recursive estimation of motion structure and focal length presents a formulation for recursive recovery of motion pointwise structure and focal length from feature correspondences tracked through an image sequence in addition to adding focal length to the state vector several representational improvements are made over earlier structure from motion formulations yielding a stable and accurate estimation framework which applies uniformly to both true perspective and orthographic projection results on synthetic and real imagery illustrate the performance of the estimator

structure and motion from line segments in multiple images this paper presents a new method for recovering the three dimensional structure of a scene composed of straight line segments using the image data obtained from a moving camera the recovery algorithm is formulated in terms of an objective function which measures the total squared distance in the image plane between the observed edge segments and the projections perspective of the reconstructed lines this objective function is minimized with respect to the line parameters and the camera positions to obtain an estimate for the structure of the scene the effectiveness of this approach is demonstrated quantitatively through extensive simulations and qualitatively with actual image sequences the implementation is being made publicly available

cross domain soft partition clustering with diversity measure and knowledge reference conventional soft partition clustering approaches such as fuzzy c means fcm maximum entropy clustering mec and fuzzy clustering by quadratic regularization fc qr are usually incompetent in those situations where the data are quite insufficient or much polluted by underlying noise or outliers in order to address this challenge the quadratic weights and gini simpson diversity based fuzzy clustering model qwgsd fc is first proposed as a basis of our work based on qwgsd fc and inspired by transfer learning two types of cross domain soft partition clustering frameworks and their corresponding algorithms referred to as type i type ii knowledge transfer oriented c means ti kt cm and tii kt cm are subsequently presented respectively the primary contributions of our work are four fold 1 the delicate qwgsd fc model inherits the most merits of fcm mec and fc qr with the weight factors in the form of quadratic memberships similar to fcm it can more effectively calculate the total intra cluster deviation than the linear form recruited in mec and fc qr meanwhile via gini simpson diversity index like shannon entropy in mec and equivalent to the quadratic regularization in fc qr qwgsd fc is prone to achieving the unbiased probability assignments 2 owing to the reference knowledge from the source domain both ti kt cm and tii kt cm demonstrate high clustering effectiveness as well as strong parameter robustness in the target domain 3 ti kt cm refers merely to the historical cluster centroids whereas tii kt cm simultaneously uses the historical cluster centroids and their associated fuzzy memberships as the reference this indicates that tii kt cm features more comprehensive knowledge learning capability than ti kt cm and tii kt cm consequently exhibits more perfect cross domain clustering performance and 4 neither the historical cluster centroids nor the historical cluster centroid based fuzzy memberships involved in ti kt cm or tii kt cm can be inversely mapped into the raw data this means that both ti kt cm and tii kt cm can work without disclosing the original data in the source domain i e they are of good privacy protection for the source domain in addition the convergence analyses regarding both ti kt cm and tii kt cm are conducted in our research the experimental studies thoroughly evaluated and demonstrated our contributions on both synthetic and real life data scenarios the novel qwgsd fc model is designed for soft partition clustering two cross domain clustering methods ti tii kt cm are subsequently proposed ti tii kt cm are superior to or competitive with other existing methods the convergences of both ti kt cm and tii kt cm are proved

fitting parameterized three dimensional models to images model based recognition and motion tracking depend upon the ability to solve for projection and model parameters that will best fit a 3 d model to matching 2 d image features the author extends current methods of parameter solving to handle objects with arbitrary curved surfaces and with any number of internal parameters representing articulation variable dimensions or surface deformations numerical stabilization methods are developed that take account of inherent inaccuracies in the image measurements and allow useful solutions to be determined even when there are fewer matches than unknown parameters the levenberg marquardt method is used to always ensure convergence of the solution these techniques allow model based vision to be used for a much wider class of problems than was possible with previous methods their application is demonstrated for tracking the motion of curved parameterized objects

a nonlinear thermoelastic bresse system global existence and exponential stability abstract in this paper we study a dissipative bresse system with nonlinear motion equation where the dissipation is given by thermal effects acting in the shear equation under general hypothesis on the nonlinearities we prove the existence and uniqueness of small global solutions as well as the exponential stability

