stochastic perturbation of reduced gradient grg methods for nonconvex programming problems in this paper we consider nonconvex differentiable programming under linear and nonlinear differentiable constraints a reduced gradient and grg generalized reduced gradient descent methods involving stochastic perturbation are proposed and we give a mathematical result establishing the convergence to a global minimizer numerical examples are given in order to show that the method is effective to calculate namely we consider classical tests such as the statistical problem the octagon problem the mixture problem and an application to the linear optimal control servomotor problem

shape description and matching using integral invariants on eccentricity transformed images matching occluded and noisy shapes is a problem frequently encountered in medical image analysis and more generally in computer vision to keep track of changes inside the breast for example it is important for a computer aided detection system to establish correspondences between regions of interest shape transformations computed both with integral invariants ii and with geodesic distance yield signatures that are invariant to isometric deformations such as bending and articulations integral invariants describe the boundaries of planar shapes however they provide no information about where a particular feature lies on the boundary with regard to the overall shape structure conversely eccentricity transforms ecc can match shapes by signatures of geodesic distance histograms based on information from inside the shape but they ignore the boundary information we describe a method that combines the boundary signature of a shape obtained from ii and structural information from the ecc to yield results that improve on them separately

fixed width multiple comparison procedures using common random numbers for steady state simulations abstract suppose that there are k 2 different systems i e stochastic processes where each system has an unknown steady state mean performance we consider the problem of running a two stage simulation using common random numbers to construct fixed width confidence intervals for two multiple comparison problems under the assumptions that the stochastic processes representing the simulation output of the different systems satisfy a functional central limit theorem and that the asymptotic covariance matrix satisfies a condition known as sphericity we prove that our confidence intervals are asymptotically valid as the desired half width of the confidence intervals tend to zero we develop both absolute and relative width confidence intervals empirical results are presented indicating the procedures robustness to violations of the sphericity assumption

a deterministic analysis of stochastic approximation with randomized directions we study the convergence of two stochastic approximation algorithms with randomized directions the simultaneous perturbation stochastic approximation algorithm and the random direction kiefer wolfowitz algorithm we establish deterministic necessary and sufficient conditions on the random directions and noise sequences for both algorithms and these conditions demonstrate the effect of the random directions on the sample path behavior of the algorithms studied we discuss ideas for further research in the analysis and design of these algorithms

is the selected population the best random variables x i sim n theta i 1 i 1 2 cdots k are observed suppose x s is the largest observation if the inference theta s max i neq s theta i is made whenever x s max i neq s x i c then the probability of a false inference is maximized when two theta i are equal and the rest are infty equivalently the inference can be made whenever a two sample two sided test for difference of means based on the largest two observations would reject the hypothesis of no difference the result also holds in the case of unknown estimable common variance and in fact for location families with monotone likelihood ratio

a new procedure for selecting good populations summary suppose we have k normal populations with means ii1 k and common unknown variance o2 a population is good if its mean exceeds u k 1 where p k is the largest of the u s a procedure is proposed to select a subset of populations satisfying the requirement that the probability of including all good populations exceeds a prespecified value p simultaneous inference that can be made with the selection procedure is considered furthermore if populations with means below p k e2 are bad where 92 el a selection procedure is proposed and a sample size is determined so that the probability of either omitting a good population or selecting a bad population is less than or equal to 1 p

on the use of an spsa based model free feedback controller in active noise control for periodic disturbances in a duct in this paper a feedback active noise control fanc system using a model free mf controller based on simultaneous perturbation stochastic approximation spsa algorithm is considered the structure of the fanc system is first described and the spsa algorithm is briefly reviewed subsequently the spsa based mf control algorithm employed in the fanc system is derived computer simulations are carried out to suggest that the spsa based mf control algorithm is effective for anc system and much more efficient than the finite difference stochastic approximation fdsa algorithm the controller based on the spsa based mf control algorithm is implemented on the texas instruments digital signal processor dsp tms320vc33 experimental results show that the proposed scheme is able to significantly reduce periodic disturbances without the need to model the secondary path at the same time the simulations and the experimental verification tests also show that the convergence rate of the spsa based mf control algorithm is acceptable and the spsa based mf control algorithm has better tracking ability under variable secondary path this observation implies that the spsa based mf controller eliminates the need of modeling of the secondary path for the fanc system

