long time behavior of a model of extensible beams with nonlinear boundary dissipations abstract this paper is concerned with the long time behavior of a model of extensible beams u t t u x x x x m 0 l u x 2 d x u x x h defined in a bounded interval 0 l where m is a continuous nonnegative function and h is a static load to this problem little is known with nonlinear boundary conditions one considers the case where a nonlinear forcing interacts with the shear force at the boundary then the existence of a global attractor is proved with a sole boundary damping

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

statistical comparison of dlt versus ilssc in the calibration of a photogrammetric stereo system this paper compares the dlt and ilssc approaches in the geometrical calibration of a photogrammetric stereo system in terms of accuracy and speed to come up with an unbiased quantitative evaluation of the accuracy of the algorithms the concept of reliable estimate has been introduced the statistical distribution of the accuracy is assessed over different calibration experiments performed with the same data but with different noise distribution and different test sets results show that in the simulations where the only error on the two dimensional points was gaussian zero mean and on real data which were corrected for distortions through polynomial or linear interpolation the accuracy of the two methods was quite similar dlt showed more accurate than ilssc on simulated data with residual distortion errors and on real data which were not corrected for distortions as far as speed is concerned a fast triangulation algorithm is associated with ilssc while the simultaneous solution of two pairs of dlt equations is associated to dlt the first algorithm is much faster requiring 113 flops per point versus 259 of dlt the fast triangulation with dlt parameters does not achieve the same accuracy on the reconstructed three dimensional position taken all together the results suggest that ilssc can be theoretically considered the best approach to three dimensional reconstruction provided that distortions are corrected in advance the statistical evaluation of the accuracy allows a fair judgement of the performances of the algorithms to be obtained unbiased by particular distributions of measurement errors and test points

a precision analysis of camera distortion models this paper addresses the question of identifying the right camera direct or inverse distortion model permitting a high subpixel precision to fit to real camera distortion five classic camera distortion models are reviewed and their precision is compared for direct or inverse distortion by definition the three radially symmetric models can only model a distortion radially symmetric around some distortion center they can be extended to deal with non radially symmetric distortions by adding tangential distortion components but still may be too simple for very accurate modeling of real cameras the polynomial and the rational models instead miss a physical or optical interpretation but can cope equally with radially and non radially symmetric distortions indeed they do not require the evaluation of a distortion center when requiring high precisions we found that the distortion modeling must also be evaluated primarily as a numerical problem indeed all models except the polynomial involve a non linear minimization which increases the numerical risk the estimation of a polynomial distortion model leads instead to a linear problem which is secure and much faster we concluded by extensive numerical experiments that although high degree polynomials were required to reach a high precision of 1 100 pixels such polynomials were easily estimated and produced a precise distortion modeling without overfitting our conclusion is validated by three independent experimental setups the models were compared first on the lens distortion database of the lensfun library by their distortion simulation and inversion power second by fitting real camera distortions estimated by a non parametric algorithm and finally by the absolute correction measurement provided by the photographs of tightly stretched strings warranting a high straightness

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

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

image based lens geometric distortion correction using minimization of average bicoherence index in this paper a lens geometric distortion correction method for low cost digital cameras is described the lens distortion coefficient is estimated by the value minimizing average bicoherence index which denotes image dependent higher order correlations in the frequency domain in order to formulate the minimization of the average bicoherence index in terms of the lens distortion coefficient alone the feasibility of a square pixel assumption and the effect of the image center bias on the image quality are shown experimentally at the same time a computationally efficient method for calculating the bicoherence index is proposed which comprises an approximation of coordinate resampling and development of a relationship between the lens distortion coefficients of the original and its reduced image depending on the spatial distribution of image features the performance of the proposed method can be made comparable to that of precision camera calibration

fractal wavelet dimensions and localization in this paper we want to give a new definition of fractal dimensions as small scale behavior of theq energy of wavelet transforms this is a generalization of previous multi fractal approaches with this particular definition we will show that the 2 dimension correlation dimension of the spectral measure determines the long time behavior of the time evolution generated by a bounded self adjoint operator acting in some hilbert space it will be proved that for we have mathop lim inf limits t to infty frac log int 0 t d omega left left langle psi left e ia omega right phi right rangle right 2 log t kappa 2 and that mathop lim sup limits t to infty frac log int 0 t d omega left left langle psi left e ia omega right phi right rangle right 2 log t kappa 2 wherek 2 are the upper and lower correlation dimensions of the spectral measure associated with and a quantitative version of the rage theorem shall also be given

