camera calibration with one dimensional objects camera calibration has been studied extensively in computer vision and photogrammetry and the proposed techniques in the literature include those using 3d apparatus two or three planes orthogonal to each other or a plane undergoing a pure translation etc 2d objects planar patterns undergoing unknown motions and 0d features self calibration using unknown scene points yet the paper proposes a new calibration technique using 1d objects points aligned on a line thus filling the missing dimension in calibration in particular we show that camera calibration is not possible with free moving 1d objects but can be solved if one point is fixed a closed form solution is developed if six or more observations of such a 1d object are made for higher accuracy a nonlinear technique based on the maximum likelihood criterion is then used to refine the estimate singularities have also been studied besides the theoretical aspect the proposed technique is also important in practice especially when calibrating multiple cameras mounted apart from each other where the calibration objects are required to be visible simultaneously

b rep object description from multiple range views we present a system which computes an integrated description of an object from multiple range images the object description is in the form of b rep boundary representation which has not been achieved by the computer vision community to do so we emphasize the inherent difficulties and ambiguities in the low to mid level vision and present novel techniques of resolving them in this system each view of the object is represented as an attributed graph where nodes correspond to the surfaces vertices and links represent the relationship between surfaces the main issue in surface extraction is contour closure which is formulated as a dynamic network the underlying principle for this network is weak smoothness and geometric cohesion and is modeled as the interaction between long and short term variables long term variables represent the initial boundary grouping computed from the low level surface features and short term variables represent the competing hypotheses that cooperate with the long term variables the matching problem involves matching visible surfaces and vertices and provides the necessary basis for volumetric reconstruction from multiple views the matching strategy is a two step process where in each step uses the hopfield network at each step we specify a set of local adjacency and global constraints and define an appropriate energy function to be minimized at the first level of this hierarchy surface patches are matched and the rigidity transformation is computed at the second level the mapping is refined by matching the corresponding vertices and the transformation is verified the multiple view reconstruction consists of two steps first we build a composite graph that contains the bounding surfaces and their corresponding attributes and then intersect these surfaces so that the edges and vertices corresponding to the b rep description are identified we present results on objects with planar as well as quadratically curved surfaces

optimum asymptotic multiuser efficiency of randomly spread cdma this correspondence analyzes the high signal to noise ratio snr performance of optimum multiuser detectors for synchronous direct sequence spread spectrum with random spreading in an additive white gaussian noise channel under very general conditions on the received powers we show that the optimum asymptotic efficiency of a k user system with spreading gain n converges to 1 almost surely as k spl rarr spl infin and k n is kept equal to an arbitrary nonzero constant therefore the asymptotic behavior of the minimum bit error rate is equivalent to that of a single user system

the spectral radius of large random matrices let m ij i 1 2 ldots j 1 2 ldots be iid random variables with em 11 0 and em 2 11 sigma 2 for each n define m n m ij 1 leq i j leq n the n times n matrix whose i j component is m ij we show that lim sup n rightarrow infty rho n leq sigma a s where rho n is the spectral radius of m n sqrt n evidence from computer experiments indicates that in fact rho n rightarrow sigma a s

outliers in the spectrum of iid matrices with bounded rank perturbations it is known that if one perturbs a large iid random matrix by a bounded rank error then the majority of the eigenvalues will remain distributed according to the circular law however the bounded rank perturbation may also create one or more outlier eigenvalues we show that if the perturbation is small then the outlier eigenvalues are created next to the outlier eigenvalues of the bounded rank perturbation but if the perturbation is large then many more outliers can be created and their law is governed by the zeroes of a random laurent series with gaussian coefficients on the other hand these outliers may be eliminated by enforcing a row sum condition on the final matrix

on the singularity of adjacency matrices for random regular digraphs we prove that the non symmetric adjacency matrix of a uniform random d regular directed graph on n vertices is asymptotically almost surely invertible assuming min d n d ge c log 2n for a sufficiently large constant c 0 the proof makes use of a coupling of random regular digraphs formed by shuffling the neighborhood of a pair of vertices as well as concentration results for the distribution of edges proved in cook random struct algorithms arxiv 1410 5595 2014 we also apply our general approach to prove asymptotically almost surely invertibility of hadamard products varsigma mathrm circ varxi where varxi is a matrix of iid uniform pm 1 signs and varsigma is a 0 1 matrix whose associated digraph satisfies certain expansion properties