multiple comparison procedures for steady state simulations suppose that there are k 2 different systems i e stochastic processes where each system has an unknown steady state mean performance and unknown asymptotic variance we allow for the asymptotic variances to be unequal and for the distributions of the k systems to be different we consider the problem of running independent single stage simulations to make multiple comparisons of the steady state means of the different systems we derive asymptotically valid as the run lengths of the simulations of the systems tend to infinity simultaneous confidence intervals for each of the following problems all pairwise comparisons of means all contrasts multiple comparisons with a control and multiple comparisons with the best our confidence intervals are based on standardized time series methods and we establish the asymptotic validity of each under the sole assumption that the stochastic processes representing the simulation output of the different systems satisfy a functional central limit theorem although simulation is the context of this paper the results naturally apply to asymptotically stationary time series

simultaneous confidence intervals for all distances from the best in practice comparisons with the best are often the ones of primary interest in this paper parametric and nonparametric simultaneous upper confidence intervals for all distances from the best are derived under the location model their improvement upon the results of bechhofer 1954 gupta 1956 1965 fabian 1962 and desu 1970 in the parametric case is discussed in the nonparametric case no comparable confidence statements were available previously

graphical procedures for multiple comparisons under general dependence abstractit has been more than half a century since tukey first introduced graphical displays that relate nonoverlap of confidence intervals to statistically significant differences between parameter estimates in this article we show how tukey s graphical overlap procedure can be modified to accommodate general forms of dependence within and across samples we also develop a procedure that can be used to more effectively resolve rankings within the tails of the distributions of parameter values thereby generalizing existing methods for multiple comparisons with the best we show that these new procedures retain the simplicity of tukey s original procedure while maintaining asymptotic control of the familywise error rate under very general conditions simple examples are used throughout to illustrate the procedures supplementary materials for this article are available online

model based recognition of 3d objects from single images in this work we treat major problems of object recognition which have received relatively little attention lately among them are the loss of depth information in the projection from a 3d object to a single 2d image and the complexity of finding feature correspondences between images we use geometric invariants to reduce the complexity of these problems there are no geometric invariants of a projection from 3d to 2d however given certain modeling assumptions about the 3d object such invariants can be found the modeling assumptions can be either a particular model or a generic assumption about a class of models here we use such assumptions for single view recognition we find algebraic relations between the invariants of a 3d model and those of its 2d image under general projective projection these relations can be described geometrically as invariant models in a 3d invariant space illuminated by invariant light rays and projected onto an invariant version of the given image we apply the method to real images

space and time bounds on indexing 3d models from 2d images model based visual recognition systems often match groups of image features to groups of model features to form initial hypotheses which are then verified in order to accelerate recognition considerably the model groups can be arranged in an index space hashed offline such that feasible matches are found by indexing into this space for the case of 2d images and 3d models consisting of point features bounds on the space required for indexing and on the speedup that such indexing can achieve are demonstrated it is proved that even in the absence of image error each model must be represented by a 2d surface in the index space this places an unexpected lower bound on the space required to implement indexing and proves that no quantity is invariant for all projections of a model into the image theoretical bounds on the speedup achieved by indexing in the presence of image error are also determined and an implementation of indexing for measuring this speedup empirically is presented it is found that indexing can produce only a minimal speedup on its own however when accompanied by a grouping operation indexing can provide significant speedups that grow exponentially with the number of features in the groups