a note on spectrum and quantum dynamics abstract we show in the same vein of simon s wonderland theorem that typically in baire s sense the rates with whom the solutions of the schrodinger equation escape in time average from every finite dimensional subspace depend on subsequences of time going to infinite

fourier asymptotics of fractal measures abstract a measure on r n will be called locally uniformly dimensional if br x cr for all r 1 and all x where br x denotes the ball of radius r about x for l 2 d the measure d is in i so d is well defined we show it is locally in l2 and sup r 1 r n b r y f d 2 d c f 2 under additional hypotheses we show that lim r r n b r y f d 2 2 d is comparable in size to 2 2 a number of other related results are established the special case when is an integer and is the surface measure on a c1 manifold was treated by s agmon and l hormander j analyse math 30 1976 1 38

quantum return probability for substitution potentials we propose an effective exponent ruling the algebraic decay of the average quantum return probability for discrete schrodinger operators we compute it for some non periodic substitution potentials with different degrees of randomness and do not find a complete qualitative agreement with the spectral type of the substitution sequences themselves i e the more random the sequence the smaller such an exponent

on designing an isotropic fiducial mark the crame spl acute r rao lower bound crlb of image registration error using an isotropic fiducial mark is derived the derived crlb is a function of the intensity profile of the fiducial mark following the development of the crlb a new method for designing an isotropic fiducial mark suitable for digital image registration is presented a parameterization method of the fiducial intensity profile is introduced which guarantees no aliasing effect when the fiducial mark is digitized with the proper sampling rate a method for computing the fiducial intensity profile based on minimization of the crlb registration error and subject to certain practical constraints is developed for imaging systems with a significant low pass effect it is proposed to pre emphasize the high frequency components of the fiducial mark by converting the designed gray scale fiducial marks into binary fiducial marks experimental results show that the designed fiducial mark can provide very accurate registration results and that the registration accuracy is independent of its location

dynamical upper bounds on wavepacket spreading we derive a general upper bound on the spreading rate of wavepackets in the framework of schrodinger time evolution our result consists of showing that a portion of the wavepacket cannot escape outside a ball whose size grows dynamically in time where the rate of this growth is determined by properties of the spectral measure and by spatial properties of solutions of an associated time independent schrodinger equation we also derive a new lower bound on the spreading rate which is strongly connected with our upper bound we apply these new bounds to the fibonacci hamiltonian the most studied one dimensional model of quasicrystals as a result we obtain for this model upper and lower dynamical bounds establishing wavepacket spreading rates which are intermediate between ballistic transport and localization the bounds have the same qualitative behavior in the limit of large coupling

de localization in the prime schrodinger operator we report a combined numerical approach to study the localization properties of the one dimensional tight binding model with potential modulated along the prime numbers a localization delocalization transition was found as a function of the potential intensity it is also argued that there are delocalized states for any value of the potential intensity

remarks on the relation between quantum dynamics and fractal spectra abstract we investigate the large time behaviour of various solutions of the schrodinger equation in terms of some local and global dimensions of the spectral measure we emphasize in particular the role of the hausdorff and correlation dimensions for the growth exponents of position moments we also discuss the stability of such exponents under local perturbations

calibrating a video camera pair with a rigid bar abstract in this paper a new procedure to determine all the geometrical parameters of a stereo system is presented it is based on surveying a rigid bar carrying two markers on its extremities moved inside the working volume and it does not require grids or complex calibration structures the external parameters are estimated through the epipolar geometry up to a scale factor which is determined from the true length of the bar the focal lengths are determined using the properties of the absolute conic in the projective space the principal points are computed through a non linear minimisation carried out through an evolutionary optimisation the accuracy of the method is assessed on real data and it compares favourably with that obtained through classical approaches based on control points of known 3d coordinates

singular continuous spectrum on a cantor set of zero lebesgue measure for the fibonacci hamiltonian it is rigorously proven that the spectrum of the tight binding fibonacci hamiltonian h mn m n 1 m n 1 m n n 1 n where 5 1 2 and means integer part is a cantor set of zero lebesgue measure for all real nonzero and the spectral measures are purely singular continuous this follows from a recent result by kotani coupled with the vanishing of the lyapunov exponent in the spectrum