how many eigenvalues of a random matrix are real let a be an n x n matrix whose elements are independent random variables with standard normal distributions as n oo the expected number of real eigenvalues is asymptotic to v 7r we obtain a closed form expres sion for the expected number of real eigenvalues for finite n and a formula for the density of a real eigenvalue for finite n asymptotically a real normalized eigenvalue al ii of such a random matrix is uniformly distributed on the in terval 1 1 analogous but strikingly different results are presented for the real generalized eigenvalues we report on numerical experiments confirming these results and suggesting that the assumption of normality is not important for the asymptotic results department of mathematics massachusetts institute of technology cambridge massachusetts 02139 e mail address edelmanfmath mit edu arts and sciences kapi olani community college 4303 diamond head road honolulu hawaii 98616 e mail address kostlanfkahuna math hawaii edu tj watson rsearch center 32 2 ibm yorktown heights new york 10598 0218 e mail address shubqwatson ibm com this content downloaded from 157 55 39 29 on tue 12 apr 2016 08 54 01 utc all use subject to http about jstor org terms

lyapunov exponents for products of rectangular real complex and quaternionic ginibre matrices we study the joint density of eigenvalues for products of independent rectangular real complex and quaternionic ginibre matrices in the limit where the number of matrices tends to infinity it is shown that the joint probability density function for the eigenvalues forms a permanental point process for all three classes the moduli of the eigenvalues become uncorrelated and log normal distributed while the distribution for the phases of the eigenvalues depends on whether real complex or quaternionic ginibre matrices are considered in the derivation for a product of real matrices we explicitly use the fact that all eigenvalues become real when the number of matrices tends to infinity finally we compare our results with known results for the lyapunov exponents as well as numerical simulations

the circular law for random matrices we consider the joint distribution of real and imaginary parts of eigenvalues of random matrices with independent real entries with mean zero and unit variance we prove the convergence of this distribution to the uniform distribution on the unit disc without assumptions on the existence of a density for the distribution of entries we assume that the entries have a finite moment of order larger than two and consider the case of sparse matrices the results are based on previous work of bai rudelson and the authors extending results to a larger class of sparse matrices

extension of dynamic link matching by introducing local linear maps it is well known that dynamic link matching dlm is a flexible pattern matching model tolerant of deformation or nonlinear transformation however previous models cannot treat severely deformed data pattern in which local features do not have their counterparts in a template pattern we extend dlm by introducing local linear maps llms our model has a reference vector and an llm for each lattice point of a data pattern the reference vector maps the lattice point into a template pattern and the llm carries the information regarding how the local neighborhood is mapped our model transforms local features by llms in a data pattern and then matches them with their counterparts in a template pattern therefore our model is adaptable to larger transformations for simplicity we restricted llms to rotations neighboring llms are diffusionally coupled with each other the model is numerically demonstrated to be very flexible in dealing with deformation and rotation compared to previous models the framework of our model can be easily extended to models with more general llms expansion contraction and so on

rapid and brief communication camera calibration with one dimensional objects moving under gravity camera calibration using one dimensional 1d rigid objects is arresting the attentions of researchers since the easy to construct geometrical structure of the apparatuses in this paper we extend the motion patterns applicable for calibration with the motion of 1d objects we show that a 1d object with three or more markers rotating around one marker which is moving in a plane provides constraint equations on camera intrinsic parameters a stick moving under gravity without other forces acting on performs such a motion simulated tests show the feasibility and numerical robustness of this method

limit of the smallest eigenvalue of a large dimensional sample covariance matrix in this paper the authors show that the smallest if p leq n or the p n 1 th smallest if p n eigenvalue of a sample covariance matrix of the form 1 n xx tends almost surely to the limit 1 sqrt y 2 as n rightarrow infty and p n rightarrow y in 0 infty where x is a p times n matrix with iid entries with mean zero variance 1 and fourth moment finite also as a by product it is shown that the almost sure limit of the largest eigenvalue is 1 sqrt y 2 a known result obtained by yin bai and krishnaiah the present approach gives a unified treatment for both the extreme eigenvalues of large sample covariance matrices