dynamic 3d models with local and global deformations deformable superquadrics the authors present a physically based approach to fitting complex three dimensional shapes using a novel class of dynamic models that can deform both locally and globally they formulate the deformable superquadrics which incorporate the global shape parameters of a conventional superellipsoid with the local degrees of freedom of a spline the model s six global deformational degrees of freedom capture gross shape features from visual data and provide salient part descriptors for efficient indexing into a database of stored models the local deformation parameters reconstruct the details of complex shapes that the global abstraction misses the equations of motion which govern the behavior of deformable superquadrics make them responsive to externally applied forces the authors fit models to visual data by transforming the data into forces and simulating the equations of motion through time to adjust the translational rotational and deformational degrees of freedom of the models model fitting experiments involving 2d monocular image data and 3d range data are presented

constraints on deformable models recovering 3d shape and nongrid motion abstract inferring the 3d structures of nonrigidly moving objects from images is a difficult yet basic problem in computational vision our approach makes use of dynamic elastically deformable object models that offer the geometric flexibility to satisfy a diversity of real world visual constraints we specialize these models to include intrinsic forces inducing a preference for axisymmetry image based constraints are applied as extrinsic forces that mold the symmetry seeking model into shapes consistent with image data we describe an extrinsic force that applies constraints derived from profiles of monocularly viewed objects we generalize this constraint force to incorporate profile information from multiple views and use it to exploit binocular image data for time varying images the force becomes dynamic and the model is able to infer not only depth but nonrigid motion as well we demonstrate the recovery of 3d shape and nonrigid motion from natural imagery

closed form solutions for physically based shape modeling and recognition the authors present a closed form physically based solution for recovering a three dimensional 3 d solid model from collections of 3 d surface measurements given a sufficient number of independent measurements the solution is overconstrained and unique except for rotational symmetries the proposed approach is based on the finite element method fem and parametric solid modeling using implicit functions this approach provides both the convenience of parametric modeling and the expressiveness of the physically based mesh formulation and in addition can provide great accuracy at physical simulation a physically based object recognition method that allows simple closed form comparisons of recovered 3 d solid models is presented the performance of these methods is evaluated using both synthetic range data with various signal to noise ratios and using laser rangefinder data

shadowed c means integrating fuzzy and rough clustering a new method of partitive clustering is developed in the framework of shadowed sets the core and exclusion regions of the generated shadowed partitions result in a reduction in computations as compared to conventional fuzzy clustering unlike rough clustering here the choice of threshold parameter is fully automated the number of clusters is optimized in terms of various validity indices it is observed that shadowed clustering can efficiently handle overlapping among clusters as well as model uncertainty in class boundaries the algorithm is robust in the presence of outliers a comparative study is made with related partitive approaches experimental results on synthetic as well as real data sets demonstrate the superiority of the proposed approach

c ondensation conditional density propagation forvisual tracking the problem of tracking curves in dense visual clutter is challenging kalman filtering is inadequate because it is based on gaussian densities which being unimo dal cannot represent simultaneous alternative hypotheses the condensation algorithm uses factored sampling previously applied to the interpretation of static images in which the probability distribution of possible interpretations is represented by a randomly generated set condensation uses learned dynamical models together with visual observations to propagate the random set over time the result is highly robust tracking of agile motion notwithstanding the use of stochastic methods the algorithm runs in near real time

sequential updating of projective and affine structure from motion a structure from motion algorithm is described which recovers structure and camera position modulo a projective ambiguity camera calibration is not required and camera parameters such as focal length can be altered freely during motion the structure is updated sequentially over an image sequence in contrast to schemes which employ a batch process a specialisation of the algorithm to recover structure and camera position modulo an affine transformation is described together with a method to periodically update the affine coordinate frame to prevent drift over time we describe the constraint used to obtain this specialisation structure is recovered from image corners detected and matched automatically and reliably in real image sequences results are shown for reference objects and indoor environments and accuracy of recovered structure is fully evaluated and compared for a number of reconstruction schemes a specific application of the work is demonstrated affine structure is used to compute free space maps enabling navigation through unstructured environments and avoidance of obstacles the path planning involves only affine constructions

lines and points in three views and the trifocal tensor this paper discusses the basic role of the trifocal tensor in scene reconstruction from three views this 3 times 3 times 3 tensor plays a role in the analysis of scenes from three views analogous to the role played by the fundamental matrix in the two view case in particular the trifocal tensor may be computed by a linear algorithm from a set of 13 line correspondences in three views it is further shown in this paper that the trifocal tensor is essentially identical to a set of coefficients introduced by shashua to effect point transfer in the three view case this observation means that the 13 line algorithm may be extended to allow for the computation of the trifocal tensor given any mixture of sufficiently many line and point correspondences from the trifocal tensor the camera matrices of the images may be computed and the scene may be reconstructed for unrelated uncalibrated cameras this reconstruction will be unique up to projectivity thus projective reconstruction of a set of lines and points may be carried out linearly from three views