expectation values of observables in time dependent quantum mechanics let u t be the evolution operator of the schrodinger equation generated by a hamiltonian of the form h0 t w t where h0 t commutes for all twith a complete set of time independent projectors p j j 1 infty consider the observable a jpj jwhere j j 0 for jlarge assuming that the matrix elements of w t behave as for p 0 large enough we prove estimates on the expectation value langle u t phi au t phi rangle equiv langle a rangle phi t for large times of the type where 0 depends on pand typical applications concern the energy expectation h0 t in case h0 t h0or the expectation of the position operator x2 t on the lattice where w t is the discrete laplacian or a variant of it and h0 t is a time dependent multiplicative potential

singular continuous spectrum under rank one perturbations and localization for random hamiltonians we consider a selfadjoint operator a and a selfadjoint rank one projection p onto a vector which is cyclic for a in terms of the spectral measure d a we give necessary and sufficient conditions for a p to have empty singular continuous spectrum or to have only point spectrum for a e we apply these results to questions of localization in the one and multi dimensional anderson models

correcting the geometry and color of digital images a unified method for correcting the geometry and color of digital images is presented the method uses a color chart with a prearranged array of known color patches using the true geometry and color of the chart and geometry and color of the image of the chart transformation functions that describe the geometry and color characteristics of the camera are determined the transformation functions are then used to correct the geometry and color of obtained images experimental results of the proposed method on images acquired under different scene illuminations and camera settings are presented and evaluated

high accuracy and robust localization of large control markers for geometric camera calibration accurate measurement of the position of features in an image is subject to a fundamental compromise the features must be both small to limit the effect of nonlinear distortions and large to limit the effect of noise and discretization this constrains both the accuracy and the robustness of image measurements which play an important role in geometric camera calibration as well as in all subsequent measurements based on that calibration in this paper we present a new geometric camera calibration technique that exploits the complete camera model during the localization of control markers thereby abolishing the marker size compromise large markers allow a dense pattern to be used instead of a simple disc resulting in a significant increase in accuracy and robustness when highly planar markers are used geometric camera calibration based on synthetic images leads to true errors of 0 002 pixels even in the presence of artifacts such as noise illumination gradients compression blurring and limited dynamic range the camera parameters are also accurately recovered even for complex camera models

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

radial multi focal tensors the 1d radial camera maps all points on a plane containing the principal axis onto the radial line which is the intersection of that plane and the image plane it is a sufficiently general model to express both central and non central cameras since the only assumption it makes is of known center of distortion in this paper we study the multi focal tensors arising out of 1d radial cameras there exist no two view constraints like the fundamental matrix for 1d radial cameras however the 3 view and 4 view cases are interesting for the 4 view case we have the radial quadrifocal tensor which has 15 d o f and 2 internal constraints for the 3 view case we have the radial trifocal tensor which has 7 d o f and no internal constraints under the assumption of a purely rotating central camera this can be used to do a non parametric estimation of the radial distortion of a 1d camera even in the case of a non rotating camera it can be used to do parametric estimation assuming a planar scene finally we examine the mixed trifocal tensor which models the case of two 1d radial cameras and one standard pin hole camera of the above radial multifocal tensors only the radial trifocal tensor is useful practically since it doesn t require any knowledge of the scene and is extremely robust we demonstrate results based on real images for this for the quadrifocal tensor too we present a way to do a metric reconstruction of the scene and to undistort the image given a sufficiently dense set of point correspondences we also show results on synthetic images however it must be noted that currently the quadrifocal and mixed trifocal tensors are useful only from a theoretical stand point

rigorous spectral analysis of the metal insulator transition in a limit periodic potential we consider the limit periodic jacobi matrices associated with the real julia sets of f a z z2 a for which ae 2 oo can be seen as the strength of the limit periodic coefficients the typical local spectral exponent of their spectral measures is shown to be a harmonic function in a decreasing logarithmically from 1 to 0

mixed lower bounds for quantum transport let h be a self adjoint operator on a separable hilbert space h h 1 given an orthonormal basis b en of h we consider the time averaged moments x p t of the position operator associated to b we derive lower bounds for the moments in terms of both spectral measure and generalized eigenfunctions u n x of the state as a particular corollary we generalize the recently obtained lower bound in terms of multifractal dimensions of and give some equivalent forms of it which can be useful in applications we establish in particular the relations between the lq norms q 1 2 of the imaginary part of borel transform of probability measures and the corresponding multifractal dimensions