on the spectra of gaussian matrices abstract we give a simple characterization of the moduli of the eigenvalues of a complex gaussian matrix in terms of x 2 distributions we also show that the spectral radius of a k k complex gaussian matrix is stochastically smaller than the norm of a k k 1 real gaussian matrix

invertibility of sparse non hermitian matrices abstract we consider a class of sparse random matrices of the form a n i j i j i j 1 n where i j are i i d centered random variables and i j are i i d bernoulli random variables taking value 1 with probability p n and prove a quantitative estimate on the smallest singular value for p n log n n under a suitable assumption on the spectral norm of the matrices this establishes the invertibility of a large class of sparse matrices for p n n with some 0 1 we deduce that the condition number of a n is of order n with probability tending to one under the optimal moment assumption on i j this in particular extends a conjecture of von neumann about the condition number to sparse random matrices with heavy tailed entries in the case that the random variables i j are i i d sub gaussian we further show that a sparse random matrix is singular with probability at most exp c n p n whenever p n is above the critical threshold p n log n n the results also extend to the case when i j have a non zero mean we further find quantitative estimates on the smallest singular value of the adjacency matrix of a directed erd s reyni graph whenever its edge connectivity probability is above the critical threshold log n n

the littlewood offord problem and invertibility of random matrices abstract we prove two basic conjectures on the distribution of the smallest singular value of random n n matrices with independent entries under minimal moment assumptions we show that the smallest singular value is of order n 1 2 which is optimal for gaussian matrices moreover we give a optimal estimate on the tail probability this comes as a consequence of a new and essentially sharp estimate in the littlewood offord problem for i i d random variables x k and real numbers a k determine the probability p that the sum k a k x k lies near some number v for arbitrary coefficients a k of the same order of magnitude we show that they essentially lie in an arithmetic progression of length 1 p

the distribution of overlaps between eigenvectors of ginibre matrices we study the overlaps between eigenvectors of nonnormal matrices they quantify the stability of the spectrum and characterize the joint eigenvalues increments under dyson type dynamics well known work by chalker and mehlig calculated the expectation of these overlaps for complex ginibre matrices for the same model we extend their results by deriving the distribution of diagonal overlaps the condition numbers and their correlations we prove i convergence of condition numbers for bulk eigenvalues to an inverse gamma distribution more generally we decompose the quenched overlap i e conditioned on eigenvalues as a product of independent random variables ii asymptotic expectation of off diagonal overlaps both for microscopic or mesoscopic separation of the corresponding eigenvalues iii decorrelation of condition numbers associated to eigenvalues at mesoscopic distance at polynomial speed in the dimension iv second moment asymptotics to identify the fluctuations order for off diagonal overlaps when the related eigenvalues are separated by any mesoscopic scale v a new formula for the correlation between overlaps for eigenvalues at microscopic distance both diagonal and off diagonal these results imply estimates on the extreme condition numbers the volume of the pseudospectrum and the diffusive evolution of eigenvalues under dyson type dynamics at equilibrium

no eigenvalues outside the support of the limiting spectral distribution of large dimensional sample covariance matrices let b n 1 n t n 1 2 x n x n t n 1 2 where x n is n times n with i i d complex standardized entries having finite fourth moment and t n 1 2 is a hermitian square root of the nonnegative definite hermitian matrix t n it is known that as n to infty if n n converges to a positive number and the empirical distribution of the eigenvalues of t n converges to a proper probability distribution then the empirical distribution of the eigenvalues of b n converges a s to a nonrandom limit in this paper we prove that under certain conditions on the eigenvalues of t n for any closed interval outside the support of the limit with probability 1 there will be no eigenvalues in this interval for all n sufficiently large

maximum of the characteristic polynomial of the ginibre ensemble we compute the leading asymptotics for the maximum of the centered logarithm of the absolute value of the characteristic polynomial denoted psi n of the ginibre ensemble as the dimension of the random matrix n tends to infty the method relies on the log correlated structure of the field psi n and we obtain the lower bound for the maximum by constructing a family of gaussian multiplicative chaos measures associated with certain regularization of psi n at small mesoscopic scales we also obtain the leading asymptotics for the dimensions of the sets of thick points and verify that they are consistent with the predictions coming from the gaussian free field a key technical input is the approach from ameur et al ann probab 43 3 1157 1201 2015 to derive the necessary asymptotics as well as the results from webb and wong proc lond math soc 3 118 5 1017 1056 2019

