uniqueness of 3d pose under weak perspective a geometrical proof we present a purely geometrical proof that under the weak perspective model the 3d pose of a 3 point configuration is determined uniquely up to a reflection by its 2d projection

projection distortion analysis for flattened image mosaicing from straight uniform generalized cylinders this paper presents a new approach for reconstructing images mapped or painted on straight uniform generalized cylinders sugc a set of monocular images is taken from di erent viewpoints in order to be mosaiced and to represent the entire scene in detail the expressions of the sugc s projection axis are derived from two cross sections projected onto the image plane based on these axes we derive the sugc localization in the camera coordinate system we explain how we can nd a virtual image representation when the intersection of the two axes is matched to the image center we analyze the perspective distortions when attening a scene which is mapped on a sugc we evaluate the lower and the upper bounds of the necessary number of views in order to represent the entire scene from a sugc by considering the distortions produced by perspective projection a region matching based mosaicing method is proposed to be applied on the attened images in order to obtain the complete scene the mosaiced scene is visualized on a new synthetic surface by a mapping procedure the proposed algorithm is used for the representation of mural paintings located on sugcs with closed cross sections circles for columns or opened cross sections ellipses or parabolas for vaults 2001 pattern recognition society published by elsevier science ltd all rights reserved

building an identifiable latent class model with covariate effects on underlying and measured variables in recent years latent class models have proven useful for analyzing relationships between measured multiple indicators and covariates of interest such models summarize shared features of the multiple indicators as an underlying categorical variable and the indicators substantive associations with predictors are built directly and indirectly in unique model parameters in this paper we provide a detailed study on the theory and application of building models that allow mediated relationships between primary predictors and latent class membership but that also allow direct effects of secondary covariates on the indicators themselves theory for model identification is developed we detail an expectation maximization algorithm for parameter estimation standard error calculation and convergent properties comparison of the proposed model with models underlying existing latent class modeling software is provided a detailed analysis of how visual impairments affect older persons functioning requiring distance vision is used for illustration

adding a variable in generalized linear models the likelihood ratio statistic can be used to determine the significance of an explanatory variable in a generalized linear model in order to obtain such a statistic however we need two sets of iterations for two maximum likelihoods moreover the statistic is not directed to detect influential or outlying observations that affect the importance of the variable considered therefore we develop relatively simple procedures to help the analyst select an appropriate model and detect the effects of such observations on adding a variable into any model two examples are given for illustration

model based object pose in 25 lines of code in this paper we describe a method for finding the pose of an object from a single image we assume that we can detect and match in the image four or more noncoplanar feature points of the object and that we know their relative geometry on the object the method combines two algorithms the first algorithm pos pose from orthography and scaling approximates the perspective projection with a scaled orthographic projection and finds the rotation matrix and the translation vector of the object by solving a linear system the second algorithm posit pos with iterations uses in its iteration loop the approximate pose found by pos in order to compute better scaled orthographic projections of the feature points then applies pos to these projections instead of the original image projections posit converges to accurate pose measurements in a few iterations posit can be used with many feature points at once for added insensitivity to measurement errors and image noise compared to classic approaches making use of newton s method posit does not require starting from an initial guess and computes the pose using an order of magnitude fewer floating point operations it may therefore be a useful alternative for real time operation when speed is not an issue posit can be written in 25 lines or less in mathematica the code is provided in an appendix

a robust o n solution to the perspective n point problem we propose a noniterative solution for the perspective n point rm p n rm p problem which can robustly retrieve the optimum by solving a seventh order polynomial the central idea consists of three steps 1 to divide the reference points into 3 point subsets in order to achieve a series of fourth order polynomials 2 to compute the sum of the square of the polynomials so as to form a cost function and 3 to find the roots of the derivative of the cost function in order to determine the optimum the advantages of the proposed method are as follows first it can stably deal with the planar case ordinary 3d case and quasi singular case and it is as accurate as the state of the art iterative algorithms with much less computational time second it is the first noniterative rm p n rm p solution that can achieve more accurate results than the iterative algorithms when no redundant reference points can be used n le 5 third large size point sets can be handled efficiently because its computational complexity is o n

localization and homing using combinations of model views abstract navigation involves recognizing the environment identifying the current position within the environment and reaching particular positions we present a method for localization the act of recognizing the environment positioning the act of computing the exact coordinates of a robot in the environment and homing the act of returning to a previously visited position from visual input the method is based on representing the scene as a set of 2d views and predicting the appearances of novel views by linear combinations of the model views the method accurately approximates the appearance of scenes under weak perspective projection analysis of this projection as well as experimental results demonstrate that in many cases this approximation is sufficient to accurately describe the scene when weak perspective approximation is invalid either a larger number of models can be acquired or an iterative solution to account for the perspective distortions can be employed the method has several advantages over other approaches it uses relatively rich representations the representations are 2d rather than 3d and localization can be done from only a single 2d view without calibration the same principal method is applied for both the localization and positioning problems and a simple qualitative algorithm for homing is derived from this method

complete solution classification for the perspective three point problem we use two approaches to solve the perspective three point p3p problem the algebraic approach and the geometric approach in the algebraic approach we use wu ritt s zero decomposition algorithm to give a complete triangular decomposition for the p3p equation system this decomposition provides the first complete analytical solution to the p3p problem we also give a complete solution classification for the p3p equation system i e we give explicit criteria for the p3p problem to have one two three and four solutions combining the analytical solutions with the criteria we provide an algorithm cassc which may be used to find complete and robust numerical solutions to the p3p problem in the geometric approach we give some pure geometric criteria for the number of real physical solutions