a validity measure for fuzzy clustering the authors present a fuzzy validity criterion based on a validity function which identifies compact and separate fuzzy c partitions without assumptions as to the number of substructures inherent in the data this function depends on the data set geometric distance measure distance between cluster centroids and more importantly on the fuzzy partition generated by any fuzzy algorithm used the function is mathematically justified via its relationship to a well defined hard clustering validity function the separation index for which the condition of uniqueness has already been established the performance of this validity function compares favorably to that of several others the application of this validity function to color image segmentation in a computer color vision system for recognition of ic wafer defects which are otherwise impossible to detect using gray scale image processing is discussed

motion and structure from line correspondences closed form solution uniqueness and optimization this work discusses estimating motion and structure parameters from line correspondences of a rigid scene the authors present a closed form solution to motion and structure parameters from line correspondences through three monocular perspective views the algorithm makes use of redundancy in the data to improve the accuracy of the solutions the uniqueness of the solution is established and necessary and sufficient conditions for degenerate spatial line configurations are given optimization has been employed to further improve the accuracy of the estimates in the presence of noise simulations have shown that the errors of the optimized estimates are close to the theoretical lower error bound

mildly dissipative nonlinear timoshenko systems global existence and exponential stability we consider nonlinear systems of timoshenko type in a one dimensional bounded domain the system has a dissipative mechanism being present only in the equation for the rotation angle it is a damping effect through heat conduction the global existence of small smooth solutions as well as the exponential stability are investigated

toward a theory of fuzzy information granulation and its centrality in human reasoning and fuzzy logic there are three basic concepts that underlie human cognition granulation organization and causation informally granulation involves decomposition of whole into parts organization involves integration of parts into whole and causation involves association of causes with effects granulation of an object a leads to a collection of granules of a with a granule being a clump of points objects drawn together by indistinguishability similarity proximity or functionality for example the granules of a human head are the forehead nose cheeks ears eyes etc in general granulation is hierarchical in nature a familiar example is the granulation of time into years months days hours minutes etc modes of information granulation ig in which the granules are crisp c granular play important roles in a wide variety of methods approaches and techniques crisp ig however does not reflect the fact that in almost all of human reasoning and concept formation the granules are fuzzy f granular the granules of a human head for example are fuzzy in the sense that the boundaries between cheeks nose forehead ears etc are not sharply defined furthermore the attributes of fuzzy granules e g length of nose are fuzzy as are their values long short very long etc the fuzziness of granules their attributes and their values is characteristic of ways in which humans granulate and manipulate information

three way fuzzy partitions defined by shadowed sets abstract pedrycz introduces the notion of a shadowed set as a three way approximation of a fuzzy set given a pair of thresholds a shadowed set approximates a fuzzy set by three regions an core of the fuzzy set the difference between a support and the core and the complement of the support a fuzzy partition is a family of nonempty fuzzy sets satisfying certain conditions when applying ideas of shadowed sets to a family of nonempty fuzzy sets the result is a three way approximation of the family that is a family of shadowed sets this enables us to study a new type of three way fuzzy partitions we introduce and examine three pairs of properties for defining a three way fuzzy partition disjointness property overlap property and coverage property of cores and supports we propose a general definition of a three way fuzzy partition by using two sets of properties by considering all possible non equivalent subsets of properties we obtain 21 classes of three way fuzzy partition we study three classes of three way fuzzy partition and establish their connections to partitions fuzzy partitions and interval set clusters