simulation based optimization with stochastic approximation using common random numbers the method of common random numbers is a technique used to reduce the variance of difference estimates in simulation optimization problems these differences are commonly used to estimate gradients of objective functions as part of the process of determining optimal values for parameters of a simulated system asymptotic results exist which show that using the common random numbers method in the iterative finite difference stochastic approximation optimization algorithm fdsa can increase the optimal rate of convergence of the algorithm from the typical rate of k 1 3 to the faster k 1 2 where k is the algorithm s iteration number simultaneous perturbation stochastic approximation spsa is a newer and often much more efficient optimization algorithm and we will show that this algorithm too converges faster when the common random numbers method is used we will also provide multivariate asymptotic covariance matrices for both the spsa and fdsa errors

motion and structure from orthographic projections s ullman s classical 1979 results on motion structure from orthographic views are revisited specifically two results are presented 1 two orthographic views allow an uncountably infinite number of solutions to motion structure of a rigid body and 2 a linear algorithm for solving motion structure from four point correspondences over three views

when is it possible to identify 3d objects from single images using class constraints one approach to recognizing objects seen from arbitrary viewpoint is by extracting invariant properties of the objects from single images such properties are found in images of 3d objects only when the objects are constrained to belong to certain classes e g bilaterally symmetric objects existing studies that follow this approach propose how to compute invariant representations for a handful of classes of objects a fundamental question regarding the invariance approach is whether it can be applied to a wide range of classes to answer this question it is essential to study the set of classes for which invariance exists this paper introduces a new method for determining the existence of invariant functions for classes of objects together with the set of images from which these invariants can be computed we develop algebraic tests that determine whether the objects in a given class can be identified from single images these tests apply to classes of objects undergoing affine projection in addition these tests allow us to determine the set of views of the objects which are degenerate we apply these tests to several classes of objects and determine which of them is identifiable and which of their views are degenerate

multiple comparisons with the best treatment abstract let 1 2 k be k 2 sources of observations treatments populations and suppose the goodness of treatment i is characterized by the size of an unknown real valued parameter i let k max1 i k i if i is preferred to j when i j the parameters i k i i 1 2 k reflect in an inverse sense the goodness of each treatment relative to the best treatment a general technique for obtaining simultaneous confidence intervals on the i is demonstrated with several examples this technique can be applied in any setting where comparison with control intervals can be computed regarding any j as the control these results have special importance in ranking and selection problems in that the process of generating upper bounds on the i generates traditional confidence statements of both the indifference zone and the subset selection schools simultaneously as established by hsu 1981

optimal random perturbations for stochastic approximation using a simultaneous perturbation gradient approximation the simultaneous perturbation stochastic approximation spsa algorithm has attracted considerable attention for challenging optimization problems where it is difficult or impossible to obtain a direct gradient of the objective say loss function the approach is based on a highly efficient simultaneous perturbation approximation to the gradient based on loss function measurements spsa is based on picking a simultaneous perturbation random vector in a monte carlo fashion as part of generating the approximation to the gradient this paper derives the optimal distribution for the monte carlo process the objective is to minimize the mean square error of the estimate the authors also consider maximization of the likelihood that the estimate be confined within a bounded symmetric region of the true parameter the optimal distribution for the components of the simultaneous perturbation vector is found to be a symmetric bernoulli in both cases the authors end the paper with a numerical study related to the area of experiment design

geometric invariants and object recognition we discuss the role of the general invariance concept in object recognition and review the classical and recent literature on projective invariance invariants help solve major problems of object recognition for instance different images of the same object often differ from each other because of the different viewpoint from which they were obtained to match the two images common methods thus need to find the correct viewpoint a difficult problem that can involve search in a high dimensional space of all possible points of view and or finding point correspondences geometric invariants are shape descriptors computed from the geometry of the shape that remain unchanged under geometric transformations such as changing the viewpoint thus they can be matched without search deformations of objects are another important class of geometric changes for which invariance is useful

constrained simultaneous confidence intervals for multiple comparisons with the best for comparing k treatment effects 01 02 ok often the parameters of primary interest are 0i maxeioi0 i 1 k in this article we develop constrained 100p two sided simultaneous confidence intervals for 0i maxj i0j which we refer to as constrained mcb intervals it turns out that the lower bounds of the intervals imply indifference zone selection inference and the upper bounds of these intervals imply subset selection inference each given at the same confidence level 100p as mcb we also extend our