universal lower bounds for quantum diffusion abstract we study the connections between dynamical properties of schrodinger operators h on separable hilbert space h and the properties of corresponding spectral measures our main result establishes a relation for the moment of order p of the form x p t t t 1 t 0 x p 2 e ith 2 h dt l p d t 1 here l p d t is a function connected to the behavior of the fourier transform of measures in the subclass of measures absolutely continuous with respect to the spectral measure beyond the intrinsic interest of the general formulation 1 this result allows us to derive necessary conditions for dynamical localization in the presence of a pure point spectrum on the other hand if we focus on subsequences of time t k we can exhibit lower bounds which are in certain cases strictly larger than the well known power law lower bound for all t expressed in terms of the hausdorff dimension of spectral measures

intrinsic parameter calibration procedure for a high distortion fish eye lens camera with distortion model and accuracy estimation this paper presents a calibration procedure for a fish eye lens a high distortion lens mounted on a ccd tv camera the method is designed to account for the differences in images acquired via a distortion free lens camera setup and the images obtained by a fish eye lens camera the calibration procedure essentially defines a mapping between points in the world coordinate system and their corresponding point locations in the image plane this step is important for applications in computer vision which involve quantitative measurements the objective of this mapping is to estimate the internal parameters of the camera including the effective focal length one pixel width on the image plane image distortion center and distortion coefficients the number of parameters to be calibrated is reduced by using a calibration pattern with equally spaced dots and assuming a pin hole model camera behavior for the image center thus assuming negligible distortion at the image distortion center our method employs a non linear transformation between points in the world coordinate system and their corresponding location on the image plane a lagrangian minimization method is used to determine the coefficients of the transformation the validity and effectiveness of our calibration and distortion correction procedure are confirmed by application of this procedure on real images

adaptive homogeneity directed demosaicing algorithm a cost effective digital camera uses a single image sensor applying alternating patterns of red green and blue color filters to each pixel location a way to reconstruct a full three color representation of color images by estimating the missing pixel components in each color plane is called a demosaicing algorithm this paper presents three inherent problems often associated with demosaicing algorithms that incorporate two dimensional 2 d directional interpolation misguidance color artifacts interpolation color artifacts and aliasing the level of misguidance color artifacts present in two images can be compared using metric neighborhood modeling the proposed demosaicing algorithm estimates missing pixels by interpolating in the direction with fewer color artifacts the aliasing problem is addressed by applying filterbank techniques to 2 d directional interpolation the interpolation artifacts are reduced using a nonlinear iterative procedure experimental results using digital images confirm the effectiveness of this approach

a note on the generalized fractal dimensions of a probability measure we prove the following result on the generalized fractal dimensions dq of a probability measure on rn let g be a complex valued measurable function on rn satisfying the following conditions 1 g is rapidly decreasing at infinity 2 g is continuous and nonvanishing at at least one point 3 g 0 define the partition function a q an q 1 ga lim qq where ga x a ng a 1x and is the convolution in rn then for all q 1 we have dq 1 q 1 limr 0 infsup log a r q log r

improvement of depth position in 2 d 3 d registration of knee implants using single plane fluoroscopy two dimensional 2 d three dimensional 3 d registration techniques using single plane fluoroscopy are highly important for analyzing 3 d kinematics in applications such as total knee arthroplasty tka implants the accuracy of single plane fluoroscopy based techniques in the determination of translation perpendicular to the image plane depth position however is relatively poor because a change in the depth position causes only small changes in the 2 d silhouette accuracies achieved in depth position using conventional 2 d 3 d registration techniques are insufficient for clinical applications therefore we propose a technique for improving the accuracy of depth position determination in order to develop a system for analyzing knee kinematics over the full six degrees of freedom 6 dof using single plane fluoroscopy in preliminary experiments the behaviors of errors for each free variable were quantified as evaluation curves by examining changes in cost function with variations in the free variable the evaluation curve for depth position was more jagged and the curve peak less pointy compared to the evaluation curves of the other five variables and the curve was found to behave differently depth position is therefore optimized independently of the other variables using an approximate evaluation curve of depth position prepared after initial registration accuracy of the proposed technique was evaluated by computer simulation and in vitro tests with validation of absolute position and orientation performed for each knee component in computer simulation tests root mean square error rmse in depth position was improved from 2 6 mm conventional to 0 9 mm proposed whereas for in vitro tests rmse improved from 3 2 mm to 1 4 mm accuracy of the estimation of the remaining two translational and three rotational variables was found to be almost the same as that obtained by conventional techniques results of in vivo tests are also described in which the possibility of full 6 dof kinematic analysis of tka implants is shown