gaussian fluctuations for non hermitian random matrix ensembles consider an ensemble of n n non hermitian matrices in which all entries are independent identically distributed complex random variables of mean zero and absolute mean square one if the entry distributions also possess bounded densities and finite 4 moments then z d bai ann probab 25 1997 494 529 has shown the ensemble to satisfy the circular law after scaling by a factor of 1 sqrt n and letting n the empirical measure of the eigenvalues converges weakly to the uniform measure on the unit disk in the complex plane in this note we investigate fluctuations from the circular law in a more restrictive class of non hermitian matrices for which higher moments of the entries obey a growth condition the main result is a central limit theorem for linear statistics of type xn f k 1nf k where 1 2 n denote the ensemble eigenvalues and the test function f is analytic on an appropriate domain the proof is inspired by bai and silverstein ann probab 32 2004 533 605 where the analogous result for random sample covariance matrices is established

overcrowding estimates for zeroes of planar and hyperbolic gaussian analytic functions we consider the point process of zeroes of certain gaussian analytic functions and find the asymptotics for the probability that there are more than m points of the process in a fixed disk of radius r as r rightarrow infty for the planar gaussian analytic function sum n geq 0 frac a n z n sqrt n we show that this probability is asymptotic to e frac 1 2 m 2 log m for the hyperbolic gaussian analytic functions sum n geq 0 rho choose n 1 2 a n z n rho 0 we show that this probability decays like e cm 2

spectrum of large random reversible markov chains heavy tailed weights on the complete graph we consider the random reversible markov kernel k obtained by assigning i i d non negative weights to the edges of the complete graph over n vertices and normalizing by the corresponding row sum the weights are assumed to be in the domain of attraction of an alpha stable law with alpha in 0 2 when 1 alpha 2 we show that for a suitable regularly varying sequence kappa n of index 1 1 alpha the limiting spectral distribution mu alpha of kappa n k coincides with the one of the random symmetric matrix of the un normalized weights levy matrix with i i d entries in contrast when 0 alpha 1 we show that the empirical spectral distribution of k converges without rescaling to a non trivial law wmu alpha supported on 1 1 whose moments are the return probabilities of the random walk on the poisson weighted infinite tree pwit introduced by aldous the limiting spectral distributions are given by the expected value of the random spectral measure at the root of suitable self adjoint operators defined on the pwit this characterization is used together with recursive relations on the tree to derive some properties of mu alpha and wmu alpha we also study the limiting behavior of the invariant probability measure of k

random stochastic matrices from classical compact lie groups and symmetric spaces we consider random stochastic matrices m with elements given by mij uij 2 with u being uniformly distributed on one of the classical compact lie groups or some of the associated symmetric spaces we observe numerically that for large dimensions the spectral statistics of m discarding the perron frobenius eigenvalue 1 are similar to those of the gaussian orthogonal ensemble for symmetric matrices and to those of the real ginibre ensemble for nonsymmetric matrices we compute some spectral statistics using weingarten functions and establish connections with some difficult enumerative problems involving permutations

eigen inference for energy estimation of multiple sources in this paper a new method is introduced to blindly estimate the transmit power of multiple signal sources in multiantenna fading channels when the number of sensing devices and the number of available samples are sufficiently large compared to the number of sources recent advances in the field of large dimensional random matrix theory are used that result in a simple and computationally efficient consistent estimator of the power of each source a criterion to determine the minimum number of sensors and the minimum number of samples required to achieve source separation is then introduced simulations are performed that corroborate the theoretical claims and show that the proposed power estimator largely outperforms alternative power inference techniques