generalization to novel views universal class based andmodel based processing a major problem in object recognition is that a novel image of a given object can be different from all previously seen images images can vary considerably due to changes in viewing conditions such as viewing position and illumination in this paper we distinguish between three types of recognition schemes by the level at which generalization to novel images takes place universal class and model based the first is applicable equally to all objects the second to a class of objects and the third uses known properties of individual objects we derive theoretical limitations on each of the three generalization levels for the universal level previous results have shown that no invariance can be obtained here we show that this limitation holds even when the assumptions made on the objects and the recognition functions are relaxed we also extend the results to changes of illumination direction for the class level previous studies presented specific examples of classes of objects for which functions invariant to viewpoint exist here we distinguish between classes that admit such invariance and classes that do not we demonstrate that there is a tradeoff between the set of objects that can be discriminated by a given recognition function and the set of images from which the recognition function can recognize these objects furthermore we demonstrate that although functions that are invariant to illumination direction do not exist at the universal level when the objects are restricted to belong to a given class an invariant function to illumination direction can be defined a general conclusion of this study is that class based processing that has not been used extensively in the past is often advantageous for dealing with variations due to viewpoint and illuminant changes

matching 3 d models to 2 d images we consider the problem of analytically characterizing the set of all 2 d images that a group of 3 d features may produce and demonstrate that this is a useful thing to do our results apply for simple point features and point features with associated orientation vectors when we model projection as a 3 d to 2 d affine transformation we show how to represent the set of images that a group of 3 d points produces with two lines 1 d subspaces one in each of two orthogonal high dimensional spaces where a single image group corresponds to one point in each space the images of groups of oriented point features can be represented by a 2 d hyperbolic surface in a single high dimensional space the problem of matching an image to models is essentially reduced to the problem of matching a point to simple geometric structures moreover we show that these are the simplest and lowest dimensional representations possible for these cases we demonstrate the value of this way of approaching matching by applying our results to a variety of vision problems in particular we use this result to build a space efficient indexing system that performs 3 d to 2 d matching by table lookup this system is analytically built and accessed accounts for the effects of sensing error and is tested on real images we also derive new results concerning the existence of invariants and non accidental properties in this domain finally we show that oriented points present unexpected difficulties indexing requires fundamentally more space with oriented than with simple points we must use more images in a motion sequence to determine the affine structure of oriented points and the linear combinations result does not hold for oriented points

sequential implementation of stepwise procedures for identifying the maximum tolerated dose this article considers the problem of finding the maximum tolerated dose mtd of a drug in human trials the mtd is defined as the maximum test dose with toxicity probability less than or equal to a target toxicity rate we adopt the multiple test framework with step down tests used in an escalation stage and step up tests used in a deescalation stage to allow sequential dose assignments for ethical purposes by formulating the estimation problem as a testing problem the proposed procedures formally control the error probability of selecting an unsafe dose in addition we can control the probability of correctly selecting the mtd under a parameter subspace where no toxicity probability lies in an interval bracketed by the target toxicity rate and an unacceptably high toxicity rate the so called indifference zone this frequentist property which is currently lacking in the conduct of dose finding trials in humans is appealing from a regulatory standpoint we give the general expressions of the se

self calibration of catadioptric camera with two planar mirrors from silhouettes if an object is interreflected between two planar mirrors we may take an image containing both the object and its multiple reflections i e simultaneously imaging multiple views of an object by a single pinhole camera this paper emphasizes the problem of recovering both the intrinsic and extrinsic parameters of the camera using multiple silhouettes from one single image view pairs among views in a single image can be divided into two kinds by the relationship between the two views in the pair reflected by some mirror real or virtual and in a circular motion epipoles in the first kind of pairs can be easily determined from intersections of common tangent lines of silhouettes based on the projective properties of these epipoles efficient methods are proposed to recover both the imaged circular points and the included angle between two mirrors epipoles in the second kind of pairs can be recovered simultaneously with the projection of intersection line between two mirrors by solving a simple 1d optimization problem using the consistency constraint of epipolar tangent lines fundamental matrices among views in a single image are all recovered using the estimated intrinsic and extrinsic parameters of the camera a euclidean reconstruction can be obtained experiments validate the proposed approach