a new method for distortion correction of electronic endoscope images a new method to correct the barrel distortion of an electronic endoscope image is presented a correction model assuming circularly symmetric distortion is introduced with the following model parameters the center of distortion and the coefficients of polynomials representing the distortion correction in the radial direction if the imaging system is distortion free straight lines in the object space should be imaged as straight lines based on this criterion a distorted image of a standard pattern consisting of a grid of several straight lines is recorded and the model parameters are then estimated as a basis for straightening distorted lines this method has the advantage of not needing a careful placement of the standard pattern for calibration correction results are presented for the grid pattern chart to verify a sufficient degree of correction examples of distortion correction of real intestinal images and physicians comments are also presented

transitory image sequences asymptotic properties and estimation of motion and structure a transitory image sequence is one in which no scene element is visible through the entire sequence this article deals with some major theoretical and algorithmic issues associated with the task of estimating structure and motion from transitory image sequences it is shown that integration with a transitory sequence has properties that are very different from those with a nontransitory one two representations world centered wc and camera centered cc behave very differently with a transitory sequence the asymptotic error rates derived in this article indicate that one representation is significantly superior to the other depending on whether one needs camera centered or world centered estimates we introduce an efficient cross frame estimation technique for the cc representation for the wc representation our analysis indicates that a good technique should be based on camera global pose instead of interframe motions rigorous experiments were conducted with real image sequences taken by a fully calibrated camera system

on rigorous mathematical definitions of correlation dimension and generalized spectrum for dimensions we consider different definitions of the correlation dimension and find some relationships between them and other characteristics of dimension type such as hausdorff dimension box dimension etc we also introduce different ways to define and study the generalized spectrum for dimensions a one parameter family of characteristics of dimension type

existence of a positive solution for a kirchhoff problem type with critical growth via truncation argument abstract in this paper we shall show an existence result of a positive solution for a kirchhoff problem type in a bounded domain of r n that is for the problem m u 2 d x u f x u u 2 2 u in u 0 on we shall study the asymptotic behavior of this solution when converges to infinity our approach is based on the variational method an appropriated truncated argument and a priori estimates to obtain the solution

uniform spectral properties of one dimensional quasicrystals iii α continuity we study the spectral properties of one dimensional whole line schrodinger operators especially those with sturmian potentials building upon the jitomirskaya last extension of the gilbert pearson theory of subordinacy we demonstrate how to establish continuity of a whole line operator from power law bounds on the solutions on a half line however we require that these bounds hold uniformly in the boundary condition

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

a new approach for nonlinear distortion correction in endoscopic images based on least squares estimation images captured with a typical endoscope show spatial distortion which necessitates distortion correction for subsequent analysis here a new methodology based on least squares estimation is proposed to correct the nonlinear distortion in the endoscopic images a mathematical model based on polynomial mapping is used to map the images from distorted image space onto the corrected image space the model parameters include the polynomial coefficients distortion center and corrected center the proposed method utilizes a line search approach of global convergence for the iterative procedure to obtain the optimum expansion coefficients a new technique to find the distortion center of the image based on curvature criterion is presented a dual step approach comprising token matching and integrated neighborhood search is also proposed for accurate extraction of the centers of the dots contained in a rectangular grid used for the model parameter estimation the model parameters were verified with different grid patterns the distortion correction model is applied to several gastrointestinal images and the results are presented the proposed technique provides high speed response and forms a key step toward online camera calibration which is required for accurate quantitative analysis of the images

fractal measures and mean p variations abstract recently strichartz proved that if is locally uniformly dimensional on r d then where 0 d and bt denotes the ball of radius t center at 0 if is self similar and satisfies a certain open set condition he also obtained a formula for the so that 0 lim sup t 1 t d b t f s 2 the can serve in some sense as the dimensional index of the measure by using the mean p variation and the tauberian theorems we extend the first inequality and its variants to p q forms and give necessary and sufficient conditions on for such inequalities to hold we then use the mean quadratic variation to study some self similar measures on r which do not satisfy the open set condition the s that are constructed from s 1 x x s 2 x x 1 1 2 with weights 1 2 each the index for corresponding to 5 1 2 is calculated the expression for such is significantly different from the one obtained by strichartz