application of lie algebras to visual servoing a novel approach to visual servoing is presented which takes advantage of the structure of the lie algebra of affine transformations the aim of this project is to use feedback from a visual sensor to guide a robot arm to a target position the target position is learned using the principle of teaching by showing in which the supervisor places the robot in the correct target position and the system captures the necessary information to be able to return to that position the sensor is placed in the end effector of the robot the camera in hand approach and thus provides direct feedback of the robot motion relative to the target scene via observed transformations of the scene these scene transformations are obtained by measuring the affine deformations of a target planar contour under the weak perspective assumption captured by use of an active contour or snake deformations of the snake are constrained using the lie groups of affine and projective transformations properties of the lie algebra of affine transformations are exploited to provide a novel method for integrating observed deformations of the target contour these can be compensated with appropriate robot motion using a non linear control structure the local differential representation of contour deformations is extended to allow accurate integration of an extended series of small perturbations this differs from existing approaches by virtue of the properties of the lie algebra representation which implicitly embeds knowledge of the three dimensional world within a two dimensional image based system these techniques have been implemented using a video camera to control a 5 dof robot arm experiments with this implementation are presented together with a discussion of the results

blended deformable models this paper develops a new class of parameterized models based on the linear interpolation of two parameterized shapes along their main axes using a blending function this blending function specifies the relative contribution of each component shape on the resulting blended shape the resulting blended shape can have aspects of each of the component shapes using a small number of additional parameters blending extends the coverage of shape primitives while also providing abstraction of shape in particular it offers the ability to construct shapes whose genus can change blended models are incorporated into a physics based shape estimation framework which uses dynamic deformable models finally we present experiments involving the extraction of complex shapes from range data including examples of dynamic genus change

3 d shape recovery using distributed aspect matching an approach to the recovery of 3 d volumetric primitives from a single 2 d image is presented the approach first takes a set of 3 d volumetric modeling primitives and generates a hierarchical aspect representation based on the projected surfaces of the primitives conditional probabilities capture the ambiguity of mappings between levels of the hierarchy from a region segmentation of the input image the authors present a formulation of the recovery problem based on the grouping of the regions into aspects no domain independent heuristics are used only the probabilities inherent in the aspect hierarchy are exploited once the aspects are recovered the aspect hierarchy is used to infer a set of volumetric primitives and their connectivity as a front end to an object recognition system the approach provides the indexing power of complex 3 d object centered primitives while exploiting the convenience of 2 d viewer centered aspect matching aspects are used to represent a finite vocabulary of 3 d parts from which objects can be constructed

rigidity checking of 3d point correspondences under perspective projection an algorithm is described which rapidly verifies the potential rigidity of three dimensional point correspondences from a pair of two dimensional views under perspective projection the output of the algorithm is a simple yes or no answer to the question could these corresponding points from two views be the projection of a rigid configuration potential applications include 3d object recognition from a single previous view and correspondence matching for stereo or motion over widely separated views the rigidity checking problem is different from the structure from motion problem because it is often the case that two views cannot provide an accurate structure from motion estimate due to ambiguity and ill conditioning whereas it is still possible to give an accurate yes no answer to the rigidity question rigidity checking verifies point correspondences using 3d recovery equations as a matching condition the proposed algorithm improves upon other methods that fall under this approach because it works with as few as six corresponding points under full perspective projection handles correspondences from widely separated views makes full use of the disparity of the correspondences and is integrated with a linear algorithm for 3d recovery due to kontsevich 1993 results are given for experiments with synthetic and real image data a complete implementation of this algorithm is being made publicly available

recovery of nonrigid motion and structure the authors introduce a physically correct model of elastic nonrigid motion this model is based on the finite element method but decouples the degrees of freedom by breaking down object motion into rigid and nonrigid vibration or deformation modes the result is an accurate representation for both rigid and nonrigid motion that has greatly reduced dimensionality capturing the intuition that nonrigid motion is normally coherent and not chaotic because of the small number of parameters involved this representation is used to obtain accurate overstrained estimates of both rigid and nonrigid global motion it is also shown that these estimates can be integrated over time by use of an extended kalman filter resulting in stable and accurate estimates of both three dimensional shape and three dimensional velocity the formulation is then extended to include constrained nonrigid motion examples of tracking single nonrigid objects and multiple constrained objects are presented

validity index for crisp and fuzzy clusters abstract in this article a cluster validity index and its fuzzification is described which can provide a measure of goodness of clustering on different partitions of a data set the maximum value of this index called the pbm index across the hierarchy provides the best partitioning the index is defined as a product of three factors maximization of which ensures the formation of a small number of compact clusters with large separation between at least two clusters we have used both the k means and the expectation maximization algorithms as underlying crisp clustering techniques for fuzzy clustering we have utilized the well known fuzzy c means algorithm results demonstrating the superiority of the pbm index in appropriately determining the number of clusters as compared to three other well known measures the davies bouldin index dunn s index and the xie beni index are provided for several artificial and real life data sets

