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

natural norm a posteriori error estimators for reduced basis approximations we present a technique for the rapid and reliable prediction of linear functional outputs of coercive and noncoercive linear elliptic partial differential equations with affine parameter dependence the essential components are i rapidly convergent global reduced basis approximations galerkin projection onto a space wn spanned by solutions of the governing partial differential equation at n judiciously selected points in parameter space ii a posteriori error estimation relaxations of the error residual equation that provide inexpensive yet sharp bounds for the error in the outputs of interest and iii offiine online computational procedures methods which decouple the generation and projection stages of the approximation process the operation count for the online stage in which given a new parameter value we calculate the output of interest and associated error bound depends only on n typically very small and the parametric complexity of the problem in this paper we propose a new natural norm formulation for our reduced basis error estimation framework that a greatly simplifies and improves our inf sup lower bound construction offline and evaluation online a critical ingredient of our a posteriori error estimators and b much better controls significantly sharpens our output error bounds in particular through deflation for parameter values corresponding to nearly singular solution behavior we apply the method to two illustrative problems a coercive laplacian heat conduction problem which becomes singular as the heat transfer coefficient tends to zero and a non coercive helmholtz acoustics problem which becomes singular as we approach resonance in both cases we observe very economical and sharp construction of the requisite natural norm inf sup lower bound rapid convergence of the reduced basis approximation reasonable effectivities even for near singular behavior for our deflated output error estimators and significant several order of magnitude online computational savings relative to standard finite element procedures

efficient estimation of integral functionals of a density bickel and ritov s estimator is a quite intricate expression based on kernel estimators of the density in this paper we propose an alternative and somehow simpler method of estimation based on orthogonal projections this

recognizing planar symbols with severe perspective deformation a common problem encountered in recognizing real scene symbols is the perspective deformation in this paper a recognition method resistant to perspective deformation is proposed based on cross ratio spectrum descriptor this method shows good resistance to severe perspective deformation and good discriminating power to similar symbols

estimating divergence functionals and the likelihood ratio by convex risk minimization we develop and analyze m estimation methods for divergence functionals and the likelihood ratios of two probability distributions our method is based on a nonasymptotic variational characterization of f divergences which allows the problem of estimating divergences to be tackled via convex empirical risk optimization the resulting estimators are simple to implement requiring only the solution of standard convex programs we present an analysis of consistency and convergence for these estimators given conditions only on the ratios of densities we show that our estimators can achieve optimal minimax rates for the likelihood ratio and the divergence functionals in certain regimes we derive an efficient optimization algorithm for computing our estimates and illustrate their convergence behavior and practical viability by simulations

estimation of integral functionals of a density let be a smooth function of k 2 variables we shall investigate in this paper the rates of convergence of estimators of t f f f x f x f k x x dx when f belongs to some class of densities of smoothness s we prove that when 2k 1 4 one can define an estimator t n of t f based on n i i d observations of density f on the real line which converges at the semiparametric rate 1 n on the other hand when s 2k 1 4 t f cannot be estimated at a rate faster than n with 4 s k 4s 1 we shall also provide some extensions to the multidimensional case those results extend previous works of levit of bickel and ritov and of donoho and nussbaum on estimation of quadratic functionals

on nonparametric tests of positivity monotonicity convexity we consider the problem of estimating the distance from an unknown signal observed in a white noise model to convex cones of positive monotone convex functions we show that when the unknown function belongs to a holder class the risk of estimating the l r distance 1 r from the signal to a cone is essentially the same up to a logarithmic factor as that of estimating the signal itself the same risk bounds hold for the test of positivity monotonicity and convexity of the unknown signal we also provide an estimate for the distance to the cone of positive functions for which risk is by a logarithmic factor smaller than that of the plug in estimate

reconstruction of linearly parameterized models from single images with a camera of unknown focal length this paper deals with the problem of recovering the dimensions of an object and its pose from a single image acquired with a camera of unknown focal length it is assumed that the object in question can be modeled as a polyhedron where the coordinates of the vertices can be expressed as a linear function of a dimension vector the reconstruction program takes as input a set of correspondences between features in the model and features in the image from this information the program determines an appropriate projection model for the camera the dimensions of the object its pose relative to the camera and in the case of perspective projection the focal length of the camera this paper describes how the reconstruction problem can be framed as an optimization over a compact set with low dimension no more than four this optimization problem can be solved efficiently by coupling standard nonlinear optimization techniques with a multistart method the result is an efficient reliable solution system that does not require initial estimates for any of the parameters being estimated