spectral properties of one dimensional quasi crystals in this paper we prove that the one dimensional schrodinger operator onl 2 with potential given by upsilon n lambda chi 1 alpha 1 x n alpha alpha notin mathbb q has a cantor spectrum of zero lebesgue measure for any irrational and any 0 we can thus extend the kotani result on the absence of absolutely continuous spectrum for this model to all mathtype mtef 2 1 feaafiart1ev1aaatcvaufebsjuyzl2yd9gzlbvynv2caerbulwbln hiov2dgi1btfmbaexatlxbi9gbaerbd9wdylwzybitldharqqtubsr 4rnchbgeagqivu0je9sqqrpepc0xbbl8f4rqqrffpeea0xe9lq jc9 vqaqpepm0xbba9pwe9q8fs0 yqaqpepae9pg0firpepge9fr xfr x frpewzqaaeaabigaciaacaqabeaadaqaaqaaaoqaaiaadihaiiaacq wfiiiztuudjxwak1uy0hmmaehbfv3yslgzg0uy0hgiud3bagqbbiab nj8ubaa 4628 x in mathbb t

correlation dimension wonderland theorems existence of generic sets of self adjoint operators related to correlation dimensions of spectral measures is investigated in separable hilbert spaces typical results say that given an orthonormal basis the set of operators whose corresponding spectral measures are both 0 lower and 1 upper correlation dimensional is generic the proofs rely on details of the relations among fourier transform of spectral measures and hausdorff and packing measures on the real line then such results are naturally combined with the wonderland theorem applications are to classes of discrete one dimensional schrodinger operators and general bounded self adjoint operators as well physical consequences include a proof of exotic dynamical behavior of singular continuous spectrum in some settings

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

automatic correction of barrel distorted images using a cascaded evolutionary estimator all optical systems are to some extent burdened by one or more aberrations barrel distortion of an image is also an aberration in this paper we used an innovative method to solve the problem of the centric radial distortion of a static image which serves for biometric identification of persons using 2d contour of a human hand the method proposed uses a cascaded arrangement of two algorithms the classic meta heuristic referred to as jde differential evolution and an algorithm called covariance matrix adaptation evolution strategy optimizers use methods of inverse engineering and numerical mathematics to resolve the question of how to determine the correct parameters of the algebraic polynomial equation of the nth degree by the application of which it is possible to obtain an image free of barrel distortion from an image affected by this distortion the proposed method provides a high quality and time acceptable method of optimization and the option of choosing the approximation accuracy with the use of the coefficients obtained it is then possible to use a method called back mapping to permanently correct the centric radial distortion aberration in the biometric scanner extensive experiments presented in this paper enable a better understanding of relationships the accuracy obtained and options of using evolutionary optimizers in a larger sense

spectral properties of one dimensional schrodinger operators with potentials generated by substitutions we investigate one dimensional discrete schrodinger operators whose potentials are invariant under a substitution rule the spectral properties of these operators can be obtained from the analysis of a dynamical system called the trace map we give a careful derivation of these maps in the general case and exhibit some specific properties under an additional easily verifiable ypothesis concerning the structure of the trace map we present an analysis of their dynamical properties that allows us to prove that the spectrum of the underlying schrodinger operator is singular and supported on a set of zero lebesgue measure a condition allowing to exclude point spectrum is also given the application of our theorems is explained on a series of examples

imposing semi local geometric constraints for accurate correspondences selection in structure from motion a game theoretic perspective most structure from motion pipelines are based on the iterative refinement of an initial batch of feature correspondences typically this is performed by selecting a set of match candidates based on their photometric similarity an initial estimate of camera intrinsic and extrinsic parameters is then computed by minimizing the reprojection error finally outliers in the initial correspondences are filtered by enforcing some global geometric property such as the epipolar constraint in the literature many different approaches have been proposed to deal with each of these three steps but almost invariably they separate the first inlier selection step which is based only on local image properties from the enforcement of global geometric consistency unfortunately these two steps are not independent since outliers can lead to inaccurate parameter estimation or even prevent convergence leading to the well known sensitivity of all filtering approaches to the number of outliers especially in the presence of structured noise which can arise for example when the images present several repeated patterns in this paper we introduce a novel stereo correspondence selection scheme that casts the problem into a game theoretic framework in order to guide the inlier selection towards a consistent subset of correspondences this is done by enforcing geometric constraints that do not depend on full knowledge of the motion parameters but rather on some semi local property that can be estimated from the local appearance of the image features the practical effectiveness of the proposed approach is confirmed by an extensive set of experiments and comparisons with state of the art techniques