a general model of decision theoretic three way approximations of fuzzy sets based on a heuristic algorithm abstract a model of decision theoretic three way approximations of fuzzy sets that can calculate a pair of interpretable thresholds by combining shadowed sets with three way decisions was established by deng in that model the significant contribution is that the value 0 5 which denotes a membership grade with the highest uncertainty is used to replace the uncertain region with the interval 0 1 in shadowed sets from the principle of the minimum decision cost although the lowest overall cost can be achieved precisely in some data distributions based on the value 0 5 there is a difference between the obtained overall cost and the least cost in some cases therefore in this paper based on deng s model the concept of a general three way approximation of a fuzzy set is proposed to replace 0 5 with a variable value c 0

building roadmaps of minima and transitions in visual models becoming trapped in suboptimal local minima is a perennial problem when optimizing visual models particularly in applications like monocular human body tracking where complicated parametric models are repeatedly fitted to ambiguous image measurements we show that trapping can be significantly reduced by building roadmaps of nearby minima linked by transition pathways paths leading over low mountain passes in the cost surface found by locating the transition state codimension 1 saddle point at the top of the pass and then sliding downhill to the next minimum we present two families of transition state finding algorithms based on local optimization in eigenvector tracking unconstrained newton minimization is modified to climb uphill towards a transition state while in hypersurface sweeping a moving hypersurface is swept through the space and moving local minima within it are tracked using a constrained newton method these widely applicable numerical methods which appear not to be known in vision and optimization generalize methods from computational chemistry where finding transition states is critical for predicting reaction parameters experiments on the challenging problem of estimating 3d human pose from monocular images show that our algorithms find nearby transition states and minima very efficiently but also underline the disturbingly large numbers of minima that can exist in this and similar model based vision problems

algebraic functions for recognition in the general case a trilinear relationship between three perspective views is shown to exist the trilinearity result is shown to be of much practical use in visual recognition by alignment yielding a direct reprojection method that cuts through the computations of camera transformation scene structure and epipolar geometry moreover the direct method is linear and sets a new lower theoretical bound on the minimal number of points that are required for a linear solution for the task of reprojection the proof of the central result may be of further interest as it demonstrates certain regularities across homographics of the plane and introduces new view invariants experiments on simulated and real image data were conducted including a comparative analysis with epipolar intersection and the linear combination methods with results indicating a greater degree of robustness in practice and a higher level of performance in reprojection tasks

fuzzy entropy a more comprehensible perspective for interval shadowed sets of fuzzy sets shadowed sets proposed by pedrycz provide a three way approximation scheme for transforming the universe of a fuzzy set into three disjoint areas i e elevated area reduced area and shadow area to calculate a pair of decision making thresholds an analytic method was proposed by solving a minimization problem of the uncertainty arising from the three areas however some uncertainty will be lost in the process of constructing the shadowed set model using pedrycz s method moreover few references on how to measure the uncertainty of shadow sets exist in this article a comprehensible method for measuring the fuzzy entropy of a shadowed set i e interval fuzzy entropy is defined based on the interval fuzzy entropy a new shadowed set model namely interval shadowed sets is proposed compared with pedrycz s model the main difference is that the range of the shadow area in this model is beta alpha 0 leq beta while not 0 1 by solving a fuzzy entropy loss minimization problem a pair of optimal thresholds alpha and beta can be obtained finally the results of the instance analysis of different types of representative membership functions and many experiments show that the fuzzy entropy loss of the interval shadowed set is lower than that of the traditional shadowed set of a fuzzy set these results enrich shadowed set theory from a new perspective

an entropy based uncertainty measurement approach in neighborhood systems abstract uncertainty measures can provide us with principled methodologies to analyze uncertain data and unveil the substantive characteristics of the data sets accuracy and roughness proposed by pawlak are two main tools to deal with uncertainty measurement issue in rough set theory many uncertainty measure methodologies for discrete valued information systems or discrete valued decision systems have been developed however there are only limited on the uncertainty measurement for neighborhood systems in this paper we address the issues of uncertainty of a neighborhood system and extend the traditional accuracy and roughness measures to deal with neighborhood systems in particular a concept called neighborhood entropy is first introduced to evaluate the uncertainty of a neighborhood information system consequently the entropy based roughness and approximation roughness measures of neighborhood system are presented theoretical analysis indicates that entropy based measures can be used to evaluate the uncertainty in neighborhood systems experiments are conducted on artificial data sets and standard uci data sets to test our proposed methodologies results demonstrate that the entropy based measures are effective and valid for evaluating the uncertainty of neighborhood systems