harmonic analysis in phase space and finite weyl heisenberg ensembles weyl heisenberg ensembles are translation invariant determinantal point processes on mathbb r 2d associated with the schrodinger representation of the heisenberg group and include as examples the ginibre ensemble and the polyanalytic ensembles which model the higher landau levels in physics we introduce finite versions of the weyl heisenberg ensembles and show that they behave analogously to the finite ginibre ensembles more specifically guided by the observation that the ginibre ensemble with n points is asymptotically close to the restriction of the infinite ginibre ensemble to the disk of area n we define finite wh ensembles as adequate finite approximations of the restriction of infinite wh ensembles to a given domain omega we provide a precise rate for the convergence of the corresponding one point intensities to the indicator function of omega as omega is dilated and the process is rescaled proportionally thermodynamic regime the construction and analysis rely neither on explicit formulas nor on the asymptotics for orthogonal polynomials but rather on phase space methods second we apply our construction to study the pure finite ginibre type polyanalytic ensembles which model finite particle systems in a single landau level and are defined in terms of complex hermite polynomials on a technical level we show that finite wh ensembles provide an approximate model for finite polyanalytic ginibre ensembles and we quantify the corresponding deviation by means of this asymptotic description we derive estimates for the rate of convergence of the one point intensity of polyanalytic ginibre ensembles in the thermodynamic limit

absolute continuity and singularity of palm measures of the ginibre point process we prove a dichotomy between absolute continuity and singularity of the ginibre point process mathsf g and its reduced palm measures mathsf g mathbf x mathbf x in mathbb c ell ell 0 1 2 ldots namely reduced palm measures mathsf g mathbf x and mathsf g mathbf y for mathbf x in mathbb c ell and mathbf y in mathbb c n are mutually absolutely continuous if and only if ell n they are singular each other if and only if ell not n furthermore we give an explicit expression of the radon nikodym density d mathsf g mathbf x d mathsf g mathbf y for mathbf x mathbf y in mathbb c ell

circular law theorem for random markov matrices let xjk jk 1 be i i d nonnegative random variables with bounded density mean m and finite positive variance 2 let m be the n n random markov matrix with i i d rows defined by m jk x jk x j1 cdots x jn in particular when x11 follows an exponential law the random matrix m belongs to the dirichlet markov ensemble of random stochastic matrices let 1 n be the eigenvalues of sqrt n m i e the roots in mathbb c of its characteristic polynomial our main result states that with probability one the counting probability measure frac 1 n delta lambda 1 cdots frac 1 n delta lambda n converges weakly as n to the uniform law on the disk z in mathbb c z leq m 1 sigma the bounded density assumption is purely technical and comes from the way we control the operator norm of the resolvent

weighted similarity invariant linear algorithm for camera calibration with rotating 1 d objects in this paper a weighted similarity invariant linear algorithm for camera calibration with rotating 1 d objects is proposed first we propose a new estimation method for computing the relative depth of the free endpoint on the 1 d object and prove its robustness against noise compared with those used in previous literature the introduced estimator is invariant to image similarity transforms resulting in a similarity invariant linear calibration algorithm which is slightly more accurate than the well known normalized linear algorithm then we use the reciprocals of the standard deviations of the estimated relative depths from different images as the weights on the constraint equations of the similarity invariant linear calibration algorithm and propose a weighted similarity invariant linear calibration algorithm with higher accuracy experimental results on synthetic data as well as on real image data show the effectiveness of our proposed algorithm

dimension reduction by local principal component analysis reducing or eliminating statistical redundancy between the components of high dimensional vector data enables a lower dimensional representation without significant loss of information recognizing the limitations of principal component analysis pca researchers in the statistics and neural network communities have developed nonlinear extensions of pca this article develops a local linear approach to dimension reduction that provides accurate representations and is fast to compute we exercise the algorithms on speech and image data and compare performance with pca and with neural network implementations of nonlinear pca we find that both nonlinear techniques can provide more accurate representations than pca and show that the local linear techniques outperform neural network implementations

in defense of the eight point algorithm the fundamental matrix is a basic tool in the analysis of scenes taken with two uncalibrated cameras and the eight point algorithm is a frequently cited method for computing the fundamental matrix from a set of eight or more point matches it has the advantage of simplicity of implementation the prevailing view is however that it is extremely susceptible to noise and hence virtually useless for most purposes this paper challenges that view by showing that by preceding the algorithm with a very simple normalization translation and scaling of the coordinates of the matched points results are obtained comparable with the best iterative algorithms this improved performance is justified by theory and verified by extensive experiments on real images

learning symmetry groups with hidden units beyond the perceptron learning to recognize mirror rotational and translational symmetries is a difficult problem for massively parallel network models these symmetries cannot be learned by first order perceptrons or hopfield networks which have no means for incorporating additional adaptive units that are hidden from the input and output layers we demonstrate that the boltzmann learning algorithm is capable of finding sets of weights which turn hidden units into useful higher order feature detectors capable of solving symmetry problems