nonmetric calibration of camera lens distortion differential methods and robust estimation this paper addresses the problem of calibrating camera lens distortion which can be significant in medium to wide angle lenses our approach is based on the analysis of distorted images of straight lines we derive new distortion measures that can be optimized using nonlinear search techniques to find the best distortion parameters that straighten these lines unlike the other existing approaches we also provide fast closed form solutions to the distortion coefficients we prove that including both the distortion center and the decentering coefficients in the nonlinear optimization step may lead to instability of the estimation algorithm our approach provides a way to get around this and at the same time it reduces the search space of the calibration problem without sacrificing the accuracy and produces more stable and noise robust results in addition while almost all existing nonmetric distortion calibration methods needs user involvement in one form or another we present a robust approach to distortion calibration based on the least median of squares estimator our approach is thus able to proceed in a fully automatic manner while being less sensitive to erroneous input data such as image curves that are mistakenly considered projections of three dimensional linear segments experiments to evaluate the performance of this approach on synthetic and real data are reported

camera calibration with distortion models and accuracy evaluation a camera model that accounts for major sources of camera distortion namely radial decentering and thin prism distortions is presented the proposed calibration procedure consists of two steps 1 the calibration parameters are estimated using a closed form solution based on a distribution free camera model and 2 the parameters estimated in the first step are improved iteratively through a nonlinear optimization taking into account camera distortions according to minimum variance estimation the objective function to be minimized is the mean square discrepancy between the observed image points and their inferred image projections computed with the estimated calibration parameters the authors introduce a type of measure that can be used to directly evaluate the performance of calibration and compare calibrations among different systems the validity and performance of the calibration procedure are tested with both synthetic data and real images taken by tele and wide angle lenses

practical ways to calculate camera lens distortion for real time camera calibration in this paper we address practical methods for calculating camera lens distortion for real time applications although the lens distortion problem can be easily ignored for constant parameter lenses it becomes important in the eld of real time camera calibrations particularly for zoom lenses tsai s camera calibration method which is adopted in this paper for real time application consists of two stages while some camera parameters can be calculated algebraically in the rst stage a nonlinear optimization process is involved in the second stage for calculating other parameters including lens distortion which requires a large number of calculations however if the lens distortion can be calculated independently of the other camera parameters we can easily calibrate a camera with a linear method without a computational burden we propose two di erent methods for calculating lens distortion independently these methods are so simple and require so few calculations that the lens distortion can be rapidly calculated even in real time applications the rst one uses a look up table lut of focal length and lens distortion which can be constructed in the initialization process the second one is a feature based method using the relationship between the feature points found in an image experiments were carried out for both methods results of which show that the proposed methods are favorably comparable in performance with the non real time full optimization method 2001 pattern recognition society published by elsevier science ltd all rights reserved

power law bounds on transfer matrices and quantum dynamics in one dimension ii abstract we establish quantum dynamical lower bounds for a number of discrete one dimensional schrodinger operators these dynamical bounds are derived from power law upper bounds on the norms of transfer matrices we develop further the approach from part i and study many examples particular focus is put on models with finitely or at most countably many exceptional energies for which one can prove power law bounds on transfer matrices the models discussed in this paper include substitution models sturmian models a hierarchical model the prime model and a class of moderately sparse potentials

robust metric calibration of non linear camera lens distortion camera lens distortion is crucial to obtain the best performance cameral model up to now different techniques exist which try to minimize the calibration error using different lens distortion models or computing them in different ways some compute lens distortion camera parameters in the camera calibration process together with the intrinsic and extrinsic ones others isolate the lens distortion calibration without using any template and basing the calibration on the deformation in the image of some features of the objects in the scene like straight lines or circles these lens distortion techniques which do not use any calibration template can be unstable if a complete camera lens distortion model is computed they are named non metric calibration or self calibration methods traditionally a camera has been always best calibrated if metric calibration is done instead of self calibration this paper proposes a metric calibration technique which computes the camera lens distortion isolated from the camera calibration process under stable conditions independently of the computed lens distortion model or the number of parameters to make it easier to resolve this metric technique uses the same calibration template that will be used afterwards for the calibration process therefore the best performance of the camera lens distortion calibration process is achieved which is transferred directly to the camera calibration process