shadowed sets in the characterization of rough fuzzy clustering in this study we develop a technique of an automatic selection of a threshold parameter which determines approximation regions in rough set based clustering the proposed approach exploits a concept of shadowed sets all patterns data to be clustered are placed into three categories assuming a certain perspective established by an optimization process as a result a lack of knowledge about global relationships among objects caused by the individual absolute distance in rough c means clustering or individual membership degree in rough fuzzy c means clustering can be circumvented subsequently relative approximation regions of each cluster are detected and described by integrating several technologies of granular computing including fuzzy sets rough sets and shadowed sets we show that the resulting characterization leads to an efficient description of information granules obtained through the process of clustering including their overlap regions outliers and boundary regions comparative experimental results reported for synthetic and real world data illustrate the essence of the proposed idea

shape and motion from image streams under orthography a factorization method inferring scene geometry and camera motion from a stream of images is possible in principle but is an ill conditioned problem when the objects are distant with respect to their size we have developed a factorization method that can overcome this difficulty by recovering shape and motion under orthography without computing depth as an intermediate step an image stream can be represented by the 2fxp measurement matrix of the image coordinates of p points tracked through f frames we show that under orthographic projection this matrix is of rank 3 based on this observation the factorization method uses the singular value decomposition technique to factor the measurement matrix into two matrices which represent object shape and camera rotation respectively two of the three translation components are computed in a preprocessing stage the method can also handle and obtain a full solution from a partially filled in measurement matrix that may result from occlusions or tracking failures the method gives accurate results and does not introduce smoothing in either shape or motion we demonstrate this with a series of experiments on laboratory and outdoor image streams with and without occlusions

decision theoretic three way approximations of fuzzy sets abstract a three way three valued or three region approximation of a fuzzy set is constructed from a pair of thresholds on the fuzzy membership function an element whose membership grade equals to or is greater than is put into the positive region an element whose membership grade equals to or is less than is put into the negative region and an element whose membership grade is between and is put into the boundary region a fundamental issue is the determination and interpretation of the required pair of thresholds in the framework of shadowed sets i e an example of three way approximations of fuzzy sets pedrycz provides an analytic solution to computing the thresholds by searching for a balance of uncertainty introduced by the three regions to gain further insights into three way approximations of fuzzy sets we introduce an alternative decision theoretic formulation in which the required thresholds are computed by minimizing decision cost

motion of points and lines in the uncalibrated case in the present paper we address the problem of computing structure and motion given a set point and or line correspondences in a monocular image sequence when the camera is not calibrated

recovery of parametric models from range images the case for superquadrics with global deformations a method for recovery of compact volumetric models for shape representation of single part objects in computer vision is introduced the models are superquadrics with parametric deformations bending tapering and cavity deformation the input for the model recovery is three dimensional range points model recovery is formulated as a least squares minimization of a cost function for all range points belonging to a single part during an iterative gradient descent minimization process all model parameters are adjusted simultaneously recovery position orientation size and shape of the model such that most of the given range points lie close to the model s surface a specific solution among several acceptable solutions where are all minima in the parameter space can be reached by constraining the search to a part of the parameter space the many shallow local minima in the parameter space are avoided as a solution by using a stochastic technique during minimization results using real range data show that the recovered models are stable and that the recovery procedure is fast

a clustering procedure for exploratory mining of vector time series a two step procedure is developed for the exploratory mining of real valued vector multivariate time series using partition based clustering methods the proposed procedure was tested with model generated data multiple sensor based process data as well as simulation data the test results indicate that the proposed procedure is quite effective in producing better clustering results than a hidden markov model hmm based clustering method if there is a priori knowledge about the number of clusters in the data two existing validity indices were tested and found ineffective in determining the actual number of clusters determining the appropriate number of clusters in the case that there is no a priori knowledge is a known unresolved research issue not only for our proposed procedure but also for the hmm based clustering method and further development is necessary

