on the sequential accumulation of evidence in this paper we introduce a method for sequentially accumulating evidence as it pertains to an active observer seeking to identify an object in a known environment we develop a probabilistic framework based on a generalized inverse theory where assertions are represented by conditional probability density functions this leads to a sequential recognition strategy in which evidence is accumulated over successive viewpoints using bayesian chaining until a definitive assertion can be made to illustrate the theory we show how the characteristics of belief distributions can be exploited in a model based recognition problem where the task is to identify an unknown model from a database of known objects on the basis of parameter estimates we illustrate the robustness of the algorithm through recognition experiments in two very different contexts 1 a highly structured recognition context where 3 d parametric models can be estimated directly from range data 2 a complex environment where the relationship between the data and the model is learned through an appearance based strategy specifically the flow fields computed through the object s motion are used as structural signatures for recognition

on correlations of cm type maass waveforms under the horocyclic flow maass waveforms of cm type are a special kind of eigenfunction of the hyperbolic laplacian whose defining components namely eigenvalue and fourier coefficients are given by simple formulae involving algebraic integers chosen from a suitable number field k in this paper we report on some computer experiments aimed at ascertaining the extent to which the autocorrelation behaviour of cm forms agrees with that of mock i e random waveforms in the limit of high energy our results suggest that no significant differences are seen

the determination of implicit polynomial canonical curves a new method is presented for identifying and comparing closed bounded free form curves that are defined by even implicit polynomial ip equations in the x y cartesian coordinates the method provides a new expression for an ip involving a product of conic factors with unique conic factor centers the critical points for an ip curve are also defined the conic factor centers and the critical points are shown to be useful related points that directly map to one another under affine transformations in particular the explicit determination of such points implies both a canonical form for the curves and the transformation matrix which relates affine equivalent curves

rate of quantum ergodicity in euclidean billiards for a large class of quantized ergodic flows the quantum ergodicity theorem states that almost all eigenfunctions become equidistributed in the semiclassical limit in this work we give a short introduction to the formulation of the quantum ergodicity theorem for general observables in terms of pseudodifferential operators and show that it is equivalent to the semiclassical eigenfunction hypothesis for the wigner function in the case of ergodic systems of great importance is the rate by which the quantum mechanical expectation values of an observable tend to their mean value this is studied numerically for three euclidean billiards stadium cosine and cardioid billiard using up to 6000 eigenfunctions we find that in configuration space the rate of quantum ergodicity is strongly influenced by localized eigenfunctions such as bouncing ball modes or scarred eigenfunctions we give a detailed discussion and explanation of these effects using a simple but powerful model for the rate of quantum ergodicity in momentum space we observe a slower decay we also study the suitably normalized fluctuations of the expectation values around their mean and find good agreement with a gaussian distribution

can billiard eigenstates be approximated by superpositions of plane waves the plane wave decomposition method pwdm is one of the most popular strategies for numerical solution of the quantum billiard problem the method is based on the assumption that each eigenstate in a billiard can be approximated by a superposition of plane waves at a given energy from the classical results on the theory of differential operators this can indeed be justified for billiards in convex domains in contrast in the present work we demonstrate that eigenstates of non convex billiards in general cannot be approximated by any solution of the helmholtz equation regular everywhere in r2 in particular by linear combinations of a finite number of plane waves having the same energy from this we infer that pwdm cannot be applied to billiards in non convex domains furthermore it follows from our results that unlike the properties of integrable billiards where each eigenstate can be extended into the billiard exterior as a regular solution of the helmholtz equation the eigenstates of non convex billiards in general do not admit such an extension

poincare husimi representation of eigenstates in quantum billiards for the representation of eigenstates on a poincare section at the boundary of a billiard different variants have been proposed we compare these poincare husimi functions discuss their properties and based on this select one particularly suited definition for the mean behavior of these poincare husimi functions an asymptotic expression is derived including a uniform approximation we establish the relation between the poincare husimi functions and the husimi function in phase space from which a direct physical interpretation follows using this a quantum ergodicity theorem for the poincare husimi functions in the case of ergodic systems is shown

strong stochastic bounds for the stationary distribution of a class of multicomponent performability models we consider a class of models for multicomponent systems in which components can break down and be repaired in a dependent manner and where breakdown and repair times can be arbitrarily distributed the problem of calculating the equilibrium distribution and from this the expected performability for these models is intractable unless certain assumptions are made about breakdowns and repairs in this paper we show that the performability of multicomponent systems that do not satisfy these rules can be bounded by tractable modifications our results are proved by stochastic comparability arguments and a markov reward technique which is of interest in itself as it enables one to prove that the equilibrium distribution of one process can be bounded by that of another even when the sample paths of the process are not this is illustrated by an example