limiting behavior of the norm of products of random matrices and two problems of geman hwang abstract in the theory of large random matrices how to dominate the norm of a random matrix is a very important problem this paper considers a different type of random matrices namely w to the k power i e a power of a square random matrix with iid entries the first result in this paper is the limit as n approaches infinity of the absolute value of w sq rt n to the k power is or 1 k sigma to the k power where n is the size of w and here sigma sq is the variance of the entries of w we assume only the existence of the 4 th moment of the entries of w from this result it is easy to show that the spectral radius of w sq rt n is not greater then sigma with probability 1 this result is known only for iid n o sigma sq case in proving the above result a new kind of graphs has to be discussed carefully and the truncation method used in yin bai krishnaiah is also important here

geometric camera calibration using circular control points modern ccd cameras are usually capable of a spatial accuracy greater than 1 50 of the pixel size however such accuracy is not easily attained due to various error sources that can affect the image formation process current calibration methods typically assume that the observations are unbiased the only error is the zero mean independent and identically distributed random noise in the observed image coordinates and the camera model completely explains the mapping between the 3d coordinates and the image coordinates in general these conditions are not met causing the calibration results to be less accurate than expected in the paper a calibration procedure for precise 3d computer vision applications is described it introduces bias correction for circular control points and a nonrecursive method for reversing the distortion model the accuracy analysis is presented and the error sources that can reduce the theoretical accuracy are discussed the tests with synthetic images indicate improvements in the calibration results in limited error conditions in real images the suppression of external error sources becomes a prerequisite for successful calibration

quantitative estimates of the convergence of the empirical covariance matrix in log concave ensembles let k be an isotropic convex body in rn given e 0 how many independent points xi uniformly distributed on k are neededfor the empirical covariance matrix to approximate the identity up to e with overwhelming probability our paper answers this question from 12 more precisely let x rn be a centered random vector with a log concave distribution and with the identity as covariance matrix an example of such a vector x is a random point in an isotropic convex body we show that for any e 0 there existsc e 0 su ch that if n c e n and xi i n are i i d copies of 1 n x then n i 1 xi xi id e with probability larger than 1 exp c n

camera calibration with moving one dimensional objects in this paper we show that the rotating 1d calibrating object used in the literature is in essence equivalent to a familiar 2d planar calibration object in addition we also show that when the 1d object undergoes a planar motion rather than rotating around a fixed point such equivalence still holds but the traditional way fails to handle it experiments are carried out to verify the theoretical correctness and numerical robustness of our results

random matrices universality of esds and the circular law given an n x n complex matrix a let mu a x y 1 n vertical bar 1 i n re lambda i x im lambda i y vertical bar be the empirical spectral distribution esd of its eigenvalues lambda i is an element of c i l n we consider the limiting distribution both in probability and in the almost sure convergence sense of the normalized esd mu 1 root n an of a random matrix a n a ij 1 i j n where the random variables a ij e a ij are i i d copies of a fixed random variable x with unit variance we prove a universality principle for such ensembles namely that the limit distribution in question is independent of the actual choice of x in particular in order to compute this distribution one can assume that x is real or complex gaussian as a related result we show how laws for this esd follow from laws for the singular value distribution of 1 root n a n zi for complex z as a corollary we establish the circular law conjecture both almost surely and in probability which asserts that mu 1 root n an converges to the uniform measure on the unit disc when the a ij have zero mean

spectrum of non hermitian heavy tailed random matrices let x jk j k 1 be i i d complex random variables such that x jk is in the domain of attraction of an alpha stable law with 0 alpha 2 our main result is a heavy tailed counterpart of girko s circular law namely under some additional smoothness assumptions on the law of x jk we prove that there exists a deterministic sequence a n n 1 alpha and a probability measure mu alpha on c depending only on alpha such that with probability one the empirical distribution of the eigenvalues of the rescaled matrix a n 1 x jk 1 j k n converges weakly to mu alpha as n tends to infinity our approach combines aldous steele s objective method with girko s hermitization using logarithmic potentials the underlying limiting object is defined on a bipartized version of aldous poisson weighted infinite tree recursive relations on the tree provide some properties of mu alpha in contrast with the hermitian case we find that mu alpha is not heavy tailed