recognition using region correspondences recognition systems attempt to recover information about the identity of observed objects and their location in the environment a fundamental problem in recognition is pose estimation this is the problem of using a correspondence between some portions of an object model and some portions of an image to determine whether the image contains an instance of the object and in case it does to determine the transformation that relates the model to the image the current approaches to this problem are divided into methods that use global properties of the object e g centroid and moments of inertia and methods that use local properties of the object e g corners and line segments global properties are sensitive to occlusion and specifically to self occlusion local properties are difficult to locate reliably and their matching involves intensive computation we present a novel method for recognition that uses region information in our approach the model and the image are divided into regions given a match between subsets of regions without any explicit correspondence between different pieces of the regions the alignment transformation is computed the method applies to planar objects under similarity affine and projective transformations and to projections of 3 d objects undergoing affine and projective transformations the new approach combines many of the advantages of the previous two approaches while avoiding some of their pitfalls like the global methods our approach makes use of region information that reflects the true shape of the object but like local methods our approach can handle occlusion

exact and approximate solutions of the perspective three point problem model based pose estimation techniques that match image and model triangles require large numbers of matching operations in real world applications the authors show that by using approximations to perspective 2d lookup tables can be built for each of the triangles of the models an approximation called weak perspective has been applied previously to this problem the authors consider two other perspective approximations paraperspective and orthoperspective these approximations produce lower errors for off center image features than weak perspective

filtering closed curves a closed curve in the plane can be described in several ways we show that a simple representation in terms of radius of curvature versus normal direction has certain advantages in particular convolutional filtering of the extended circular image leads to a closed curve similar filtering operations applied to some other representations of the curve do not guarantee that the result corresponds to a closed curve in one case where a closed curve is produced it is smaller than the original a description of a curve can be based on a sequence of smoothed versions of the curve this is one reason why smoothing of closed curves is of interest

geometric probing of dense range data a new method is presented for the efficient and reliable pose determination of 3d objects in dense range image data the method is based upon a minimalistic geometric probing strategy that hypothesizes the intersection of the object with some selected image point and searches for additional surface data at locations relative to that point the strategy is implemented in the discrete domain as a binary decision tree classifier the tree leaf nodes represent individual voxel templates of the model with one template per distinct model pose the internal nodes represent the union of the templates of their descendant leaf nodes the union of all leaf node templates is the complete template set of the model over its discrete pose space each internal node also encodes a single voxel which is the most common element of its child node templates traversing the free is equivalent to efficiently matching the large set of templates at a selected image seed location the method was implemented and extensive experiments were conducted for a variety of combinations of tree designs and traversals under isolated cluttered and occluded scene conditions the results demonstrated a tradeoff between efficiency and reliability it was concluded that there exist combinations of tree design and traversal which are both highly efficient and reliable

sampling of images for efficient model based vision the problem of matching two planar sets of points in the presence of geometric uncertainty has important applications in pattern recognition image understanding and robotics the first set of points corresponds to the template the other set corresponds to the image that possibly contains one or more deformed versions of the template embedded in a cluttered image significant progress has been made on this problem and various polynomial time algorithms have been proposed we show how to sample the image in linear time reducing the number of foreground points n by a factor of two six for commonly occurring images without degrading the quality of the matching results the direct consequence is a time saving by a factor of 2 sup p 6 sup p for an o n sup p matching algorithm our result applies to a fairly large class of available matching algorithms

cross weighted moments and affine invariants for image registration and matching a framework for deriving a class of new global affine invariants for both object matching and positioning based on a novel concept of cross weighted moments with fractional weights is presented the fractional weight factor allows for a more flexible range to balance between the capability to discriminate between objects that differ only in small shape details and the sensitivity of small shape details to the presence of the noise moreover it makes it possible to arrive at low order zero order affine invariants that are more robust than those derived from higher order regular moments the affine transformation parameters are recovered from the zero and the first order cross weighted moments without requiring any feature point correspondence information the equations used to find the affine transformation parameters are linear algebraic the sensitivity of the cross weighted moment invariants to noise missing data and perspective effects is shown on real images

the complexity of spherical p spin models a second moment approach recently auffinger ben arous and cern initiated the study of critical points of the hamiltonian in the spherical pure pp spin spin glass model and established connections between those and several notions from the physics literature denoting the number of critical values less than nunu by crtn u crtn u they computed the asymptotics of 1nlog ecrtn u 1nlog ecrtn u as nn the dimension of the sphere goes to we compute the asymptotics of the corresponding second moment and show that for p 3p 3 and sufficiently negative uu it matches the first moment e crtn u 2 e crtn u 2 1 as an immediate consequence we obtain that crtn u e crtn u 1crtn u e crtn u 1 in l2l2 and thus in probability for any uu for which ecrtn u ecrtn u does not tend to 00 we prove that the moments match on an exponential scale

a fast expected time algorithm for the 2 d point pattern matching problem point set pattern matching is an integral part ofmany pattern recognition problems we study a randomized algorithm f or the alignment approach to model based recognition under certain mild assumptions we show that ifour scene is a set of n points and our model is a set of min points our algorithm has expected running time o n log m 3 2 for 5nding an occurrence of the model in the scene this is signi5cantly faster than any existing algorithms in the literature we then describe some experimental results on randomly generated data using a practical version ofour algorithm these results agree well with the theoretical analysis 2004 pattern recognition society published by elsevier ltd all rights reserved