an adaptive and stable method for fitting implicit polynomial curves and surfaces representing 2d and 3d data sets with implicit polynomials ips has been attractive because of its applicability to various computer vision issues therefore many ip fitting methods have already been proposed however the existing fitting methods can be and need to be improved with respect to computational cost for deciding on the appropriate degree of the ip representation and to fitting accuracy while still maintaining the stability of the fit we propose a stable method for accurate fitting that automatically determines the moderate degree required our method increases the degree of ip until a satisfactory fitting result is obtained the incrementability of qr decomposition with gram schmidt orthogonalization gives our method computational efficiency furthermore since the decomposition detects the instability element precisely our method can selectively apply ridge regression based constraints to that element only as a result our method achieves computational stability while maintaining fitting accuracy experimental results demonstrate the effectiveness of our method compared with prior methods

motion recovery by integrating over the joint image manifold recovery of epipolar geometry is a fundamental problem in computer vision the introduction of the joint image manifold jim allows to treat the recovery of camera motion and epipolar geometry as the problem of fitting a manifold to the data measured in a stereo pair the manifold has a singularity and boundary therefore special care must be taken when fitting it four fitting methods are discussed direct algebraic geometric and the integrated maximum likelihood iml based method the first three methods are the exact analogues of three common methods for recovering epipolar geometry the more recently introduced iml method seeks the manifold which has the highest support in the sense that the largest measure of its points are close to the data while computationally more intensive than the other methods its results are better in some scenarios both simulations and experiments suggest that the advantages of iml manifold fitting carry over to the task of recovering epipolar geometry especially when the extent of the data and or the motion are small

separating the regular and irregular energy levels and their statistics in a hamiltonian system with mixed classical dynamics we look at the high lying eigenstates from the 10001 to the 13000 in the robnik billiard defined as a quadratic conformal map of the unit disk with the shape parameter lambda 0 15 all the 3000 eigenstates have been numerically calculated and examined in the configuration space and in the phase space which in comparison with the classical phase space enabled a clear cut classification of energy levels into regular and irregular this is the first successful separation of energy levels based on purely dynamical rather than special geometrical symmetry properties we calculate the fractional measure of regular levels as rho 1 0 365 or 0 01 which is in remarkable agreement with the classical estimate rho 1 0 360 or 0 001 this finding confirms the percival s 1973 classification scheme the assumption in berry robnik 1984 theory and the rigorous result by lazutkin 1981 1991 the regular levels obey the poissonian statistics quite well whereas the irregular sequence exhibits the fractional power law level repulsion and globally brody like statistics with beta 0 286 or 0 001 this is due to the strong localization of irregular eigenstates in the classically chaotic regions therefore in the entire spectrum we see that the berry robnik regime is not yet fully established so that the level spacing distribution is correctly captured by the berry robnik brody distribution

ergodicity of eigenfunctions for ergodic billiards we give a simple proof of ergodicity of eigenfunctions of the laplacian with dirichlet boundary conditions on compact riemannian manifolds with piecewise smooth boundaries and ergodic billiards examples include the bunimovich stadium the sinai billiard and the generic polygonal billiard tables of kerckhoff masur and smillie

closed form line segment extraction using the hough transform this paper proposes a novel closed form solution to complete line segment extraction given a voting angle in image space the voting distribution is analyzed and two functional relationships are deduced regarding the corresponding column in hough space voting along the distance axis is considered as being a random variable and voting values in cells are considered as forming a probability distribution statistical characteristics of this distribution are used to fit a quadratic polynomial curve and a linear curve direction length and width of a line segment are simultaneously computed in a closed form based on coefficients of fitted quadratic polynomial curves the midpoint of a line segment is determined based on the fitted linear curve the method is tested on simulated and real world images results show that the proposed closed form solution is feasible in the presence of quantization errors or image noise highlightswe proposed a method for obtaining the complete set of line segment parameters the direction length and width of a line segment are extracted simul taneously in a closed form we provided a complete theoretical derivation of voting variance with respect to voting angle the midpoint of a line segment is determined by the coefficients of the fitted linear curve parallel crossing and aligned line segments are discussed by analysing events in image space and hough space

classical dynamics of a family of billiards with analytic boundaries the classical dynamics of a billiard which is a quadratic conformal image of the unit disc is investigated the author gives the stability analysis of major periodic orbits present the poincare maps demonstrate the mixing properties by following the evolution of a small element in phase space show the existence of homoclinic points and calculate the lyapunov exponent and the kolmogorov entropy h it turns out that the system becomes strongly chaotic positive h for sufficiently large deformations of the unit disc the system shows a generic stochastic transition the computations suggest that the system is mixing if the boundary is not convex

poisson arrivals see time averages in many stochastic models particularly in queueing theory poisson arrivals both observe see a stochastic process and interact with it in particular cases and or under restrictive assumptions it has been shown that the fraction of arrivals that see the process in some state is equal to the fraction of time the process is in that state in this paper we present a proof of this result under one basic assumption the process being observed cannot anticipate the future jumps of the poisson process

line fitting in a noisy image the conventional least squared distance method of fitting a line to a set of data points is unreliable when the amount of random noise in the input such as an image is significant compared with the amount of data correlated to the line itself points which are far away from the line outliers are usually just noise but they contribute the most to the distance averaging skewing the line from its correct position the author presents a statistical method of separating the data of interest from random noise using a maximum likelihood principle

