shown that asymptotically the number of elements in the urns follows a Truncated at Zero Poisson Distribution.

We study, using standard Probability Theory results, the ability of the Hopfield model of associative memory using the Hebb rule to learn mean values from examples in the presence of noise. We state and prove properties concerning this ability.

A parallel algorithm for the diagonalization of symmetric matrices is presented. The Givens-Jacobi rotator method is extended and modified to solve the eigensystem problem of symmetric matrices in a full parallel way. The algorithm solves the diagonalization of symmetric matrices in approximately N "parallel" iterations for large N, while the Givens-Jacobi algorithm requires 3N to 5N "parallel" iterations. A proof of the convergence for small rotation angles is presented. Preliminary simulations done with arbitrary randomly generated symmetric matrices sustain the efficiency of the algorithm.

.a simple one. It happened that both were chosen to be linear functions and the resulting DTNNSuIOF is presented in Fig. 2. For the researchers from the robot control field it might be amusing to look at this totally linear (delay element is irrelevant) DTNNSuIOF as a proposal for the robot control. Precision of the order 10 in the training is guaranteed. (See the paper.) The appearance of the constant gains equaling 50 is also an intriguing one. The matrices and were not given in this example. Therefore, there is no comment on this part. At this point without any additional information, we may say that the whole algorithm failed. DTNNSuIOF cannot generalize. This is the real curse for any NN indeed. The author personally admitted that but, understandably, he put it much more softly: “The high accuracy of the testing results does not guarantee the high stage of neural network robustness, which will be investigated and discussed in the next paper. ” Few basic remarks are needed here. In the world of NN, both the test, i.e., validation phase and generalization properties are defined in terms of previously unseen inputs. However, there are no test results in the paper at all. The highly accurate results presented in Fig. 5 of the paper are the outputs of the DTNNSuIOF on training inputs. The fact that the very error during the training is of the order 10 does not say anything about the generalization properties of NN. In the NN field, the stories about the overtrained NN having high variance and low bias are very well known. (Here, the bias 0!) Let us paraphrase the author correctly—it is highly likely that the high accuracy of testing results does guarantee the high stage of neural network robustness, which does not have to be investigated and discussed in the next paper. One thing is obvious, the whole algorithm relies on and believes in overwhelming power of the (pseudo) inversion operation. The accuracy in training phase presented in the paper shows merely the accuracy of the supporting software in calculation of a matrix pseudo inverse. In highly nonlinear, high-dimensional and noisy environment, DTNNSuIOF approach as given in the paper cannot result with any useful NN design algorithm.

In this work, a method for the estimation of the probabilities of a non stationary source is proposed in order to adapt quickly to the source statistics changes. This estimation is based on the time intervals between occurrences of each symbol. The method is applied to lossless compression of images.

A model that attempts to simulate animal memory under stress is presented. For this purpose a model of selectable multiple associative memories is given. We consider two underlying types of memories: stressed and unstressed, implemented on the same neural network. In our model, learning into one or the other type of memory is done according to the stress of the individual at the time of learning. Memory retrieval is obtained according to a continuous function of the stress of the individual at the time of retrieval, who for low stress retrieves unstressed associations and for high stress retrieves stressed associations. Several biological results supporting this model are presented. A mathematical proof on the behaviour of the basins of attraction of the network as a function of stress is presented. Also a generalization to selectable multiple coexisting memories is given, and engineering and other applications of the model are suggested.

Single image stereograms (SIS) create a vivid illusion of depth from a 2D image based on the stereo vision process. The method does not require special equipment, and has attracted attention in recent years. Here, the principles of SIS are discussed, as well as the most well known generating methods. We introduce a modification to the random-dot based algorithms, that leads to SIS patterns with less high-frequency content. This improves the 3D capture effect and the aesthetic aspect of the SIS, and avoids ink-spreading problems in high resolution output devices. A correlation function that measures the local match between the images seen by each eye is computed. This allows a direct evaluation of the correctness of the algorithms.

The chains-of-rare-events model (ChRE) is extended. The ChRE was originally introduced in order to analyze occurrences which can be produced with simple, double, triple, etc., multiplicity. In the original ChRE, each occurrence of multiplicity (i) is independently distributed according to a Poisson law with parameter /spl lambda//sub i/; and a simple relation for these parameters is considered. In this way, ChRE can be applied to analyze outcomes produced in occurrences with multiple events, such as failures, queuing, automobile accidents, telephone calls, and accidents in a factory. The original ChRE is extended to analyze the total number of outcomes in which a given total number of occurrences of different multiplicity occur. The model can be analyzed as a compound Poisson distribution where the compounding distribution is Poisson truncated at zero. Applications to reliability and queuing processes data are presented. The results compare favorably with those from other models.