rudiments of rough sets abstract worldwide there has been a rapid growth in interest in rough set theory and its applications in recent years evidence of this can be found in the increasing number of high quality articles on rough sets and related topics that have been published in a variety of international journals symposia workshops and international conferences in recent years in addition many international workshops and conferences have included special sessions on the theory and applications of rough sets in their programs rough set theory has led to many interesting applications and extensions it seems that the rough set approach is fundamentally important in artificial intelligence and cognitive sciences especially in research areas such as machine learning intelligent systems inductive reasoning pattern recognition mereology knowledge discovery decision analysis and expert systems in the article we present the basic concepts of rough set theory and point out some rough set based research directions and applications

a multi frame approach to visual motion perception one of the main issues in the area of motion estimation given the correspondences of some features in a sequence of images is sensitivity to error in the input the main way to attack the problem as with several other problems in science and engineering is redundancy in the data up to now all the algorithms developed either used two frames or depended on assumptions about the motion or the shape of the scene we present in this paper an algorithm based on multiple frames that employs only the rigidity assumption is simple and mathematically elegant and experimentally proves to be a major improvement over the two frame algorithms the algorithm does minimization of the squared error which we prove equivalent to an eigenvalue minimization problem one of the side effects of this mean square method is that the algorithm can have a very descriptive physical interpretation in terms of the loaded spring model

principles for constructing three way approximations of fuzzy sets a comparative evaluation based on unsupervised learning abstract three way approximations of fuzzy sets are an important scheme of granular computing by abstracting a fuzzy set to its discrete three option alternatives which adhere to human cognitive behaviors and reduce the computational burden the key point of such three way approximations of fuzzy sets is how to choose a suitable design leading to their realization undesired three way approximations might be produced if the selected mechanism is unsuitable to data distribution in this study the principles for constructing three way approximations of fuzzy sets are summarized the following taxonomy of these principles is provided namely i uncertainty balance based principle ii prototype based principle and iii model based invoking the tradeoff between classification error and the number of data that have to be classified a number of detailed optimization models are discussed in detail to evaluate the performance of different construction principles a general unsupervised learning framework based on three way approximations of fuzzy sets is exhibited some synthetic data sets along with sixteen data sets from uci repository are involved for experiments friedman testing followed by holm bonferroni testing are exploited to test the performance significance of the proposed criteria which can provide insights and deliver guidance when choosing a principle for constructing three way approximations of fuzzy sets in the real world scenarios the research methods in this paper can also be extended to supervised and semi supervised learning areas

incremental model based estimation using geometric constraints we present a model based framework for incremental adaptive object shape estimation and tracking in monocular image sequences parametric structure and motion estimation methods usually assume a fixed class of shape representation splines deformable superquadrics etc that is initialized prior to tracking since the model shape coverage is fixed a priori the incremental recovery of structure is decoupled from tracking thereby limiting both processes in their scope and robustness in this work we describe a model based framework that supports the automatic detection and integration of low level geometric primitives lines incrementally such primitives are not explicitly captured in the initial model but are moving consistently with its image motion the consistency tests used to identify new structure are based on trinocular constraints between geometric primitives the method allows not only an increase in the model scope but also improves tracking accuracy by including the newly recovered features in its state estimation the formulation is a step toward automatic model building since it allows both weaker assumptions on the availability of a prior shape representation and on the number of features that would otherwise be necessary for entirely bottom up reconstruction we demonstrate the proposed approach on two separate image based tracking domains each involving complex 3d object structure and motion

asymptotic stability of thermoelastic systems of bresse type abstract we provide a comprehensive stability analysis of the thermoelastic bresse system also known as the circular arch problem in particular assuming a temperature evolution of gurtin pipkin type we establish a necessary and sufficient condition for exponential stability in terms of the structural parameters of the problem as a byproduct a complete characterization of the longtime behavior of bresse type systems with fourier maxwell cattaneo and coleman gurtin thermal laws is obtained our main theorem also subsumes some recent achievements in the stability properties of thermoelastic timoshenko systems with classical and nonclassical heat conduction

asymptotic stability for bresse systems abstract in this paper consider a vibrating system of bresse type in a one dimensional bounded domain with a nonlinear damping acting in the equation of the shear angle displacement and nonlinear localized damping in other equations we show the asymptotic stability without imposing conditions about the equal speed wave propagation using a method developed by lasiecka and tataru 9