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

hierarchies of nonlinear integrable q difference equations from series of lax pairs we present two hierarchies of nonlinear integrable q difference equations one of which includes a q difference form of each of the second and fifth painleve equations and the other includes all the equations have multiple free parameters a method to calculate a 2 2 lax pair for each equation in the hierarchy is also given

schwarz waveform relaxation methods for parabolic equations in space frequency domain some schwarz waveform relaxation algorithms based on frequency domain analysis for parabolic equations are proposed and analyzed in this paper we mainly study an overlapping process with dirichlet transmission conditions and a non overlapping process with robin transmission conditions the convergence conditions for these algorithms are also obtained by our frequency domain analysis numerical experiments are given to illustrate effectiveness of the algorithms

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

convergence analysis for a second order schwarz method for nonoverlapping subdomains abstract a second order schwarz method for elliptic partial differential equations is developed and analyzed at a continuous level which can be parallel implemented with local communications it uses a second order boundary condition in terms of poincare steklov operators as its transmission condition on the interfaces the convergence of the algorithm in h 1 norm is obtained by using energy estimates and convergence results hold on arbitrary geometry of subdomains with no cross points

generalizations and accelerations of lions nonoverlapping domain decomposition method for linear elliptic pde in this paper a one parameter generalization of lions nonoverlapping domain decomposition method for linear elliptic pdes is proposed and studied the generalized methods are shown to be descent direction methods for minimizing an interface bias functional iteration convergence of both the continuous and finite element versions of the proposed methods is established it is theoretically and numerically demonstrated that for generic choices of the parameter the generalized methods converge faster than lions original method algorithms are given and numerical results are presented

analysis and optimization of robin robin partitioned procedures in fluid structure interaction problems in the solution of fluid structure interaction fsi problems partitioned procedures are modular algorithms that involve separate fluid and structure solvers that interact in an iterative framework through the exchange of suitable transmission conditions at the fs interface in this work we study using fourier analysis the convergence of partitioned algorithms based on robin transmission conditions we derive for different models of the fluid and the structure a frequency dependent reduction factor at each iteration of the partitioned algorithm which is minimized by choosing optimal values of the coefficients in the robin transmission conditions two dimensional numerical results are also reported which highlight the effectiveness of the optimization procedure

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

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

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

a gradient method approach to optimization based multidisciplinary simulations and nonoverlapping domain decomposition algorithms it has been shown recently that optimization based nonoverlapping domain decomposition algorithms are connected to many well known algorithms using a gradient type iterative strategy for the optimization problem we present further discussion on how to develop various algorithms that can integrate subdomain solvers into a solver for the problem in the whole domain in particular the algorithms we discuss can be used to develop efficient solvers of multidisciplinary problems which are constructed using existing subdomain solvers without the need for making changes in the latter

on accelerated convergence of nonoverlapping schwarz methods the schwarz alternating method can be used to solve elliptic boundary value problems on domains which consist of two or more overlapping subdomains the solution is approximated by an infinite sequence of functions which results from solving a sequence of elliptic boundary value problems in each subdomain schwarz methods for nonoverlapping subdomains also exist but they have not been popular because of their slow convergence these methods contain a free parameter in the robin boundary condition of each subdomain problem the slow convergence can be attributed to an improper choice of this parameter in this paper two models are proposed to give guidance to the choice of this parameter for the poisson equation on rectangular domains these models suggest very simple expressions for the parameter in terms of the dimensions of the subdomain numerical experiments verify their effectiveness when used as a preconditioner it is demonstrated numerically in some examples that the algorithm is quite efficient

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

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

convergence estimates for an higher order optimized schwarz method for domains with an arbitrary interface optimized schwarz methods form a class of domain decomposition methods for the solution of elliptic partial differential equations optimized schwarz methods employ a first or higher order boundary condition along the artificial interface to accelerate convergence in the literature the analysis of optimized schwarz methods relies on fourier analysis and so the domains are restricted to be regular rectangular in this paper we express the interface operator of an optimized schwarz method in terms of poincare steklov operators this enables us to derive an upper bound of the spectral radius of the operator arising in this method of 1 o h 1 4 on a class of general domains where h is the discretization parameter this is the predicted rate for a second order optimized schwarz method in the literature on rectangular subdomains and is also the observed rate in numerical simulations

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

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

timely communicaton an analysis for a nonoverlapping domain decomposition iterative procedure an iterative procedure for nonoverlapping domain decomposition methods ddm is developed and analyzed which can be parallelly implemented with local communications it uses a robin boundary condition as its transmission condition on the interfaces the update of robin data of its transmission condition is a very simple relaxation between the preceding robin data and function value it need not find any derivatives at each iterative step this method can be easily applied to the discretization problems moreover it is shown that it is indeed a variant of the lions nonoverlapping ddm for the continuous problems also it can be regarded as a generalization of tang s generalized schwarz alternating method gsam in the nonoverlapping ddm