re weighting and 1 point ransac based p n n p solution to handle outliers the ability to handle outliers is essential for performing the perspective n n point p n n p approach in practical applications but conventional ransac p3p or p4p methods have high time complexities we propose a fast p n n p solution named r1pp n n p to handle outliers by utilizing a soft re weighting mechanism and the 1 point ransac scheme we first present a p n n p algorithm which serves as the core of r1pp n n p for solving the p n n p problem in outlier free situations the core algorithm is an optimal process minimizing an objective function conducted with a random control point then to reduce the impact of outliers we propose a reprojection error based re weighting method and integrate it into the core algorithm finally we employ the 1 point ransac scheme to try different control points experiments with synthetic and real world data demonstrate that r1pp n n p is faster than ransac p3p or p4p methods especially when the percentage of outliers is large and is accurate besides comparisons with outlier free synthetic data show that r1pp n n p is among the most accurate and fast p n n p solutions which usually serve as the final refinement step of ransac p3p or p4p compared with repp n n p which is the state of the art p n n p algorithm with an explicit outliers handling mechanism r1pp n n p is slower but does not suffer from the percentage of outliers limitation as repp n n p

probabilistic 3d object recognition a probabilistic 3d object recognition algorithm is presented in order to guide the recognition process the probability that match hypotheses between image features and model features are correct is computed a model is developed which uses the probabilistic peaking effect of measured angles and ratios of lengths by tracing iso angle and iso ratio curves on the viewing sphere the model also accounts for various types of uncertainty in the input such as incomplete and inexact edge detection for each match hypothesis the pose of the object and the pose uncertainty which is due to the uncertainty in vertex position are recovered this is used to find sets of hypotheses which reinforce each other by matching features of the same object with compatible uncertainty regions a probabilistic expression is used to rank these hypothesis sets the hypothesis sets with the highest rank are output the algorithm has been fully implemented and tested on real images

an algorithm for projective point matching in the presence of spurious points point matching is the task of finding correspondences between two sets of points such that the two sets of points are aligned with each other pure point matching uses only the location of the points to constrain the problem this is a problem with broad practical applications but it has only been well studied when the geometric transformation relating the two point sets is of a relatively low order here we present a heuristic local search algorithm that can find correspondences between point sets in two dimensions that are related by a projective transform point matching is a harder problem when spurious points appear in the sets to be matched we present a heuristic algorithm which minimizes the effects of spurious points

the illumination invariant recognition of 3d objects using local color invariants traditional approaches to three dimensional object recognition exploit the relationship between three dimensional object geometry and two dimensional image geometry the capability of object recognition systems can be improved by also incorporating information about the color of object surfaces using physical models for image formation the authors derive invariants of local color pixel distributions that are independent of viewpoint and the configuration intensity and spectral content of the scene illumination these invariants capture information about the distribution of spectral reflectance which is intrinsic to a surface and thereby provide substantial discriminatory power for identifying a wide range of surfaces including many textured surfaces these invariants can be computed efficiently from color image regions without requiring any form of segmentation the authors have implemented an object recognition system that indexes into a database of models using the invariants and that uses associated geometric information for hypothesis verification and pose estimation the approach to recognition is based on the computation of local invariants and is therefore relatively insensitive to occlusion the authors present several examples demonstrating the system s ability to recognize model objects in cluttered scenes independent of object configuration and scene illumination the discriminatory power of the invariants has been demonstrated by the system s ability to process a large set of regions over complex scenes without generating false hypotheses

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

learning affine transformations under the assumption of weak perspective two views of the same planar object are related through an affine transformation in this paper we consider the problem of training a simple neural network to learn to predict the parameters of the affine transformation although the proposed scheme has similarities with other neural network schemes its practical advantages are more profound first of all the views used to train the neural network are not obtained by taking pictures of the object from different viewpoints instead the training views are obtained by sampling the space of affine transformed views of the object this space is constructed using a single view of the object fundamental to this procedure is a methodology based on singular value decomposition svd and interval arithmetic ia for estimating the ranges of values that the parameters of affine transformation can assume second the accuracy of the proposed scheme is very close to that of a traditional least squares approach with slightly better space and time requirements a front end stage to the neural network based on principal components analysis pca shows to increase its noise tolerance dramatically and also to guides us in deciding how many training views are necessary in order for the network to learn a good noise tolerant mapping the proposed approach has been tested using both artificial and real data

an algebraic method for detection and recognition of polyhedral objects from a single image abstract this paper proposes an algorithm to recognize rotated scaled or overlapping polyhedral objects using only one orthographic projection the procedure is not based on the numerical solution of nonlinear equations and does not require any a priori knowledge it is an algebraic method for testing whether a cluster of edges and vertices in a line drawing correspond to an orthographic view of a given 3d model it has the advantage of being based on simple algebraic equations which are easy to solve and do not require time consuming numerical procedures

random matrices and complexity of spin glasses cern y abstract we give an asymptotic evaluation of the complexity of spherical p spin spin glass models via random matrix theory this study enables us to obtain detailed infor mation about the bottom of the energy landscape including the absolute minimum the ground state the other local minima and describe an interesting layered structure of the low critical values for the hamiltonians of these models we also show that our ap proach allows us to compute the related tap complexity and extend the results known in the physics literature as an independent tool we prove a ldp for the k th largest eigenvalue of the goe extending the results of bdg01 how many critical values of given index and below a given level does a typical random morse function have on a high dimensional manifold our work addresses this question in a very special case we look at certain natural random gaussian functions on the n dimensional sphere known as p spin spherical spin glass models we cannot yet answer the question above about the typical number but we can study thoroughly the mean number which we show is exponentially large in n we introduce a new identity based on the classical kac rice formula relating random matrix theory and the problem of counting these critical values using this identity and tools from random matrix theory we give an asymptotic evaluation of the complexity of these spherical spin glass models the complexity mentioned here is defined as the mean number of critical points of given index whose value is below or above a given level this includes the important question of counting the mean number of local minima below a given level and in particular the question of finding the ground state energy the minimal value of the hamiltonian we show that this question is directly related to the study of the edge of the spectrum of the gaussian orthogonal ensemble goe the question of computing the complexity of mean field spin glass models has recently been thoroughly studied in the physics literature see for example clr03 and the refer ences therein mainly for a different measure of the complexity i e the mean number of solutions to the thouless anderson palmer equations or tap complexity our approach to the complexity enables us to recover known results in the physics literature about tap complexity to compute the ground state energy when p is even and to describe an interesting layered structure of the low energy levels of the hamiltonians of these models which might prove useful for the study of the metastability of langevin dynamics for these models in longer time scales than those studied in bdg01 the paper is organised as follows in section 2 we give our main results in section 3 we prove two main formulas theorem 2 1 and 2 2 relating random matrix theory specif ically the goe and spherical spin glasses these formulas are direct consequences of the kac rice formula we learned the version needed here in the book at07 for another modern account see aw09 the main new ingredient is the fact that for spherical spin glass models the hessian of the hamiltonian at a critical point conditioned on the value of the hamiltonian is a symmetric gaussian random matrix with independent entries up to symmetry plus a diagonal matrix this implies in particular that it is possible to