a nonparametric method for fitting a straight line to a noisy image in fitting a straight line to a noisy image the least squares method becomes highly unreliable either when the noise distribution is nonnormal or when it is contaminated by outliers the authors propose a nonparametric method the median of the intercepts to overcome these difficulties this method is free of assumptions about the noise distribution and insensitive to outliers and it does not require quantization of the parameter space thus unlike the hough transform its outcome does not depend on the bin size the method is efficient and its implementation does not involve practical difficulties such as local minima or poor convergence of iterative procedures

quantitative study of scars in the boundary section of the stadium billiard we construct a semiclassically invariant function on the boundary of the billiard taken as the poincare section in birkhoff coordinates based on periodic orbit information as an ansatz for the normal derivative of the eigenfunction defining an appropriate scalar product on the section we can compute the scar intensity of a given periodic orbit on an eigensate as the overlap beetween the constructed function and the normal derivative on the section of the eigenstate in this way we are able to investigate how periodic orbits scar the spectrum and how a given eigenstate decompose into scar functions we use this scheme on the bunimovich stadium

comments on robust line fitting in a noisy image by the method of moments qjidaa and radouane 1999 presented a method for robust line fitting and experimentally compared it to other methods including a method suggested by us the results attributed by qjidaa and radouane to our algorithm are incorrect we apply our algorithm to the data used by qjidaa and radouane and demonstrate its robustness and accuracy

survey of the eigenfunctions of a billiard system between integrability and chaos we study numerically the eigenfunctions and their wigner phase space distributions of the two dimensional billiard system defined by the quadratic conformal image of the unit disk as introduced by robnik 1983 this system is a generic kam system and displays a transition from integrability to almost ergodicity as the billiard shape changes we clearly identify two classes of states the regular ones associated with integrable regions and the irregular states supported on classically chaotic regions whilst the mixed type states were not found in support of percival s conjecture 1973 we confirm the existence of extremely intense scars in the classically chaotic regions and demonstrate their association with classical periodic orbits three classes of scars are revealed one orbit scars many orbit one family scars of statistically similar orbits in the homoclinic neighbourhood and many orbit many family scars we argue that it is impossible to find an a priori semiclassical theory of individual eigenstates but do not deny the usefulness of general semiclassical arguments in analysing the collective and statistical properties of eigenstates

maximum norms of chaotic quantum eigenstates and random waves abstract the growth of the maximum norms of quantum eigenstates of classically chaotic systems with increasing energy is investigated the maximum norms provide a measure for localization effects in eigenfunctions an upper bound for the maxima of random superpositions of random functions is derived for the random wave model this gives the bound c ln e in the semiclassical limit e the growth of the maximum norms of random waves is compared with the growth of the maximum norms of the eigenstates of six quantum billiards which are classically chaotic the maximum norms of these systems are numerically shown to be conform with the random wave model furthermore the distribution of the locations of the maximum norms is discussed

on three dimensional surface reconstruction methods a survey is presented of some of the surface reconstruction methods that can be found in the literature the focus is on a small recent and important subset of the published reconstruction techniques the techniques are classified based on the surface representation used implicit versus explicit functions a study is made of the important aspects of the surface reconstruction techniques one aspect is the viewpoint invariance of the methods this is an important property if object recognition is the ultimate objective the robustness of the various methods is examined it is determined whether the parameter estimates are biased and the sensitivity to obscuration is addressed the latter two aspects are particularly important for fitting functions in the implicit form a detailed description is given of a parametric reconstruction method for three dimensional object surfaces that involves numeric grid generation techniques and variational principle formulations this technique is invariant to rigid motion in dimensional space

amplitude distribution of eigenfunctions in mixed systems we study the amplitude distribution of irregular eigenfunctions in systems with mixed classical phase space for an appropriately restricted random wave model a theoretical prediction for the amplitude distribution is derived and a good agreement with numerical computations for the family of limacon billiards is found the natural extension of our result to more general systems e g with a potential is also discussed

statistical properties of eigenstate amplitudes in complex quantum systems we study the eigenstates of quantum systems with large hilbert spaces via their distribution of wave function amplitudes in a real space basis for single particle quantum billiards these real space amplitudes are known to have gaussian distribution for chaotic systems in this work we formulate and address the corresponding question for many body lattice quantum systems for integrable many body systems we examine the deviation from gaussianity and provide evidence that the distribution generically tends toward power law behavior in the limit of large sizes we relate the deviation from gaussianity to the entanglement content of many body eigenstates for integrable billiards we find several cases where the distribution has power law tails

probabilistic models of database locking solutions computational algorithms and asymptotics modelisation de l effet des conflits sur les transactions dans une base de donnees et on obtient des formules exactes pour les mesures de performances a l equilibre et des algorithmes efficaces pour leur calcul