retrieval of images of man made structures based on projective invariance in this paper we propose a geometry based image retrieval scheme that makes use of projectively invariant features cross ratio cr is an invariant feature under projective transformations for collinear points we compute the crs of point sets in quadruplets and the cr histogram is used as the feature for retrieval purposes being a geometric feature it allows us to retrieve similar images irrespective of view point and illumination changes we can retrieve the same building even if the facade has undergone a fresh coat of paints color and textural features can also be included if desired experimental results show a favorably very good retrieval accuracy when tested on an image database of size 4000 the method is very effective in retrieving images having man made objects rich in polygonal structures like buildings rail tracks etc

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

optimal confidence sets bioequivalence and the limacon of pascal abstract we begin with a decision theoretic investigation into confidence sets that minimize expected volume at a given parameter value such sets are constructed by inverting a family of uniformly most powerful tests and hence they also enjoy the optimality property of being uniformly most accurate in addition these sets possess bayesian optimal volume properties and represent the first case to our knowledge of a frequentist 1 confidence set that possesses a bayesian optimality property the hypothesis testing problem that generates these sets is similar to that encountered in bioequivalence testing our sets are optimal for testing bioequivalence in certain settings in the case of the normal distribution the optimal set is a curve known as the limacon of pascal we illustrate the use of these curves with a biopharmaceutical example

3d object recognition using invariance abstract the systems and concepts described in this paper document the evolution of the geometric invariance approach to object recognition over the last five years invariance overcomes one of the fundamental difficulties in recognising objects from images that the appearance of an object depends on viewpoint this problem is entirely avoided if the geometric description is unaffected by the imaging transformation such invariant descriptions can be measured from images without any prior knowledge of the position orientation and calibration of the camera these invariant measurements can be used to index a library of object models for recognition and provide a principled basis for the other stages of the recognition process such as feature grouping and hypothesis verification object models can be acquired directly from images allowing efficient construction of model libraries without manual intervention a significant part of the paper is a summary of recent results on the construction of invariants for 3d objects from a single perspective view a proposed recognition architecture is described which enables the integration of multiple general object classes and provides a means for enforcing global scene consistency various criticisms of the invariant approach are articulated and addressed

3 d reconstruction using mirror images based on a plane symmetry recovering method three dimensional reconstruction from a perspective 2d image using mirrors is addressed the mirrors are used to form symmetrical relations between the direct image and mirror images by finding correspondences between them the 3d shape can be reconstructed by means of plane symmetry recovering method using the vanishing point two constraints are used in determining the correspondence in the case where only one mirror is used invisible parts both in the direct image and in the mirror image may still remain using multiple mirrors however occluded parts will decrease or disappear and occlusion free object reconstruction becomes possible

using the orientation of fragmentary 3d edge segments for polyhedral object recognition several constraints are developed which impose consistency between model edge and sensed edge fragment geometries in order to collapse the search space in matching 3d edge data to 3d edge models the constraints have been demonstrated on error prone synthetic edge data and on 3d edge data obtained by stereo processing an important feature of the constraints is their ability to attach sign labels to the sensed edge fragments during matching providing consistency of edge directions between the model and data this feature progressively increases the power of the constraints and assists in finding the transformation between model and sensor spaces

model based temporal object verification using video an approach to model based dynamic object verification and identification using video is proposed from image sequences containing the moving object we compute its motion trajectory then we estimate its three dimensional 3 d pose at each time step pose estimation is formulated as a search problem with the search space constrained by the motion trajectory information of the moving object and assumptions about the scene structure a generalized hausdorff 1962 metric which is more robust to noise and allows a confidence interpretation is suggested for the matching procedure used for pose estimation as well as the identification and verification problem the pose evolution curves are used to assist in the acceptance or rejection of an object hypothesis the models are acquired from real image sequences of the objects edge maps are extracted and used for matching results are presented for both infrared and optical sequences containing moving objects involved in complex motions