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

longitudinal data analysis using generalized linear models summary this paper proposes an extension of generalized linear models to the analysis of longitudinal data we introduce a class of estimating equations that give consistent estimates of the regression parameters and of their variance under mild assumptions about the time dependence the estimating equations are derived without specifying the joint distribution of a subject s observations yet they reduce to the score equations for multivariate gaussian outcomes asymptotic theory is presented for the general class of estimators specific cases in which we assume independence m dependence and exchangeable correlation structures from each subject are discussed efficiency of the proposed estimators in two simple situations is considered the approach is closely related to quasi likelih ood some key ironh estimating equation generalized linear model longitudinal data quasi likelihood repeated measures

graph matching with a dual step em algorithm this paper describes a new approach to matching geometric structure in 2d point sets the novel feature is to unify the tasks of estimating transformation geometry and identifying point correspondence matches unification is realized by constructing a mixture model over the bipartite graph representing the correspondence match and by affecting optimization using the em algorithm according to our em framework the probabilities of structural correspondence gate contributions to the expected likelihood function used to estimate maximum likelihood transformation parameters these gating probabilities measure the consistency of the matched neighborhoods in the graphs the recovery of transformational geometry and hard correspondence matches are interleaved and are realized by applying coupled update operations to the expected log likelihood function we evaluate the technique on two real world problems

differential and numerically invariant signature curves applied to object recognition we introduce a new paradigm the differential invariant signature curve or manifold for the invariant recognition of visual objects a general theorem of e cartan implies that two curves are related by a group transformation if and only if their signature curves are identical the important examples of the euclidean and equi affine groups are discussed in detail secondly we show how a new approach to the numerical approximation of differential invariants based on suitable combination of joint invariants of the underlying group action allows one to numerically compute differential invariant signatures in a fully group invariant manner applications to a variety of fundamental issues in vision including detection of symmetries visual tracking and reconstruction of occlusions are discussed

stochastic relaxation gibbs distributions and the bayesian restoration of images we make an analogy between images and statistical mechanics systems pixel gray levels and the presence and orientation of edges are viewed as states of atoms or molecules in a lattice like physical system the assignment of an energy function in the physical system determines its gibbs distribution because of the gibbs distribution markov random field mrf equivalence this assignment also determines an mrf image model the energy function is a more convenient and natural mechanism for embodying picture attributes than are the local characteristics of the mrf for a range of degradation mechanisms including blurring nonlinear deformations and multiplicative or additive noise the posterior distribution is an mrf with a structure akin to the image model by the analogy the posterior distribution defines another imaginary physical system gradual temperature reduction in the physical system isolates low energy states annealing or what is the same thing the most probable states under the gibbs distribution the analogous operation under the posterior distribution yields the maximum a posteriori map estimate of the image given the degraded observations the result is a highly parallel relaxation algorithm for map estimation we establish convergence properties of the algorithm and we experiment with some simple pictures for which good restorations are obtained at low signal to noise ratios

local minima in disordered mean field ferromagnets we consider the complexity of random ferromagnetic landscapes on the hypercube pm 1 n given by ising models on the complete graph with i i d non negative edge weights this includes in particular the case of bernoulli disorder corresponding to the ising model on a dense random graph mathcal g n p previous results had shown that with high probability as n rightarrow infty the gradient search energy lowering algorithm initialized uniformly at random converges to one of the homogeneous global minima all plus or all minus here we devise two modified algorithms tailored to explore the landscape at near zero magnetizations where the effect of the ferromagnetic drift is minimized with these we numerically verify the landscape complexity of random ferromagnets finding a diverging number of 1 spin flip stable local minima as n rightarrow infty we then investigate some of the properties of these local minima e g typical energy and magnetization and compare to the situation where the edge weights are drawn from a heavy tailed distribution

linear logistic latent class analysis for polytomous data abstract for latent class analysis a widely known statistical method for the unmixing of an observed frequency table into several unobservable ones a flexible model is presented in order to restrain the unknown class sizes mixing weights and the unknown latent response probabilities two systems of basic equations are stated such that they simultaneously allow parameter fixations the equality of certain parameters as well as linear logistic constraints of each of the original parameters the maximum likelihood equations for the parameters of this linear logistic latent class analysis are given and their estimation by means of the em algorithm is described further the criteria for their local identifiability and statistical tests pearson and likelihood ratio 2 for goodness of fit are outlined the practical applicability of linear logistic latent class analysis is demonstrated by three examples mixed logistic regression a mixed bradley terry model for paired comparisons with ties and a lo