three dimensional object representation and invariant recognition using continuous distance transform neural networks 3d object recognition under partial object viewing is a difficult pattern recognition task in this paper we introduce a neural network solution that is robust to partial viewing of objects and noise corruption this method directly utilizes the acquired 3d data and requires no feature extraction the object is first parametrically represented by a continuous distance transform neural network cdtnn trained by the surface points of the exemplar object the cdtnn maps any 3d coordinate into a value that corresponds to the distance between the point and the nearest surface point of the object therefore a mismatch between the exemplar object and an unknown object can be easily computed when encountered with deformed objects this mismatch information can be backpropagated through the cdtnn to iteratively determine the deformation in terms of affine transform application to 3d heart contour delineation and invariant recognition of 3d rigid body objects is presented

a simple method for fitting of bounding rectangle to closed regions in this paper we introduce a new approach for fitting of a bounding rectangle to closed regions in this approach the coordinates of the vertices are computed directly using a closed form solution this approach is based on simple coordinate geometry and uses the boundary points of regions using a least square approach we determine the directions of major and minor axes of the object which gives the orientation of the object the four vertexes of the bounding rectangle are computed by pair wise solving the four straight lines examples from synthetic data and some real life data show that the approach is both accurate and efficient

the hough transform estimator this paper pursues a statistical study of the hough transform the celebrated computer vision algorithm used to detect the presence of lines in a noisy image we first study asymptotic properties of the hough transform estimator whose objective is to find the line that best fits a set of planar points in particular we establish strong consistency rates of convergence and characterize the limiting distribution of the hough transform estimator while the convergence rates are seen to be slower than those found in some standard regression methods the hough transform estimator is shown to be more robust as measured by its breakdown point we next study the hough transform in the context of the problem of detecting multiple lines this is addressed via the framework of excess mass functionals and modality testing throughout several numerical examples help illustrate various properties of the estimator relations between the hough transform and more mainstream statistical paradigms and methods are discussed as well short title the hough transform estimator

invariant matching and identification of curves using b splines curve representation there have been many techniques for curve shape representation and analysis ranging from fourier descriptors to moments to implicit polynomials to differential geometry features to time series models to b splines etc the b splines stand as one of the most efficient curve surface representations and possess very attractive properties such as spatial uniqueness boundedness and continuity local shape controllability and invariance to affine transformations these properties made them very attractive for curve representation and consequently they have been extensively used in computer aided design and computer graphics very little work however has been devoted to them for recognition purposes one possible reason might be due to the fact that the b spline curve is not uniquely described by a single set of parameters control points which made the curve matching recognition process difficult when comparing the respective parameters of the curves to be matched this paper is an attempt to find matching solutions despite this limitation and as such it deals the problem of using b splines for shape recognition and identification from curves with an emphasis on the following applications affine invariant matching and classification of 2 d curves with applications in identification of aircraft types based on image silhouettes and writer identification based on handwritten text

quantising a generic family of billiards with analytic boundaries a generic family of plane billiards has been discovered recently the shape of the boundary is given by the quadratic conformal image of the unit circle and is thus real analytic for small deformations of the unit disc the billiard is a typical kam system but becomes ergodic or even mixing when the curvature of the boundary vanishes at some point the kolmogorov entropy has been calculated and it increases with the deformation of the boundary the author studies aspects of the quantum chaos for this billiard he solves numerically the eigenvalue problem for the laplace operator with dirichlet s boundary condition he examines the spectrum and inspects the avoided crossings at which mixing of nearby states occurs the variation of the nodal structure and of the localisation properties of the eigenfunctions is studied in analysing the level spacing distribution he finds a continuous transition from the poisson distribution towards the wigner distribution the exponent in the level repulsion law varies continuously along with a generic perturbation for small perturbations it seems to be proportional to the square root of the perturbation parameter

on recognizing and positioning curved 3 d objects from image contours an approach for explicitly relating the shape of image contours to models of curved three dimensional objects is presented this relationship is used for object recognition and positioning object models consist of collections of parametric surface patches and their intersection curves this includes nearly all representations used in computer aided geometric design and computer vision the image contours considered are the projections of surface discontinuities and occluding contours elimination theory provides a method for constructing the implicit equation of these contours for an object observed under orthographic or perspective projection this equation is parameterized by the object s position and orientation with respect to the observer determining these parameters is reduced to a fitting problem between the theoretical contour and the observed data points the proposed approach readily extends to parameterized models it has been implemented for a simple world composed of various surfaces of revolution and tested on several real images

robust line estimation with errors in both variables abstract the estimator holding the central place in the theory of the multivariate errors in the variables ev model results from performing orthogonal regression on variables rescaled according to the covariance matrix of the errors our simulations on the univariate model essentially relegate this estimator to use only in large samples on data with no trace of outlier contamination a modification requiring a robust preliminary slope is proposed that essentially sets out the generalization to ev of the robust w estimator in regression it is demonstrated that the modification is robust to outlier contamination even in small samples given a sufficiently good preliminary estimator candidates for a preliminary slope estimator based on the data are discussed and the performance of one under simulation is examined