symmetry based photo editing in this paper we demonstrate how to edit digital photos based on the understanding of high level geometric knowledge imposed upon objects in the photos this is achieved by the correct recovery of the 3 d shape and relationships of the objects without explicitly performing full 3 d reconstruction symmetry is proposed as the central notion that unifies both conceptually and algorithmically all types of geometric regularities such as parallelism orthogonality and similarity the methods are extremely simple accurate easy to implement and they demonstrate the utility of applying scene knowledge to image understanding and editing

simultaneous inference with respect to the best treatment in block designs in many practical situations only inference concerning the unknown best treatment and comparisons of the individual treatments with respect to the best treatment are of primary interest we give an explicit formulation of this problem in the framework of randomized complete block designs a procedure based on sample means and two procedures based on signed ranks are proposed it is seen that for the problem considered these procedures have a substantial advantage over what can be deduced from all pairwise multiple comparisons procedures

localizing overlapping parts by searching the interpretation tree this paper discusses how local measurements of positions and surface normals may be used to identify and locate overlapping objects the objects are modeled as polyhedra or polygons having up to six degrees of positional freedom relative to the sensors the approach operates by examining all hypotheses about pairings between sensed data and object surfaces and efficiently discarding inconsistent ones by using local constraints on distances between faces angles between face normals and angles relative to the surface normals of vectors between sensed points the method described here is an extension of a method for recognition and localization of nonoverlapping parts previously described in 18 and 15

integral invariants for shape matching for shapes represented as closed planar contours we introduce a class of functionals which are invariant with respect to the euclidean group and which are obtained by performing integral operations while such integral invariants enjoy some of the desirable properties of their differential counterparts such as locality of computation which allows matching under occlusions and uniqueness of representation asymptotically they do not exhibit the noise sensitivity associated with differential quantities and therefore do not require presmoothing of the input shape our formulation allows the analysis of shapes at multiple scales based on integral invariants we define a notion of distance between shapes the proposed distance measure can be computed efficiently and allows warping the shape boundaries onto each other its computation results in optimal point correspondence as an intermediate step numerical results on shape matching demonstrate that this framework can match shapes despite the deformation of subparts missing parts and noise as a quantitative analysis we report matching scores for shape retrieval from a database

development of objective oriented groundwater models 2 robust experimental design 1 this paper continues the discussion in part 1 by considering the data collection strategy problem when the existing data are judged to be insufficient for constructing a reliable model designing an experiment for identifying a distributed parameter is very difficult because the identification of a more complex parameter structure requires more data moreover without knowing the sufficiency of a design finding an optimal design becomes meaningless these difficulties can be avoided if we turn to the construction of objective oriented models the identifiability of a distributed parameter as defined in this paper contains the reducibility of parameter structure sufficient conditions for this kind of identifiability are given when the structure error associated with a structure reduction is too large these conditions may not be satisfied no matter how much data are collected in this paper we formulate a new experimental design problem that consists of two objectives minimizing the cost and maximizing the information content with robustness and feasibility as constraints we develop an algorithm that can find a cost effective robust design for objective oriented parameter identification we also present a heuristic algorithm that can find a suboptimal design with less computational effort for real case studies the proposed methodology is used to design a pumping test for identifying a distributed hydraulic conductivity we verify the robustness of the obtained design by assuming that the true parameter may have continuous discrete random and fractured structures finally the presented procedure of constructing objective oriented models is described step by step