matrix completion from a few entries let m be an n n matrix of rank r and assume that a uniformly random subset e of its entries is observed we describe an efficient algorithm which we call optspace that reconstructs m from e o rn observed entries with relative root mean square error 1 2 rmse c nr e 1 2 with probability larger than 1 1 n3 further if r o 1 and m is sufficiently unstructured then optspace reconstructs it exactly from e o n log n entries with probability larger than 1 1 n3 this settles in the case of bounded rank a question left open by candes and recht and improves over the guarantees for their reconstruction algorithm the complexity of our algorithm is o e r log n which opens the way to its use for massive data sets in the process of proving these statements we obtain a generalization of a celebrated result by friedman kahn szemeredi and feige ofek on the spectrum of sparse random matrices

approximate input sensitive algorithms for point pattern matching we study input sensitive algorithms for point pattern matching under various transformations and the hausdorff metric as a distance function given point sets p and q in the plane the problem of point pattern matching is to determine whether p is similar to some portion of q where p may undergo transformations from a group g of allowed transformations all algorithms are based on methods for extracting small subsets from q that can be matched to a small subset of p the runtime is proportional to the number k of these subsets let d be the number of points in p that are needed to define a transformation in g the key observation is that for some set b p of cardinality larger than d the number of subsets of q of this cardinality that match b is practically small as the problem becomes more constrained we present methods to extract efficiently all these subsets in q we provide algorithms for homothetic rigid and similarity transformations in the plane and give a general method that works for any dimension and for any group of transformations the runtime of our algorithms depends roughly linearly on the number of subsets k in addition to an nlogn factor thus our approximate matching algorithms run roughly in time o nlogn kmlogn where m and n are the number of points in p and q respectively the constants hidden in the big o vary depending on the group of transformations g

bayesian inferences of latent class models with an unknown number of classes this paper focuses on analyzing data collected in situations where investigators use multiple discrete indicators as surrogates for example a set of questionnaires a very flexible latent class model is used for analysis we propose a bayesian framework to perform the joint estimation of the number of latent classes and model parameters the proposed approach applies the reversible jump markov chain monte carlo to analyze finite mixtures of multivariate multinomial distributions in the paper we also develop a procedure for the unique labeling of the classes we have carried out a detailed sensitivity analysis for various hyperparameter specifications which leads us to make standard default recommendations for the choice of priors the usefulness of the proposed method is demonstrated through computer simulations and a study on subtypes of schizophrenia using the positive and negative syndrome scale panss

a computational model of view degeneracy we quantify the observation by kender and freudenstein 1987 that degenerate views occupy a significant fraction of the viewing sphere surrounding an object for a perspective camera geometry we introduce a computational model that can be used to estimate the probability that a view degeneracy will occur in a random view of a polyhedral object for a typical recognition system parameterization view degeneracies typically occur with probabilities of 20 percent and depending on the parameterization as high as 50 percent we discuss the impact of view degeneracy on the problem of object recognition and for a particular recognition framework relate the cost of object disambiguation to the probability of view degeneracy to reduce this cost we incorporate our model of view degeneracy in an active focal length control paradigm that balances the probability of view degeneracy with the camera field of view in order to validate both our view degeneracy model as well as our active focal length control model a set of experiments are reported using a real recognition system operating on real images

optimization based model fitting for latent class and latent profile analyses statisticians typically estimate the parameters of latent class and latent profile models using the expectation maximization algorithm this paper proposes an alternative two stage approach to model fitting the first stage uses the modified k means and hierarchical clustering algorithms to identify the latent classes that best satisfy the conditional independence assumption underlying the latent variable model the second stage then uses mixture modeling treating the class membership as known the proposed approach is theoretically justifiable directly checks the conditional independence assumption and converges much faster than the full likelihood approach when analyzing high dimensional data this paper also develops a new classification rule based on latent variable models the proposed classification procedure reduces the dimensionality of measured data and explicitly recognizes the heterogeneous nature of the complex disease which makes it perfect for analyzing high throughput genomic data simulation studies and real data analysis demonstrate the advantages of the proposed method

on the limitation of spectral methods from the gaussian hidden clique problem to rank one perturbations of gaussian tensors we consider the following detection problem given a realization of a symmetric matrix x of dimension n distinguish between the hypothesis that all upper triangular variables are independent and identically distributed i i d gaussians variables with mean 0 and variance 1 and the hypothesis where x is the sum of such matrix and an independent rank one perturbation this setup applies to the situation where under the alternative there is a planted principal submatrix b of size l for which all upper triangular variables are i i d gaussians with mean 1 and variance 1 whereas all other upper triangular elements of x not in b are i i d gaussians variables with mean 0 and variance 1 we refer to this as the gaussian hidden clique problem when l 1 epsilon sqrt n epsilon 0 it is possible to solve this detection problem with probability 1 o n 1 by computing the spectrum of x and considering the largest eigenvalue of x we prove that this condition is tight in the following sense when l no algorithm that examines only the eigenvalues of x can detect the existence of a hidden gaussian clique with error probability vanishing as n to infty we prove this result as an immediate consequence of a more general result on rank one perturbations of k dimensional gaussian tensors in this context we establish a lower bound on the critical signal to noise ratio below which a rank one signal cannot be detected

tensor completion based on nuclear norm minimization for 5d seismic data reconstruction abstractmany standard seismic data processing and imaging techniques require regularly sampled data prestack seismic data are multidimensional signals that can be represented via low rank fourth order tensors in the frequency space f x domain we propose to adopt tensor completion strategies to recover unrecorded observations and to improve the signal to noise ratio of prestack seismic volumes tensor completion can be posed as an inverse problem and solved by minimizing a convex objective function the objective function contains two terms a data misfit and a nuclear norm the data misfit measures the proximity of the reconstructed seismic data to the observations the nuclear norm constraints the reconstructed data to be a low rank tensor in essence we solve the prestack seismic reconstruction problem via low rank tensor completion the cost function of the problem is minimized using the alternating direction method of multipliers we present synthetic examples to illustrate the behavior of the al