direct calibration by fitting of cuboids to a single image using differential evolution in this article we propose a new method to calibrate directly the camera by which it was taken an image of a cuboid and to find at the same time the orientation and side lengths of the cuboid this is a highly non linear optimization problem that is solved directly using a heuristic called differential evolution we show in this paper that this problem is very difficult if one tries to solve it with a conventional scalar optimization procedure although differential evolution is a heuristic we find valid results in 100 of the executions we test our method with synthetic and real images

using geometric constraints through parallelepipeds for calibration and 3d modeling this paper concerns the incorporation of geometric information in camera calibration and 3d modeling using geometric constraints enables more stable results and allows us to perform tasks with fewer images our approach is motivated and developed within a framework of semi automatic 3d modeling where the user defines geometric primitives and constraints between them in this paper first a duality that exists between the shape parameters of a parallelepiped and the intrinsic parameters of a camera is described then a factorization based algorithm exploiting this relation is developed using images of parallelepipeds it allows us to simultaneously calibrate cameras recover shapes of parallelepipeds and estimate the relative pose of all entities besides geometric constraints expressed via parallelepipeds our approach simultaneously takes into account the usual self calibration constraints on cameras the proposed algorithm is completed by a study of the singular cases of the calibration method a complete method for the reconstruction of scene primitives that are not modeled by parallelepipeds is also briefly described the proposed methods are validated by various experiments with real and simulated data for single view as well as multiview cases

on estimation of the lr norm of a regression function be observed with noise in the present paper we study the problem of nonparametric estimation of certain nonsmooth functionals of f specifically l r norms f r of f known from the literature results on functional estimation deal mostly with two extreme cases estimating a smooth differentiable in l 2 functional or estimating a singular functional like the value of f at certain point or the maximum of f in the first case the convergence rate typically is n 1 2 n being the number of observations in the second case the rate of convergence coincides with the one of estimating the function f itself in the corresponding norm we show that the case of estimating f r is in some sense intermediate between the above extremes the optimal rate of convergence is worse than n 1 2 but is better than the rate of convergence of nonparametric estimates of f the results depend on the value of r for r even integer the rate occurs to be n 2 1 1 r where is the degree of smoothness if r is not an even integer then the nonparametric rate n 2 1 can be improved but only by a logarithmic in n factor

goodness of fit testing and quadratic functional estimation from indirect observations we consider the convolution model where i i d random variables x i having unknown density f are observed with additive i i d noise independent of the x s we assume that the density f belongs to either a sobolev class or a class of supersmooth functions the noise distribution is known and its characteristic function decays either polynomially or exponentially asymptotically we consider the problem of goodness of fit testing in the convolution model we prove upper bounds for the risk of a test statistic derived from a kernel estimator of the quadratic functional f f 2 based on indirect observations when the unknown density is smoother enough than the noise density we prove that this estimator is n 1 2 consistent asymptotically normal and efficient for the variance we compute otherwise we give nonparametric upper bounds for the risk of the same estimator we give an approach unifying the proof of nonparametric minimax lower bounds for both problems we establish them for sobolev densities and for supersmooth densities less smooth than exponential noise in the two setups we obtain exact testing constants associated with the asymptotic minimax rates

predicting the output from a complex computer code when fast approximations are available s we consider prediction and uncertainty analysis for complex computer codes which can be run at different levels of sophistication in particular we wish to improve efficiency by combining expensive runs of the most complex versions of the code with relatively cheap runs from one or more simpler approximations a bayesian approach is described in which prior beliefs about the codes are represented in terms of gaussian processes an example is presented using two versions of an oil reservoir simulator 1 c complex mathematical models implemented in large computer codes have been used to study real systems in many areas of scientific research sacks et al 1989 usually because physical experimentation is too costly and sometimes impossible as in the case of large environmental systems a computer experiment involves running the code with various input values for the purpose of learning something about the real system often a simulator can be run at different levels of complexity with versions ranging from the most sophisticated high level code to the most basic for example in 4 we consider two codes which simulate oil pressure at a well of a hydrocarbon reservoir both codes use finite element analysis in which the rocks comprising the reservoir are represented by small interacting grid blocks the flow of oil within the reservoir can be simulated by considering the interaction between the blocks the two codes differ in the resolution of the grid so that we have a very accurate slow version using many small blocks and a crude approximation using large blocks which runs much faster alternatively a mathematical model could be expanded to include more of the scientific laws underlying the physical processes simple fast versions of the code may well include the most important features and are useful for preliminary investigations in real time applications the number of runs from a high level simulator may be limited by expense then there is a need to trade off the complexity of the expensive code with the availability of the simpler approximations the purpose of the current paper is to explore ways in which runs from several levels of a code can be used to make inference about the output from the most complex code we may also have uncertainty about values for the input parameters which apply in any given application uncertainty analysis of computer codes describes how this uncertainty on the inputs affects our uncertainty about the output