constraints on general motions for camera calibration with one dimensional objects this paper focuses on two problems in camera calibration with one dimensional 1d objects a to find out the general motion patterns well suited for solving the calibration problem and b to improve the robustness and accuracy of the method firstly a sufficient and necessary condition for the solvability of 1d calibration with general motions is proved then the special motion of tossing a 1d object is provided as an example to illustrate the correctness and feasibility of this condition after that some practical issues on obtaining the solution are inspected by avoiding singularities the precision and robustness of the method are improved the relative mean errors are reduced to less than 5 at the noise level of one pixel which surpasses the state of the art methods of the same category

spectrum of markov generators on sparse random graphs we investigate the spectrum of the infinitesimal generator of the continuous time random walk on a randomly weighted oriented graph this is the non hermitian random nxn matrix l defined by l j k x j k if k j and l j j sum l j k k j where x j k are i i d random weights under mild assumptions on the law of the weights we establish convergence as n tends to infinity of the empirical spectral distribution of l after centering and rescaling in particular our assumptions include sparse random graphs such as the oriented erd s renyi graph where each edge is present independently with probability p n 0 as long as np n log n 6 the limiting distribution is characterized as an additive gaussian deformation of the standard circular law in free probability terms this coincides with the brown measure of the free sum of the circular element and a normal operator with gaussian spectral measure the density of the limiting distribution is analyzed using a subordination formula furthermore we study the convergence of the invariant measure of l to the uniform distribution and establish estimates on the extremal eigenvalues of l

brown s spectral distribution measure for r diagonal elements in finite von neumann algebras abstract in 1983 l g brown introduced a spectral distribution measure for non normal elements in a finite von neumann algebra m with respect to a fixed normal faithful tracial state in this paper we compute brown s spectral distribution measure in case t has a polar decomposition t uh where u is a haar unitary and u and h are free when ker t 0 this is equivalent to that t t is an r diagonal pair in the sense of nica and speicher the measure t is expressed explicitly in terms of the s transform of the distribution t t of the positive operator t t in case t is a circular element i e t x1 ix2 2 where x1 x2 is a free semicircular system then sp t d the closed unit disk and t has constant density 1 on d

constrained optimization for neural map formation a unifying framework for weight growth and normalization computational models of neural map formation can be considered on at least three different levels of abstraction detailed models including neural activity dynamics weight dynamics that abstract from the neural activity dynamics by an adiabatic approximation and constrained optimization from which equations governing weight dynamics can be derived constrained optimization uses an objective function from which a weight growth rule can be derived as a gradient flow and some constraints from which normalization rules are derived in this article we present an example of how an optimization problem can be derived from detailed nonlinear neural dynamics a systematic investigation reveals how different weight dynamics introduced previously can be derived from two types of objective function terms and two types of constraints this includes dynamic link matching as a special case of neural map formation we focus in particular on the role of coordinate transformations to derive different weight dynamics from the same optimization problem several examples illustrate how the constrained optimization framework can help in understanding generating and comparing different models of neural map formation the techniques used in this analysis may also be useful in investigating other types of neural dynamics

random regularization of brown spectral measure abstract we generalize a recent result of haagerup namely we show that a convolution with a standard gaussian random matrix regularizes the behavior of fuglede kadison determinant and brown spectral distribution measure in this way it is possible to establish a connection between the limit eigenvalues distributions of a wide class of random matrices and the brown measure of the corresponding limits

deformation theory of dynamic link matching dynamic link matching is a self organizing topographic mapping between a template image and a data image the mapping tends to be continuous linking two points sharing similar local features which as a result can lead to its deformation to some degree in analyzing such deformation mathematically we reduced the model equation to a phase equation which enabled us to clarify the principles of the deformation process and the relationship between high dimensional models and low dimensional ones we also elucidated the characteristics of the model in the context of the standard regularization theory

zeros of the i i d gaussian power series a conformally invariant determinantal process consider the zero set of the random power series f z p anz n with i i d complex gaussian coefficientsan we show that these zeros form a determinantal process more precisely their joint intensity can be written as a minor of the bergman kernel we show that the number of zeros of f in a disk of radius r about the origin has the same distribution as the sum of independent 0 1 valued random variables xk where p xk 1 r 2k moreover the set of absolute values of the zeros of f has the