the extremal process of critical points of the pure p spin spherical spin glass model recently sharp results concerning the critical points of the hamiltonian of the p spin spherical spin glass model have been obtained by means of moments computations in particular these moments computations allow for the evaluation of the leading term of the ground state i e of the global minimum in this paper we study the extremal point process of critical points that is the point process associated to all critical values in the vicinity of the ground state we show that the latter converges in distribution to a poisson point process of exponential intensity in particular we identify the correct centering of the ground state and prove the convergence in distribution of the centered minimum to a minus gumbel variable these results are identical to what one obtains for a sequence of i i d variables correctly normalized namely we show that the model is in the universality class of rem

complexity of random smooth functions on the high dimensional sphere we analyze the landscape of general smooth gaussian functions on the sphere in dimension n when n is large we give an explicit formula for the asymptotic complexity of the mean number of critical points of finite and diverging index at any level of energy and for the mean euler characteristic of level sets we then find two possible scenarios for the bottom landscape one that has a layered structure of critical values and a strong correlation between indexes and critical values and another where even at levels below the limiting ground state energy the mean number of local minima is exponentially large we end the paper by discussing how these results can be interpreted in the language of spin glasses models

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

free energy of the spherical mean field model we compute at any temperature the free energy of the multi p spin spherical model when only terms for p even are considered

fast and globally convergent pose estimation from video images determining the rigid transformation relating 2d images to known 3d geometry is a classical problem in photogrammetry and computer vision heretofore the best methods for solving the problem have relied on iterative optimization methods which cannot be proven to converge and or which do not effectively account for the orthonormal structure of rotation matrices we show that the pose estimation problem can be formulated as that of minimizing an error metric based on collinearity in object as opposed to image space using object space collinearity error we derive an iterative algorithm which directly computes orthogonal rotation matrices and which is globally convergent experimentally we show that the method is computationally efficient that it is no less accurate than the best currently employed optimization methods and that it outperforms all tested methods in robustness to outliers

concomitant variable latent class models abstract this article introduces and illustrates a new type of latent class model in which the probability of latent class membership is functionally related to concomitant variables with known distribution the function or so called submodel may be logistic exponential or another suitable form concomitant variable models supplement latent class models incorporating grouping by providing more parsimonious representations of data for some cases also concomitant variable models are useful when grouping models involve a greater number of parameters than can be meaningfully fit to existing data sets although parameter estimates may be calculated using standard iterative procedures such as the newton raphson method sample analyses presented here employ a derivative free approach known as the simplex method a general procedure for imposing linear constraints on the parameter estimates is introduced a data set involving arithmetic test items in a mastery testing context is used to illustrate fitting a

aging of spherical spin glasses sompolinski and zippelius 1981 propose the study of dynamical systems whose invariant measures are the gibbs measures for hard to analyze statistical physics models of interest in the course of doing so physicists often report of an aging phenomenon for example aging is expected to happen for the sherrington kirkpatrick model a disordered mean field model with a very complex phase transition in equilibrium at low temperature we shall study the langevin dynamics for a simplified spherical version of this model the induced rotational symmetry of the spherical model reduces the dynamics in question to an n dimensional coupled system of ornstein uhlenbeck processes whose random drift parameters are the eigenvalues of certain random matrices we obtain the limiting dynamics for n approaching infinity and by analyzing its long time behavior explain what is aging mathematically speaking what causes this phenomenon and what is its relationship with the phase transition of the corresponding equilibrium invariant measures

a fourier view on the r transform and related asymptotics of spherical integrals abstract we estimate the asymptotics of spherical integrals of real symmetric or hermitian matrices when the rank of one matrix is much smaller than its dimension we show that it is given in terms of the r transform of the spectral measure of the full rank matrix and give a new proof of the fact that the r transform is additive under free convolution these asymptotics also extend to the case where one matrix has rank one but complex eigenvalue a result related with the analyticity of the corresponding spherical integrals

the perspective view of three points the perspective view of three noncollinear points whose image to object correspondence is known is studied such measurements are known to be ambiguous resulting in as many as four possible solutions to the perspective three point problem although there can be four solutions it is quite often the case that there are triangle configurations that cause one two three or four solutions the results also provide a justification for the common wisdom that there are usually two solutions

recognizing solid objects by alignment with an image in this paper we consider the problem of recognizing solid objects from a single two dimensional image of a three dimensional scene we develop a new method for computing a transformation from a three dimensional model coordinate frame to the two dimensional image coordinate frame using three pairs of model and image points we show that this transformation always exists for three noncollinear points and is unique up to a reflective ambiguity the solution method is closed form and only involves second order equations we have implemented a recognition system that uses this transformation method to determine possible alignments of a model with an image each of these hypothesized matches is verified by comparing the entire edge contours of the aligned object with the image edges using the entire edge contours for verification rather than a few local feature points reduces the chance of finding false matches the system has been tested on partly occluded objects in highly cluttered scenes

applications of tensor theory to object recognition and orientation determination a method is developed by which images resulting from orthogonal projection of rigid planar patch objects arbitrarily oriented in three dimensional 3 d space may be used to form systems of linear equations which are solved for the affine transform relating the images the technique is applicable to complete images and to unlabeled feature sets derived from images and with small modification may be used to transform images of unknown objects such that they represent images of those objects from a known orientation for use in object identification no knowledge of point correspondence between images is required theoretical development of the method and experimental results are presented the method is shown to be computationally efficient requiring o n multiplications and additions where depending on the computation algorithm n may equal the number of object or edge picture elements