monotonicity in generalized semi markov processes we establish stochastic monotonicity of the event epoch sequences of generalized semi markov processes through the structure of the generalized semi markov schemes on which they are based our main condition states roughly that the occurrence of more events in the short run never leads to the activation of less events in the long run we consider monotonicity with respect to two types of inputs clock times which translate to e g service and interarrival times in queueing systems and structural parameters which translate to e g buffer size number of servers and job population for the second type of comparison we replace a structural change with an equivalent change in clock times to reduce the comparison to one of the first type when applied to queueing systems our results yield new comparisons and also unify several existing results previously established using special properties of individual systems

bayesian recognition of local 3 d shape by approximating image intensity functions with quadric polynomials the recognition in image data of viewed patches of spheres cylinders and planes in the 3 d world is discussed as a first step to complex object recognition or complex object location and orientation estimation accordingly an image is partitioned into small square windows each of which is a view of a piece of a sphere or of a cylinder or of a plane windows are processed in parallel for recognition of content new concepts and techniques include approximations of the image within a window by 2 d quadric polynomials where each approximation is constrained by one of the hypotheses that the 3 d surface shape seen is either planar cylindrical or spherical a recognizer based upon these approximations to determine whether the object patch viewed is a piece of a sphere or a piece of a cylinder or a piece of a plane lowpass filtering of the image by the approximation the shape recognition is computationally simple and for large windows is approximately bayesian minimum probability of error recognition these classifications are useful for many purposes one such purpose is to enable a following processor to use an appropriate estimator to estimate shape and orientation and location parameters for the 3 d surface seen within a window

superquadric segmentation in range images via fusion of region and boundary information the high potential of superquadrics as modeling elements for image segmentation tasks has been pointed out for years in the computer vision community in this work we employ superquadrics as modeling elements for multiple object segmentation in range images segmentation is executed in two stages first a hypothesis about the values of the segmentation parameters is generated second the hypothesis is refined locally in both stages object boundary and region information are considered boundary information is derived via model based edge detection in the input range image hypothesis generation uses boundary information to isolate image regions that can be accurately described by superquadrics within hypothesis refinement a game theoretic framework is used to fuse the two information sources by associating an objective function to each information source iterative optimization of the two objective functions in succession outputs a precise description of all image objects we demonstrate experimentally that this approach substantially improves the most established method in superquadric segmentation in terms of accuracy and computational efficiency we demonstrate the applicability of our segmentation framework in real world applications by constructing a novel robotic system for automatic unloading of jumbled box like objects from platforms

robust line fitting in a noisy image by the method of moments the standard least squared distance method of fitting a line to a set of data points is known to be unreliable when the random noise in the input is significant compared with the data correlated to the line itself here we present a new statistical clustering method based on legendre moment theory and maximum entropy principle for line fitting in a noisy image we propose a new approach for estimating the underlying probability density function p d f of the data set the p d f is expanded in terms of legendre polynomials by means of the legendre moments the order of the expansion is selected according to the maximum entropy principle then the points corresponding to the maxima of the p d f will be the true points of the line to be extracted by a chaining algorithm this approach is directly generalized to multidimensional data the proposed algorithm was successfully applied to real and simulated noisy line images with comparison to some well known methods

stochastic comparisons for non markov processes a technique is developed for comparing a non markov process to a markov process on a general state space with many possible stochastic orderings two such comparisons with a common markov process yield a comparison between two non markov processes the technique which is based on stochastic monotonicity of the markov process yields stochastic comparisons of the limiting distributions and the marginal distributions at single time points but not the joint distributions these stochastic comparisons are obtained under the condition that the one step transition probabilities in discrete time or infinitesimal transition rates in continuous time are appropriately ordered uniformly in the extra information needed to add to the state to make the non markov process markov the technique is illustrated by establishing an inequality in traffic theory concerning the blocking in multi server service facilities when each customer requires service from several facilities simultaneously

probabilistic analysis of regularization in order to use interpolated data wisely it is important to have reliability and confidence measures associated with it a method for computing the reliability at each point of any linear functional of a surface reconstructed using regularization is presented the proposed method is to define a probability structure on the class of possible objects and compute the variance of the corresponding random variable this variance is a natural measure for uncertainty and experiments have shown it to correlate well with reality the probability distribution used is based on the boltzmann distribution the theoretical part of the work utilizes tools from classical analysis functional analysis and measure theory on function spaces the theory was tested and applied to real depth images it was also applied to formalize a paradigm of optimal sampling which was successfully tested on real depth images

spatial sparsity induced prediction sip for images and video a simple way to reject structured interference we propose a prediction technique that is geared toward forming successful estimates of a signal based on a correlated anchor signal that is contaminated with complex interference the corruption in the anchor signal involves intensity modulations linear distortions structured interference clutter and noise just to name a few the proposed setup reflects nontrivial prediction scenarios involving images and video frames where statistically related data is rendered ineffective for traditional methods due to cross fades blends clutter brightness variations focus changes and other complex transitions rather than trying to solve a difficult estimation problem involving nonstationary signal statistics we obtain simple predictors in linear transform domain where the underlying signals are assumed to be sparse we show that these simple predictors achieve surprisingly good performance and seamlessly allow successful predictions even under complicated cases none of the interference parameters are estimated as our algorithm provides completely blind and automated operation we provide a general formulation that allows for nonlinearities in the prediction loop and we consider prediction optimal decompositions beyond an extensive set of results on prediction and registration the proposed method is also implemented to operate inside a state of the art compression codec and results show significant improvements on scenes that are difficult to encode using traditional prediction techniques