minimax estimation of a functional on a structured high dimensional model we introduce a new method of estimation of parameters in semi parametric and nonparametric models the method is based on estimating equations that are u statistics in the observations the u statistics are based on higher order influence functions that extend ordinary linear influence functions of the parameter of interest and represent higher derivatives of this parameter for parameters for which the representation cannot be perfect the method leads to a bias variance trade off and results in estimators that converge at a slower than n rate in a number of examples the resulting rate can be shown to be optimal we are particularly interested in estimating parameters in models with a nuisance parameter of high dimension or low regularity where the parameter of interest cannot be estimated at n rate but we also consider efficient n estimation using novel nonlinear estimators the general approach is applied in detail to the example of estimating a mean response when the response is not always observed

estimating nonquadratic functionals of a density using haar wavelets consider the problem of estimating f where is a smooth function and f is a density with given order of regularity s special attention is paid to the case t t 3 it has been shown that for low values of s the n 1 2 rate of convergence is not achievable uniformly over the class of objects of regularity s in fact a lower bound for this rate is n 4s 1 4s for 0 s 1 4 as for the upper bound using a taylor expansion it can be seen that it is enough to provide an estimate for the case x x 3 that is the aim of this paper our method makes intensive use of special algebraic and wavelet properties of the haar basis

wavelet shrinkage asymptopia much recent effort has sought asymptotically minimax methods for recovering infinite dimensional objects curves densities spectral densities images from noisy data a now rich and complex body of work develops nearly or exactly minimax estimators for an array of interesting problems unfortunately the results have rarely moved into practice for a variety of reasons among them being similarity to known methods computational intractability and lack of spatial adaptivity we discuss a method for curve estimation based on n noisy data translate the empirical wavelet coefficients towards the origin by an amount 2 log n n the proposal differs from those in current use is computationally practical and is spatially adaptive it thus avoids several of the previous objections further the method is nearly minimax both for a wide variety of loss functions pointwise error global error measured in l p norms pointwise and global error in estimation of derivatives and for a wide range of smoothness classes including standard holder and sobolev classes and bounded variation this is a much broader near optimality than anything previously proposed we draw loose parallels with near optimality in robustness and also with the broad near eigenfunction properties of wavelets themselves finally the theory underlying the method is interesting as it exploits a correspondence between statistical questions and questions of optimal recovery and information based complexity

on estimation of l_ r lr norms in gaussian white noise models we provide a complete picture of asymptotically minimax estimation of l r norms for any r ge 1 of the mean in gaussian white noise model over nikolskii besov spaces in this regard we complement the work of lepski et al probab theory relat fields 113 2 221 253 1999 who considered the cases of r 1 with poly logarithmic gap between upper and lower bounds and r even with asymptotically sharp upper and lower bounds over holder spaces we additionally consider the case of asymptotically adaptive minimax estimation and demonstrate a difference between even and non even r in terms of an investigator s ability to produce asymptotically adaptive minimax estimators without paying a penalty

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

3 d modeling from a single view of a symmetric object 3 d technologies are considered as the next generation of multimedia applications currently one of the challenges faced by 3 d applications is the shortage of 3 d resources to solve this problem many 3 d modeling methods are proposed to directly recover 3 d geometry from 2 d images however these methods on single view modeling either require intensive user interaction or are restricted to a specific kind of object in this paper we propose a novel 3 d modeling approach to recover 3 d geometry from a single image of a symmetric object with minimal user interaction symmetry is one of the most common properties of natural or manmade objects given a single view of a symmetric object the user marks some symmetric lines and depth discontinuity regions on the image our algorithm first finds a set of planes to approximately fit to the object and then a rough 3 d point cloud is generated by an optimization procedure the occluded part of the object is further recovered using symmetry information experimental results on various indoor and outdoor objects show that the proposed system can obtain 3 d models from single images with only a little user interaction