a computational approach to edge detection this paper describes a computational approach to edge detection the success of the approach depends on the definition of a comprehensive set of goals for the computation of edge points these goals must be precise enough to delimit the desired behavior of the detector while making minimal assumptions about the form of the solution we define detection and localization criteria for a class of edges and present mathematical forms for these criteria as functionals on the operator impulse response a third criterion is then added to ensure that the detector has only one response to a single edge we use the criteria in numerical optimization to derive detectors for several common image features including step edges on specializing the analysis to step edges we find that there is a natural uncertainty principle between detection and localization performance which are the two main goals with this principle we derive a single operator shape which is optimal at any scale the optimal detector has a simple approximate implementation in which edges are marked at maxima in gradient magnitude of a gaussian smoothed image we extend this simple detector using operators of several widths to cope with different signal to noise ratios in the image we present a general method called feature synthesis for the fine to coarse integration of information from operators at different scales finally we show that step edge detector performance improves considerably as the operator point spread function is extended along the edge

uncertainty propagation in model based recognition robust recognition systems require a careful understanding of the effects of error in sensed features in model based recognition matches between model features and sensed image features typically are used to compute a model pose and then project the unmatched model features into the image the error in the image features results in uncertainty in the projected model features we first show how error propagates when poses are based on three pairs of 3d model and 2d image points in particular we show how to simply and efficiently compute the distributed region in the image where an unmatched model point might appear for both gaussian and bounded error in the detection of image points and for both scaled orthographic and perspective projection models next we provide geometric and experimental analyses to indicate when this linear approximation will succeed and when it will fail then based on the linear approximation we show how we can utilize linear programming to compute bounded propagated error regions for any number of initial matches finally we use these results to extend from two dimensional to three dimensional objects robust implementations of alignment interpretation tree search and transformation clustering

an effective search approach to camera parameter estimation using an arbitrary planar calibration object abstract in this paper we shall present a new method for camera parameter estimation using an arbitrary planar calibration object we begin with an approximate model for the perspective view and give a parameter free normalized line segment ratio relationship between the corresponding reference and sensed views this representation makes parameter decoupling possible and reduces the library dimension from six to one then the estimation problem can be viewed as a library search problem various mechanisms are provided to reduce the library search time including a library partition by clustering b sensed cluster identification by binary search and c sequential testing for view matching using sorted features in addition feature perturbation is also considered to achieve better robustness against feature noise both computer generated and real data are included in experiments illustrating how our method works

on photometric issues in 3d visual recognition from asingle 2d image we describe the problem of recognition under changing illumination conditions and changing viewing positions from a computational and human vision perspective on the computational side we focus on the mathematical problems of creating an equivalence class for images of the same 3d object undergoing certain groups of transformations mostly those due to changing illumination and briefly discuss those due to changing viewing positions the computational treatment culminates in proposing a simple scheme for recognizing via alignment an image of a familiar object taken from a novel viewing position and a novel illumination condition on the human vision aspect the paper is motivated by empirical evidence inspired by mooney images of faces that suggest a relatively high level of visual processing is involved in compensating for photometric sources of variability and furthermore that certain limitations on the admissible representations of image information may exist the psychophysical observations and the computational results that follow agree in several important respects such as the same apparent limitations on image representations

representation and detection of deformable shapes we describe some techniques that can be used to represent and detect deformable shapes in images the main difficulty with deformable template models is the very large or infinite number of possible nonrigid transformations of the templates this makes the problem of finding an optimal match of a deformable template to an image incredibly hard using a new representation for deformable shapes we show how to efficiently find a global optimal solution to the nonrigid matching problem the representation is based on the description of objects using triangulated polygons our matching algorithm can minimize a large class of energy functions making it applicable to a wide range of problems we present experimental results of detecting shapes in medical images and images of natural scenes we also consider the problem of learning a nonrigid shape model for a class of objects from examples we show how to learn good models while constraining them to be in the form required by the matching algorithm

the geometry of the gibbs measure of pure spherical spin glasses we analyze the statics for pure p spin spherical spin glass models with p ge 3 at low enough temperature with f n beta denoting the free energy we compute the logarithmic second order term of nf n beta and prove that for an appropriate centering c n beta nf n beta c n beta is a tight sequence we further establish the absence of temperature chaos those results follow from the following geometric picture we prove for the gibbs measure of interest by itself asymptotically the measure splits into infinitesimal spherical bands centered at deep minima playing the role of pure states for the pure models the latter makes precise the picture of many valleys separated by high mountains and significant parts of the tap analysis from the physics literature

recursive depth parametrization of monocular visual navigation observability analysis and performance evaluation abstract in this paper the theoretical and practical feasibility of estimating ego motion in monocular navigation is under investigation in particular this paper concerns the observability issues of monocular navigation models in order to recover the ego motion of the monocular camera from 2d two dimension image sequence this paper proposes a novel recursive parametric model this model differs from other traditional parametric models with the reduced state dimension and the consistent observability of system state in addition the consistent observability of different models are compared by using time varying observability analysis theory at the end of this paper two groups of experiments are implemented to validate the effectiveness of the proposed method

residual plots for detecting nonlinearity in generalized linear models the added variable plot partial residual plot and constructed variable plot are three useful diagnostic procedures in assessing the accuracy of a normal linear model the first two have been extended to the generalized linear model for detecting nonlinearity of variables i extend the last one an example is given for illustration