invariant descriptors for 3d object recognition and pose invariant descriptors are shape descriptors that are unaffected by object pose by perspective projection or by the intrinsic parameters of the camera these descriptors can be constructed using the methods of invariant theory which are briefly surveyed a range of applications of invariant descriptors in 3d model based vision is demonstrated first a model based vision system that recognizes curved plane objects irrespective of their pose is demonstrated curves are not reduced to polyhedral approximations but are handled as objects in their own right models are generated directly from image data once objects have been recognized their pose can be computed invariant descriptors for 3d objects with plane faces are described all these ideas are demonstrated using images of real scenes the stability of a range of invariant descriptors to measurement error is treated in detail

distribution of resonance strengths in microwave billiards of mixed and chaotic dynamics a new measure for statistical properties of the wave function components of quantum systems the distribution of the product of two partial widths is introduced it is tested with data obtained in analog experiments with microwave billiards where the product of two partial widths equals the resonance strengths in the microwave spectra the billiards are from the family of the limacons one with chaotic and two with mixed classical dynamics for completely chaotic systems the partial widths generically obey a porter thomas distribution we show that in this case the distribution of their product equals a k0 distribution while we find deviations of the experimental strength distribution from the k0 distribution for the billiards with mixed dynamics the distributions agree perfectly for the chaotic billiard when taking into account the experimental threshold of detection in the theoretical description hence the strength distribution provides another stringent test for the connection between statistical properties of systems with classical chaotic dynamics and random matrix theory

an analysis of the elastic net approach to the traveling salesman problem this paper analyzes the elastic net approach durbin and willshaw 1987 to the traveling salesman problem of finding the shortest path through a set of cities the elastic net approach jointly minimizes the length of an arbitrary path in the plane and the distance between the path points and the cities the tradeoff between these two requirements is controlled by a scale parameter k a global minimum is found for large k and is then tracked to a small value in this paper we show that 1 in the small k limit the elastic path passes arbitrarily close to all the cities but that only one path point is attracted to each city 2 in the large k limit the net lies at the center of the set of cities and 3 at a critical value of k the energy function bifurcates we also show that this method can be interpreted in terms of extremizing a probability distribution controlled by k the minimum at a given k corresponds to the maximum a posteriori map bayesian estimate of the tour under a natural statistical interpretation the analysis presented in this paper gives us a better understanding of the behavior of the elastic net allows us to better choose the parameters for the optimization and suggests how to extend the underlying ideas to other domains

polynomial regression with errors in the variables a polynomial functional relationship with errors in both variables can be consistently estimated by constructing an ordinary least squares estimator for the regression coefficients assuming hypothetically the latent true regressor variable to be known and then adjusting for the errors if normality of the error variables can be assumed the estimator can be simplified considerably only the variance of the errors in the regressor variable and its covariance with the errors of the response variable need to be known if the variance of the errors in the dependent variable is also known another estimator can be constructed

stochastic convexity and concavity of markov processes in this paper we consider the temporal stochastic convexity and concavity properties of markov processes x t t s in discrete time then s n 0 1 2 or in continuous time then s 0 that is we obtain conditions on the process x t t s which imply that the expectation ef x t is a monotone convex concave function of t whenever f is a monotone convex concave function the theory is illustrated through some examples after giving some background we define monotonicity and then obtain some general results concerning stochastic convexity and concavity of markov processes by using the notion of monotone operators we then introduce a method for identifying monotone operators and we discuss the relationship between our results concerning temporal convexity and other results in the literature in particular we center our attention on a notion of stochastic concavity in this respect we show that a result of shaked and shanthikumar is incorrect and we prove two alternativ

analytic line fitting in the presence of uniform random noise abstract one of the most fundamental tasks in pattern recognition involves fitting a curve such as a line segment to a given set of data points using the conventional ordinary least squares ols method of fitting a line to a set of data points is notoriously unreliable when the data contain points coming from two different populations i randomly distributed points random noise ii points correlated with the line itself e g obtained by perturbing the line with zero mean gaussian noise points which lie far away from the line i e outliers usually belong to the random noise population since they contribute the most to the squared distances they skew the line estimate from its correct position in this paper we present an analytic method of separating the components of the mixture unlike previous methods we derive a closed form solution applying a variant of the method of moments mom to the assumed mixture model yields an analytic estimate of the desired line finally we provide experimental results obtained by our method