adaptive stochastic approximation by the simultaneous perturbation method stochastic approximation sa has long been applied for problems of minimizing loss functions or root finding with noisy input information as with all stochastic search algorithms there are adjustable algorithm coefficients that must be specified and that can have a profound effect on algorithm performance it is known that choosing these coefficients according to an sa analog of the deterministic newton raphson algorithm provides an optimal or near optimal form of the algorithm however directly determining the required hessian matrix or jacobian matrix for root finding to achieve this algorithm form has often been difficult or impossible in practice the paper presents a general adaptive sa algorithm that is based on a simple method for estimating the hessian matrix while concurrently estimating the primary parameters of interest the approach applies in both the gradient free optimization kiefer wolfowitz and root finding stochastic gradient based robbins monro settings and is based on the simultaneous perturbation sp idea introduced previously the algorithm requires only a small number of loss function or gradient measurements per iteration independent of the problem dimension to adaptively estimate the hessian and parameters of primary interest aside from introducing the adaptive sp approach the paper presents practical implementation guidance asymptotic theory and a nontrivial numerical evaluation also included is a discussion and numerical analysis comparing the adaptive sp approach with the iterate averaging approach to accelerated sa

least squares matching problems abstract a large class of matching problems can be thought of in the following way one is given a group g which acts on a riemannian manifold and one is given two points x 1 and x 2 in the manifold the problem is to find g g such that d g x 1 x 2 is as small as possible if the group has finite cardinality this is a combinatorial optimization problem whereas if g is a lie group one can use the calculus to obtain necessary conditions our main results establish circumstances under which one can relax the combinatorial problem to an appropriate lie group problem and then solve it by the method of steepest descent an interesting class of applications involves embedding the permutation group on n letters in the orthogonal group o n with the latter acting on r n n 1 2 via a symmetricized tensor product the convergence properties of the descent equation which arises in this way are analyzed in some detail

recognition by linear combinations of models an approach to visual object recognition in which a 3d object is represented by the linear combination of 2d images of the object is proposed it is shown that for objects with sharp edges as well as with smooth bounding contours the set of possible images of a given object is embedded in a linear space spanned by a small number of views for objects with sharp edges the linear combination representation is exact for objects with smooth boundaries it is an approximation that often holds over a wide range of viewing angles rigid transformations with or without scaling can be distinguished from more general linear transformations of the object by testing certain constraints placed on the coefficients of the linear combinations three alternative methods of determining the transformation that matches a model to a given image are proposed

sequential multiple comparisons with the best abstract in this article we give a method of designing and analyzing an experiment for comparing k 2 treatments such that a a treatment is terminated as soon as there is statistical evidence that it is not the best treatment and b at the conclusion of the experiment one can assert at some prespecified confidence level simultaneously that those terminated treatments are not the best and those remaining treatments are respectively within certain small distances of the unknown best treatment the inference given by our method is stronger than existing sequential elimination selection inference

reconstruction based recognition of scenes with translationally repeated quadrics this paper addresses the problem of invariant based recognition of quadric configurations from a single image these configurations consist of a pair of rigidly connected translationally repeated quadric surfaces this problem is approached via a reconstruction framework a new mathematical framework using relative affine structure on the lines of luong and vieville 1996 has been proposed using this mathematical framework translationally repeated objects have been projectively reconstructed from a single image with four image point correspondences of the distinguished points on the object and its translate this has been used to obtain a reconstruction of a pair of translationally repeated quadrics we have proposed joint projective invariants of a pair of proper quadrics for the purpose of recognition of quadric configurations we compute these invariants for the pair of reconstructed quadrics experimental results on synthetic and real images establish the discriminatory power and stability of the proposed invariant based recognition strategy as a specific example we have applied this technique for discriminating images of monuments which are characterized by translationally repeated domes modeled as quadrics

on symmetry and multiple view geometry structure pose and calibration from a single image in this paper we provide a principled explanation of how knowledge in global 3 d structural invariants typically captured by a group action on a symmetric structure can dramatically facilitate the task of reconstructing a 3 d scene from one or more images more importantly since every symmetric structure admits a canonical coordinate frame with respect to which the group action can be naturally represented the canonical pose between the viewer and this canonical frame can be recovered too which explains why symmetric objects e g buildings provide us overwhelming clues to their orientation and position we give the necessary and sufficient conditions in terms of the symmetry group admitted by a structure under which this pose can be uniquely determined we also characterize when such conditions are not satisfied to what extent this pose can be recovered we show how algorithms from conventional multiple view geometry after properly modified and extended can be directly applied to perform such recovery from all hidden images of one image of the symmetric structure we also apply our results to a wide range of applications in computer vision and image processing such as camera self calibration image segmentation and global orientation large baseline feature matching image rendering and photo editing as well as visual illusions caused by symmetry if incorrectly assumed