3 d pose from 3 points using weak perspective this correspondence discusses computing the pose of a model from three matching point pairs under weak perspective projection a new approach to the problem that is motivated geometrically is described like previous methods the method here involves solving a biquadratic equation but here the biquadratic s solutions comprised of an actual and a false solution are interpreted graphically the final equations take a new form which leads to a simple expression for the image position of any unmatched model point

graphical methods for assessing logistic regression models abstract in ordinary linear regression graphical diagnostic displays can be very useful for detecting and examining anomalous features in the fit of a model to data for logistic regression models the discreteness of binary data makes it difficult to interpret such displays modifications and extensions of linear model displays lead to three methods for diagnostic checking of logistic regression models local mean deviance plots are useful for detecting overall lack of fit empirical probability plots help point out isolated departures from the fitted model partial residual plots when smoothed to show underlying structure help identify specific causes of lack of fit these methods are illustrated through the analyses of simulated and real data

factor analysis and aic the information criterion aic was introduced to extend the method of maximum likelihood to the multimodel situation it was obtained by relating the successful experience of the order determination of an autoregressive model to the determination of the number of factors in the maximum likelihood factor analysis the use of the aic criterion in the factor analysis is particularly interesting when it is viewed as the choice of a bayesian model this observation shows that the area of application of aic can be much wider than the conventional i i d type models on which the original derivation of the criterion was based the observation of the bayesian structure of the factor analysis model leads us to the handling of the problem of improper solution by introducing a natural prior distribution of factor loadings

a study of affine matching with bounded sensor error affine transformations of the plane have been used in a number of model based recognition systems because the underlying mathematics are based on exact data in practice various heuristics are used to adapt the methods to real data where there is positional uncertainty this paper provides a precise analysis of affine point matching under uncertainty we obtain an expression for the range of affine invariant values that are consistent with a given set of four points where each image point lies in an disc of uncertainty this range is shown to depend on the actualx y positions of the data points in other words given uncertainty in the data there are no representations that are invariant with respect to the cartesian coordinate system of the data this is problematic for methods such as geometric hashing that are based on affine invariant representations we also analyze the effect that uncertainty has on the probability that recognition methods using affine transformations will find false positive matches we find that there is a significant probability of false positives with even moderate levels of sensor error suggesting the importance of good verification techniques and good grouping techniques

selecting the number of classes under latent class regression a factor analytic analogue recently the regression extension of latent class analysis rlca model has received much attention in the field of medical research the basic rlca model summarizes shared features of measured multiple indicators as an underlying categorical variable and incorporates the covariate information in modeling both latent class membership and multiple indicators themselves to reduce complexity and enhance interpretability one usually fixes the number of classes in a given rlca often goodness of fit methods comparing various estimated models are used as a criterion to select the number of classes in this paper we propose a new method that is based on an analogous method used in factor analysis and does not require repeated fitting two ideas with application to many settings other than ours are synthesized in deriving the method a connection between latent class models and factor analysis and techniques of covariate marginalization and elimination a monte carlo simulation study is presented to evaluate the behavior of the selection procedure and compare to alternative approaches data from a study of how measured visual impairments affect older persons functioning are used for illustration

efficient pose clustering using a randomized algorithm pose clustering is a method to perform object recognition by determining hypothetical object poses and finding clusters of the poses in the space of legal object positions an object that appears in an image will yield a large cluster of such poses close to the correct position of the object if there are m model features and n image features then there are o m 3n 3 hypothetical poses that can be determined from minimal information for the case of recognition of three dimensional objects from feature points in two dimensional images rather than clustering all of these poses we show that pose clustering can have equivalent performance for this case when examining only o mn poses due to correlation between the poses if we are given two correct matches between model features and image features since we do not usually know two correct matches in advance this property is used with randomization to decompose the pose clustering problem into o n 2 problems each of which clusters o mn poses for a total complexity of o mn 3 further speedup can be achieved through the use of grouping techniques this method also requires little memory and makes the use of accurate clustering algorithms less costly we use recursive histograming techniques to perform clustering in time and space that is guaranteed to be linear in the number of poses finally we present results demonstrating the recognition of objects in the presence of noise clutter and occlusion

pose determination of a three dimensional object using triangle pairs a procedure is presented to estimate the unconstrained three dimensional location and orientation of an object with a known shape when it is visible in a single image using a generalized hough transform all six parameters of the object position are estimated from the distribution of values determined by matching triples of points on the object to possibly corresponding triples in the image most likely candidates for location are found and then the remaining rotational parameters are evaluated two solutions are generally admitted to the distribution by every match of triangles the number of possible matches is reduced by checking a simple geometric relation among triples even with partial occlusion experiments indicate that the procedure is very reliably accurate although optimization can further improve estimates of the parameters

on the sensitivity of the hough transform for object recognition object recognition from sensory data involves in part determining the pose of a model with respect to a scene a common method for finding an object s pose is the generalized hough transform which accumulates evidence for possible coordinate transformations in a parameter space whose axes are the quantized transformation parameters large clusters of similar transformations in that space are taken as evidence of a correct match a theoretical analysis of the behavior of such methods is presented the authors derive bounds on the set of transformations consistent with each pairing of data and model features in the presence of noise and occlusion in the image bounds are provided on the likelihood of false peaks in the parameter space as a function of noise occlusion and tessellation effects it is argued that haphazardly applying such methods to complex recognition tasks is risky as the probability of false positives can be very high

scale based description and recognition of planar curves and two dimensional shapes the problem of finding a description at varying levels of detail for planar curves and matching two such descriptions is posed and solved in this paper a number of necessary criteria are imposed on any candidate solution method path based gaussian smoothing techniques are applied to the curve to find zeros of curvature at varying levels of detail the result is the generalized scale space image of a planar curve which is invariant under rotation uniform scaling and translation of the curve these properties make the scale space image suitable for matching the matching algorithm is a modification of the uniform cost algorithm and finds the lowest cost match of contours in the scale space images it is argued that this is preferable to matching in a so called stable scale of the curve because no such scale may exist for a given curve this technique is applied to register a landsat satellite image of the strait of georgia b c manually corrected for skew to a map containing the shorelines of an overlapping area