bayesian model estimation and selection for epipolar geometry and generic manifold fitting computer vision often involves estimating models from visual input sometimes it is possible to fit several different models or hypotheses to a set of data and a decision must be made as to which is most appropriate this paper explores ways of automating the model selection process with specific emphasis on the least squares problem of fitting manifolds in particular algebraic varieties e g lines algebraic curves planes etc to data points illustrated with respect to epipolar geometry the approach is bayesian and the contribution three fold first a new bayesian description of the problem is laid out that supersedes the author s previous maximum likelihood formulations this formulation will reveal some hidden elements of the problem second an algorithm mapsac is provided to obtain the robust map estimate of an arbitrary manifold third a bayesian model selection paradigm is proposed the bayesian formulation of the manifold fitting problem uncovers an elegant solution to this problem for which a new method gric for approximating the posterior probability of each putative model is derived this approximations bears some similarity to the penalized likelihoods used by aic bic and mdl however it is far more accurate in situations involving large numbers of latent variables whose number increases with the data this will be empirically and theoretically demonstrated

behaviour of boundary functions for quantum billiards we study the behaviour of the normal derivative of eigenfunctions of the helmholtz equation inside billiards with dirichlet boundary condition these boundary functions are of particular importance because they uniquely determine the eigenfunctions inside the billiard and also other physical quantities of interest therefore they form a reduced representation of the quantum system analogous to the poincare section of the classical system for the normal derivatives we introduce an equivalent to the standard green function and derive an integral equation on the boundary based on this integral equation we compute the first two terms of the mean asymptotic behaviour of the boundary functions for large energies the first term is universal and independent of the shape of the billiard the second one is proportional to the curvature of the boundary the asymptotic behaviour is compared with numerical results for the stadium billiard different limacon billiards and the circle billiard and good agreement is found furthermore we derive an asymptotic completeness relation for the boundary functions

stochastic orderings for markov processes on partially ordered spaces the purpose of this paper is to develop a unified theory of stochastic ordering for markov processes on countable partially ordered state spaces when such a space is not totally ordered it can induce a wide range of stochastic orderings none of which are equivalent to sample path comparisons similar comparison theorems are also developed for non markov processes that are functions of markov processes and for time inhomogeneous markov processes such alternative orderings can be quite useful when analyzing multi dimensional stochastic models such as queueing networks

from uncertainty to visual exploration the authors attempt to determine what can be inferred from ambiguity in processes of visual interpretation they discuss this question in a specific context the interpretation of scene geometry in the form of parametrized volumetric models ambiguity is described as a local probabilistic property of the misfit error surface in the parameter space of superellipsoid models namely as an ellipsoid of confidence in which there is a given probability that the true parameters can be found the authors show how to project the ellipsoid of confidence back into 3d space to obtain the shell in which the true 3d surface most probably lies and introduce what they call the uncertainty as a local property of the fitted model s surface they propose a technique that can use this information to plan a new direction of view that minimizes the ambiguity of subsequent interpretation

exact theory for the quantum eigenstates of a strongly chaotic system we present an exact theory for the quantum eigenstates of a strongly chaotic system which consists of a point particle sliding freely on a two dimensional compact surface of constant negative curvature the main result is a general sum rule which relates an almost arbitrarily smoothed sum over the quantum wavefunctions to a sum over the lengths of the classical orbits as an example we apply this formula to the gaussian smoothed sum over wavefunctions the question of scars as imprints of individual closed orbits is discussed and the connection with bogomolny s semiclassical theory is explicitly worked out the investigation of the amplitude distribution p reveals that the higher excited wavefunctions behave as gaussian random waves

autocorrelation function of eigenstates in chaotic and mixed systems we study the autocorrelation function of different types of eigenfunctions in quantum mechanical systems with either chaotic or mixed classical limits we obtain an expansion of the autocorrelation function in terms of the correlation distance for localized states in billiards like bouncing ball modes or states living on tori a simple model using only classical input gives good agreement with the exact result in particular a prediction for irregular eigenfunctions in mixed systems is derived and tested for chaotic systems the expansion of the autocorrelation function can be used to test quantum ergodicity on different length scales

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

on navigating between friends and foes the problem of determining the optimal straight path between a planar set of points is considered each point contributes to the cost of a path a value that depends on the distance between the path and the point the cost function quantifying this dependence can be arbitrary and may be different for different points an algorithm to solve this problem using an extension of the hough transform is described the range of applications includes straight line fitting to a set of points in the presence of outliers navigation and path planning the proposed extended hough transform can be tuned to equivalent to well known robust least squares techniques and allows efficient approximate m estimation

uniform distribution of eigenfunctions on compact hyperbolic surfaces on demontre que les fonctions propres k du laplacien sur une surface hyperbolique compacte x devient uniformement distribuee sur x quand k

fitting a second degree curve in the presence of error this correspondence presents a statistically sound simple and fast method to estimate the parameters of a second degree curve from a set of noisy points that originated from the curve

a bayesian method for fitting parametric and nonparametric models to noisy data we present a simple paradigm for fitting models parametric and nonparametric to noisy data which resolves some of the problems associated with classical mse algorithms this is done by considering each point on the model as a possible source for each data point the paradigm can be used to solve problems which are ill posed in the classical mse approach such as fitting a segment as opposed to a line it is shown to be nonbiased and to achieve excellent results for general curves even in the presence of strong discontinuities results are shown for a number of fitting problems including lines circles elliptic arcs segments rectangles and general curves contaminated by gaussian and uniform noise