multivariate stochastic approximation using a simultaneous perturbation gradient approximation the problem of finding a root of the multivariate gradient equation that arises in function minimization is considered when only noisy measurements of the function are available a stochastic approximation sa algorithm for the general kiefer wolfowitz type is appropriate for estimating the root the paper presents an sa algorithm that is based on a simultaneous perturbation gradient approximation instead of the standard finite difference approximation of keifer wolfowitz type procedures theory and numerical experience indicate that the algorithm can be significantly more efficient than the standard algorithms in large dimensional problems

symmetry as a continuous feature symmetry is treated as a continuous feature and a continuous measure of distance from symmetry in shapes is defined the symmetry distance sd of a shape is defined to be the minimum mean squared distance required to move points of the original shape in order to obtain a symmetrical shape this general definition of a symmetry measure enables a comparison of the amount of symmetry of different shapes and the amount of different symmetries of a single shape this measure is applicable to any type of symmetry in any dimension the symmetry distance gives rise to a method of reconstructing symmetry of occluded shapes the authors extend the method to deal with symmetries of noisy and fuzzy data finally the authors consider grayscale images as 3d shapes and use the symmetry distance to find the orientation of symmetric objects from their images and to find locally symmetric regions in images

learning to track the visual motion of contours abstract a development of a method for tracking visual contours is described given an untrained tracker a training motion of an object can be observed over some extended time and stored as an image sequence the image sequence is used to learn parameters in a stochastic differential equation model these are used in turn to build a tracker whose predictor imitates the motion in the training set tests show that the resulting trackers can be markedly tuned to desired curve shapes and classes of motions

from image quadrilaterals to symmetrical trapezia abstract this paper concerns the 3 d interpretation of image quadrilaterals as the perspective projections of bilateral symmetric trapezia simple algorithms are described for reconstructing a symmetric trapezium from a given image quadrilateral and for determining the 3 d motion of a symmetric trapezium from two matched image quadrilaterals several results are established and or further verified including the necker reversal ambiguity in the interpretation of image quadrilaterals as the perspective projection of bilateral symmetric trapezia experiments with both synthetic and real images are included to demonstrate the validity of the theoretic results

testing for the supremacy of a multinomial cell probability tests for the supremacy of a multinomial cell probability are developed the tested null hypothesis states that a particular cell of interest is not more probable than all others rejection of this null leads to the conclusion that the cell of interest has a strictly greater probability than all other cells the null hypothesis constrains the multinomial probability vector to a nonconvex region that is a union of closed convex cones the likelihood ratio test for this problem is derived and shown to be equivalent to an intersection union test the least favorable configuration of the multinomial probability vector in the null parameter space is derived and the limiting null distribution of the test statistic that is stochastically greatest is shown to be a mixture of point mass at zero and a chi square distribution with a single degree of freedom asymptotic and valid finite sample testing procedures are proposed and examined via a simulation study and the analysis of two datasets the proposed procedure

model free control of nonlinear stochastic systems with discrete time measurements consider the problem of developing a controller for general nonlinear and stochastic systems where the equations governing the system are unknown using discrete time measurement this paper presents an approach for estimating a controller without building or assuming a model for the system such an approach has potential advantages in accommodating complex systems with possibly time varying dynamics the controller is constructed through use of a function approximator such as a neural network or polynomial this paper considers the use of the simultaneous perturbation stochastic approximation algorithm which requires only system measurements a convergence result for stochastic approximation algorithms with time varying objective functions and feedback is established it is shown that this algorithm can greatly enhance the efficiency over more standard stochastic approximation algorithms based on finite difference gradient approximations