integrable structure of ginibre s ensemble of real random matrices and a pfaffian integration theorem in the recent publication e kanzieper and g akemann in phys rev lett 95 230201 2005 an exact solution was reported for the probability pn k to find exactly k real eigenvalues in the spectrum of an n n real asymmetric matrix drawn at random from ginibre s orthogonal ensemble ginoe in the present paper we offer a detailed derivation of the above result by concentrating on the proof of the pfaffian integration theorem the key ingredient of our analysis of the statistics of real eigenvalues in the ginoe we also initiate a study of the correlations of complex eigenvalues and derive a formula for the joint probability density function of all complex eigenvalues of a ginoe matrix restricted to have exactly k real eigenvalues in the particular case of k 0 all correlation functions of complex eigenvalues are determined

learning to generalize from single examples in the dynamic link architecture a large attraction of neural systems lies in their promise of replacing programming by learning a problem with many current neural models is that with realistically large input patterns learning time explodes this is a problem inherent in a notion of learning that is based almost entirely on statistical estimation we propose here a different learning style where significant relations in the input pattern are recognized and expressed by the unsupervised self organization of dynamic links the power of this mechanism is due to the very general a priori principle of conservation of topological structure we demonstrate that style with a system that learns to classify mirror symmetric pixel patterns from single examples

asymptotic performance analysis of blind minimum output energy receivers for large ds cdma systems the random matrix theory is used to analyze the asymptotic performance of the blind minimum output energy moe receiver in direct sequence code division multiple access ds cdma systems in the presence of unknown multipath channel under the condition that the spreading factor and the number of users go to infinity with the same rate as a special case the asymptotic properties of the blind capon receiver are also studied and the conditions of convergence of the signal to interference plus noise ratio sinr of this receiver to that of the optimal minimum mean square error mmse receiver are discussed in particular it is shown that the sinr performances of the capon and mmse receivers are nearly identical in the uplink scenario while the performance of the capon receiver may be considerably inferior to that of the mmse receiver in the downlink transmission case as the performance of the capon receiver is closely related to the performance of the capon channel estimator the asymptotic properties of the latter estimator are also studied and the conditions of convergence of the capon channel estimate to a scaled version of the channel vector of the user of interest are obtained

optimization of linear iterative interference cancellation receivers for cdma communications iterative methods to solve a linear equation system can be used to derive multistage interference cancellers ics that converge to the decorrelating or the minimum mean square error linear detectors the link between linear multistage ic and iterative solution methods is well known however the parameters needed for fastest convergence are functions of the eigenvalues of the channel matrix in this letter we propose new methods for finding optimal parameters without eigendecomposition

a flexible new technique for camera calibration we propose a flexible technique to easily calibrate a camera it only requires the camera to observe a planar pattern shown at a few at least two different orientations either the camera or the planar pattern can be freely moved the motion need not be known radial lens distortion is modeled the proposed procedure consists of a closed form solution followed by a nonlinear refinement based on the maximum likelihood criterion both computer simulation and real data have been used to test the proposed technique and very good results have been obtained compared with classical techniques which use expensive equipment such as two or three orthogonal planes the proposed technique is easy to use and flexible it advances 3d computer vision one more step from laboratory environments to real world use

a limit theorem at the edge of a non hermitian random matrix ensemble the study of the edge behaviour in the classical ensembles of gaussian hermitian matrices has led to the celebrated distributions of tracy widom here we take up a similar line of inquiry in the non hermitian setting we focus on the family of n n random matrices with all entries independent and distributed as complex gaussian of mean zero and variance 1 n this is a fundamental non hermitian ensemble for which the eigenvalue density is known using this density our main result is a limit law for the scaled spectral radius as n as a corollary we get the analogous statement for the case where the complex gaussians are replaced by quaternion gaussians

random doubly stochastic matrices the circular law hoi h nguyenabstract let x be a matrix sampled uniformly from the set of doubly stochastic matri ces of size n n we show that the empirical spectral distribution of the normalized matrixpn x ex converges almost surely to the circular law this con rms a conjecture ofchatterjee diaconis and sly