A parametric modeling and statistical estimation approach is proposed and simulation data are shown for estimating 3-D object surfaces from images taken by calibrated cameras in two positions. The parameter estimation suggested is gradient descent, though other search strategies are also possible. Processing image data in blocks (windows) is central to the approach. After objects are modeled as patches of spheres, cylinders, planes and general quadrics-primitive objects, the estimation proceeds by searching in parameter space to simultaneously determine and use the appropriate pair of image regions, one from each image, and to use these for estimating a 3-D surface patch. The expression for the joint likelihood of the two images is derived and it is shown that the algorithm is a maximum-likelihood parameter estimator. A concept arising in the maximum likelihood estimation of 3-D surfaces is modeled and estimated. Cramer-Rao lower bounds are derived for the covariance matrices for the errors in estimating the a priori unknown object surface shape parameters.>

A simple generalization of the Hopfield memory is presented. The model proposed updates simultaneously groups of a fixed number of neurons that are disjoint in the sense that each neuron belongs to one and only one group. An analysis is presented of the case in which one of the groups is chosen at random with equal probability and then is updated according to a rule equivalent to the one given by J.J. Hopfield (1982). It is shown that the rule minimizes an energy function in the same way as the original Hopfield model. Sufficient conditions on the corresponding connection matrix as to ensure stability are given.>

An approach is introduced to estimating object surfaces in 3D space from a sequence of images. A 3D surface of interest is modeled as a function known up to the values of a few parameters. Surface estimation is then treated as the general problem of maximum-likelihood parameter estimation based on two or more functionally related data sets, which constitute a sequence of images taken at different locations and orientations. Experiments are run to illustrate the various advantages of using as many images as possible in the estimation and of distributing camera positions from first to last over as large a baseline as possible. The authors introduce the use of asymptotic Bayesian approximations to summarize the useful information in a sequence of images, thereby drastically reducing both storage and processing. This results in a Bayesian estimator for the surface parameters. All the usual tools of statistical signal analysis can be brought to bear, the information extraction appears to be robust and computationally reasonable, the concepts are geometric and simple, and essentially optimal accuracy should result.>

A new approach is introduced to 3-D parameterized object estimation and recognition. Though the theory is applicable for any parameterization, we use a model for which objects are approximated by patches of spheres, cylinders, and planes-primitive objects. These primitive surfaces are special cases of 3-D quadric surfaces. Primitive surface estimation is treated as parameter estimation using data patches in two or more noisy images taken by calibrated cameras in different locations and from different directions. Included is the case of a single moving camera. Though various techniques can be used to implement this nonlinear estimation, we discuss the use of gradient descent. Experiments are run and discussed for the case of a sphere of unknown location. It is shown that the estimation procedure can be viewed geometrically as a cross correlation of nonlinearly transformed image patches in two or more images. Approaches to object surface segmentation into primitive object surfaces, and primitive object-type recognition are briefly presented and discussed. The attractiveness of the approach is that maximum likelihood estimation and all the usual tools of statistical signal analysis can be brought to bear, the information extraction appears to be robust and computationally reasonable, the concepts are geometric and simple, and close to optimal accuracy should result.

An approach to object location and orientation estimation is discussed in which objects in 3-D space are approximated by chunks of spheres, cylinders, and planes. The surface-shape parameters of these chunks of primitive subobjects are estimated in real time from a single 2-D image assuming a Lambertian reflection model. This processing is realized by partitioning an image into small square windows and processing the windows in parallel. It is assumed that a small window views a portion of one of the spherical, cylindrical or planar chunks. The paper applies standard statistical estimators in new ways to the estimation of the 3-D shape parameters for spherical and cylindrical surfaces. Linear regression and scatter matrix eigenvalue analysis techniques are used here. The algorithms are computationally simple yet are robust and can handle noisy highly variable data.

In order to realize robust real-time 3-D object recognition and object location and orientation estimation, a 2-D image is partitioned into small square windows which are processed in parallel. It is assumed that a 3-D object can be approximated by chunks of planes, spheres, and cylinders and that one such surface type is seen within a small window. Our solutions are largely for matte surfaces (i.e. diffusely reflecting); we do touch on specular (i.e, mirror) surfaces. Two kinds of results have been obtained in this work. For the purpose of 3-D object type recognition, a simple 2-D polynomial approximation is made to the image data in a window. Based on the relationships between polynomial coefficients and 3-D surface shape-types, a reliable decision can be made as to whether the object surface seen is that of a plane, a cylinder or sphere. In addition to providing the appropriate observables for surface-type recognition, these polynomial fits act as remarkably effective nonlinear lowpass filters.