estimation of planar curves surfaces and nonplanar space curves defined by implicit equations with applications to edge and range image segmentation the author addresses the problem of parametric representation and estimation of complex planar curves in 2 d surfaces in 3 d and nonplanar space curves in 3 d curves and surfaces can be defined either parametrically or implicitly with the latter representation used here a planar curve is the set of zeros of a smooth function of two variables x y a surface is the set of zeros of a smooth function of three variables x y z and a space curve is the intersection of two surfaces which are the set of zeros of two linearly independent smooth functions of three variables x y z for example the surface of a complex object in 3 d can be represented as a subset of a single implicit surface with similar results for planar and space curves it is shown how this unified representation can be used for object recognition object position estimation and segmentation of objects into meaningful subobjects that is the detection of interest regions that are more complex than high curvature regions and hence more useful as features for object recognition

statistical properties of high lying chaotic eigenstates we study the statistical properties of the high lying chaotic eigenstates 200000 and above which are deep within the semiclassical regime the system we are analysing is the billiard system inside the region defined by the quadratic complex conformal map of the unit disk as introduced by robnik 1983 we are using heller s method of plane wave decomposition of the numerical eigenfunctions and perform extensive statistical analysis with the following conclusions i the local average probability density is in excellent agreement with the microcanonical assumption and all statistical properties are also in excellent agreement with the gaussian random model ii the autocorrelation function is found to be strongly direction dependent and only after averaging over all directions agrees well with berry s 1977 prediction iii although the scars of unstable classical periodic orbits in such an ergodic regime are expected to exist so far we have not found any around the 200000th state other than a scar like feature resembling the whispering gallery modes

what s in a set of points straight line fitting the problem of fitting a straight line to a planar set of points is reconsidered a parameter space computational approach capable of fitting one or more lines to a set of points is presented the suggested algorithm handles errors in both coordinates of the data points even when the error variances vary between coordinates and among points and can be readily made robust to outliers the algorithm is quite general and allows line fitting according to several useful optimality criteria to be performed within a single computational framework it is observed that certain extensions of the hough transform can be turned to be equivalent to well known m estimators thus allowing computationally efficient approximate m estimation

detection of object wings in fused range and intensity imagery abstract we present methods for detecting primitives in scenes containing objects whose surfaces are approximately piecewise quadric using a sensor that yields fused range and intensity the primitives detected in a fused image are viewpoint dependent and are called object wings which consist of adjacent fragments of object contour and surface wings are small enough so that some object parts can be sensed despite significant occlusion yet rich enough to be of use in indexing to candidate models in constraining object pose and in aggregation methods which combine primitives into larger structures or objects fitting procedures are defined for specific wing primitives experiments with both synthetic and real data show that classification within the wing types of planar spherical conical cylindrical can be achieved with over 90 accuracy contour information available in fitting fused data improves fitting relative to use of surface data alone moreover it is shown that only a small number of contour and surface samples are needed for extraction of primitives oc 1997 pattern recognition society

corner detection and curve segmentation by multiresolution chain code linking in this paper we propose a new method to characterise a curve by means of the hierarchical computation of a multiresolution structure this structure consisting of successive lower resolution versions of the same object is processed using the linked pyramid approach we adapt the multiresolution pixel linking algorithm to the processing of curve contours which are described by their chain code we also introduce a selective class selection process which allows application of the algorithm to segmentation and detection of contour features the resulting framework presents good performance for a wide range of object sizes without the need of any parameter tweaking and allows detection of shape detail at different scales

ellifit an unconstrained non iterative least squares based geometric ellipse fitting method a novel ellipse fitting method which is selective for digital and noisy elliptic curves is proposed in this paper the method aims at fitting an ellipse only when the data points are highly likely belong to an ellipse this is achieved using the geometric distances of the ellipse from the data points the proposed method models the non linear problem of ellipse fitting as a combination of two operators with one being linear numerically stable and easily invertible while the other being non linear but unique and easily invertible operator as a consequence the proposed ellipse fitting method has several salient properties like unconstrained stable non iterative and computationally inexpensive the efficacy of the method is compared against six contemporary and recent algorithms based on the least squares formulation using five experiments of diverse practical challenges like digitization incomplete ellipses and gaussian noise up to 30 three of the experiments comprise of a total of 44 400 ellipses positive test data while the other two are tested on 320 000 non elliptic conics negative test data the results show that the proposed method is quite selective to elliptic shapes only and provides accurate fitting results indicating potential application in medical robotics object detection and other image processing industrial applications

describing complicated objects by implicit polynomials this paper introduces and focuses on two problems first is the representation power of closed implicit polynomials of modest degree for curves in 2 d images and surfaces in 3 d range data super quadrics are a small subset of object boundaries that are well fitted by these polynomials the second problem is the stable computationally efficient fitting of noisy data by closed implicit polynomial curves and surfaces the attractive features of these polynomials for vision is discussed