computing camera focal length by zooming a single point in this paper we present a novel simple procedure to compute the focal length of a camera the method is based on zooming in and out only a single point the same approach allows computing the principal point when only two points are available on a pair of images surveyed with a different focal length experimental results show that the method is as accurate as classical full calibration methods moreover its application to augmented reality produces more accurate results than those obtained when the simple pin hole model is considered

a review on egomotion by means of differential epipolar geometry applied to the movement of a mobile robot the estimation of camera egomotion is an old problem in computer vision since the 1980s many approaches based on both the discrete and the differential epipolar constraint have been proposed the discrete case is used mainly in self calibrated stereoscopic systems whereas the differential case deals with a single moving camera this article surveys several methods for 3d motion estimation unifying the mathematics convention which are then adapted to the common case of a mobile robot moving on a plane experimental results are given on synthetic data covering more than 0 5 million estimations these surveyed algorithms have been programmed and are available on the internet

an efficient camera calibration technique offering robustness and accuracy over a wide range of lens distortion in the field of machine vision camera calibration refers to the experimental determination of a set of parameters that describe the image formation process for a given analytical model of the machine vision system researchers working with low cost digital cameras and off the shelf lenses generally favor camera calibration techniques that do not rely on specialized optical equipment modifications to the hardware or an a priori knowledge of the vision system most of the commonly used calibration techniques are based on the observation of a single 3 d target or multiple planar 2 d targets with a large number of control points this paper presents a novel calibration technique that offers improved accuracy robustness and efficiency over a wide range of lens distortion this technique operates by minimizing the error between the reconstructed image points and their experimentally determined counterparts in distortion free space this facilitates the incorporation of the exact lens distortion model in addition expressing spatial orientation in terms of unit quaternions greatly enhances the proposed calibration solution by formulating a minimally redundant system of equations that is free of singularities extensive performance benchmarking consisting of both computer simulation and experiments confirmed higher accuracy in calibration regardless of the amount of lens distortion present in the optics of the camera this paper also experimentally confirmed that a comprehensive lens distortion model including higher order radial and tangential distortion terms improves calibration accuracy

nonmetric calibration of wide angle lenses and polycameras images taken with wide angle cameras tend to have severe distortions which pull points towards the optical center this paper proposes a simple method for recovering the distortion parameters without the use of any calibration objects since distortions cause straight lines in the scene to appear as curves in the image our algorithm seeks to find the distortion parameters that map the image curves to straight lines the user selects a small set of points along the image curves recovery of the distortion parameters is formulated as the minimization of an objective function which is designed to explicitly account for noise in the selected image points experimental results are presented for synthetic data as well as real images we also present the idea of a polycamera which is defined as a tightly packed camera cluster possible configurations are proposed to capture very large fields of view such camera clusters tend to have a nonsingle viewpoint we therefore provide analysis of what we call the minimum working distance for such clusters finally we present results for a polycamera consisting of four wide angle sensors having a minimum working distance of about 4 m on undistorting the acquired images using our proposed technique we create real time high resolution panoramas

fractal dimensions and the phenomenon of intermittency in quantum dynamics we exhibit an intermittency phenomenon in quantum dynamics more precisely we derive new lower bounds for the moments of order p associated to the state t e it h and averaged in time between zero and t these lower bounds are expressed in terms of generalized fractal dimensions d 1 1 p d of the measure where d is the space dimension this improves previous results obtained in terms of hausdorff and packing dimension

when should we consider lens distortion in camera calibration abstract this work investigates the effect of neglecting lens distortion in camera calibration and presents a theoretical analysis of the calibration accuracy we derived an approximate upper envelope for the 2d prediction error which is a function of a few factors including the number of calibration points the observation error of 2d image points the radial lens distortion coefficient the image size and resolution this error envelope provides a guide line for selecting both a proper camera calibration configuration and an appropriate camera model while satisfying the desired accuracy experimental results from both computer simulations and real experiments are included in this paper