integration of geometric elements euclidean relations and motion curves for parametric shape and motion estimation this paper presents an approach to shape and motion estimation that integrates heterogeneous knowledge into a unique model based framework we describe the observed scenes in terms of structured geometric elements points line segments rectangles 3d corners sharing explicitly euclidean relationships orthogonality parallelism colinearity coplanarity camera trajectories are represented with adaptative models which account for the regularity of usual camera motions two different strategies of automatic model building lead us to reduced models for shape and motion estimation with a minimal number of parameters these models increase the robustness to noise and occlusions improve the reconstruction and provide a high level representation of the observed scene the parameters are optimally computed within a sequential bayesian estimation procedure that gives accurate and reliable results on synthetic and real video imagery

multiple view geometry under the l_ infty norm this paper presents a new framework for solving geometric structure and motion problems based on the linfin norm instead of using the common sum of squares cost function that is the l2 norm the model fitting errors are measured using the linfin norm unlike traditional methods based on l2 our framework allows for the efficient computation of global estimates we show that a variety of structure and motion problems for example triangulation camera resectioning and homography estimation can be recast as quasi convex optimization problems within this framework these problems can be efficiently solved using second order cone programming socp which is a standard technique in convex optimization the methods have been implemented in matlab and the resulting toolbox has been made publicly available the algorithms have been validated on real data in different settings on problems with small and large dimensions and with excellent performance

structure from motion using line correspondences a theory is presented for the computation of three dimensional motion and structure from dynamic imagery using only line correspondences the traditional approach of corresponding microfeatures interesting points highlights corners high curvature points etc is reviewed and its shortcomings are discussed then a theory is presented that describes a closed form solution to the motion and structure determination problem from line correspondences in three views the theory is compared with previous ones that are based on nonlinear equations and iterative methods

global regularity criterion for the 3d navier stokes equations involving one entry of the velocity gradient tensor in this paper we provide a sufficient condition in terms of only one of the nine entries of the gradient tensor that is the jacobian matrix of the velocity vector field for the global regularity of strong solutions to the three dimensional navier stokes equations in the whole space as well as for the case of periodic boundary conditions

spreading phenomena in which growth sites have a distribution of lifetimes originally studies of the growth of fractal objects such as percolation clusters assumed that the growth sites have an infinite lifetime recently bunde miyazima and stanley have studied the effect of a fixed finite lifetime and they have found that the long time growth evolves toward the kinetic growth walk with self avoiding walk critical exponents here we consider for two dimensions the general case in which each growth site is randomly assigned infinite lifetime with probability 9 or a finite lifetime with probability 1 9 the phase diagram is similar to that of site bond percolation a model used to describe solvent effects in gelation

from lines to epipoles through planes in two views this paper addresses the computation of the fundamental matrix between two views when camera motion and 3d structure are unknown but planar surfaces can be assumed we use line features which are automatically matched in two steps firstly with image based parameters a set of matches are obtained to secondly compute homographies which allows to reject wrong ones and to grow good matches in a final stage the inclusion of projective transformations gives much better results to match features with short computing overload when two or more planes are observed different homographies can be computed segmenting simultaneously the corresponding planar surfaces these can be used to obtain the fundamental matrix which gives constraints for the whole scene the results show that the global process is robust enough turning out stable and useful to obtain matches and epipolar geometry from lines in man made environments

on the regularity of weak solutions to the magnetohydrodynamic equations abstract in this paper we study the regularity of weak solution to the incompressible magnetohydrodynamic equations we obtain some sufficient conditions for regularity of weak solutions to the magnetohydrodynamic equations which is similar to that of incompressible navier stokes equations moreover our results demonstrate that the velocity field of the fluid plays a more dominant role than the magnetic field does on the regularity of solution to the magneto hydrodynamic equations

partial regularity of suitable weak solutions to the incompressible magnetohydrodynamic equations in this paper we study the local behavior of the solutions to the three dimensional magnetohydrodynamic equations we are interested in both the uniform gradient estimates for smooth solutions and regularity of weak solutions it is shown that in some neighborhood of x0 t0 the gradients of the velocity field u and the magnetic field b are locally uniformly bounded in l norm as long as that either the scaled local l2 norm of the gradient or the scaled local total energy of the velocity field is small and the scaled local total energy of the magnetic field is uniformly bounded these estimates indicate that the velocity field plays a more dominant role than that of the magnetic field in the regularity theory as an immediately corollary we can derive an estimates of hausdorff dimension on the possible singular set of a suitable weak solution as in the case of pure fluid various partial regularity results are obtained as consequences of our blow up estimates

two regularity criteria for the 3d mhd equations this work establishes two regularity criteria for the 3d incompressible mhd equations the first one is in terms of the derivative of the velocity field in one direction while the second one requires suitable boundedness of the derivative of the pressure in one direction

recovering the missing components in a large noisy low rank matrix application to sfm in computer vision it is common to require operations on matrices with missing data for example because of occlusion or tracking failures in the structure from motion sfm problem such a problem can be tackled allowing the recovery of the missing values if the matrix should be of low rank when noise free the filling in of missing values is known as imputation imputation can also be applied in the various subspace techniques for face and shape classification online recommender systems and a wide variety of other applications however iterative imputation can lead to the recovery of data that is seriously in error in this paper we provide a method to recover the most reliable imputation in terms of deciding when the inclusion of extra rows or columns containing significant numbers of missing entries is likely to lead to poor recovery of the missing parts although the proposed approach can be equally applied to a wide range of imputation methods this paper addresses only the sfm problem the performance of the proposed method is compared with jacobs and shum s methods for sfm

noise reduction in eden models ii surface structure and intrinsic width for pt i see ibid vol 20 p 257 1987 the authors suggest a picture of the intrinsic surface width in eden models and show that it is a major source of corrections to scaling of the surface roughness using the multiple hit noise reduction method they can control the intrinsic width and thereby improve the scaling behaviour systematically as is demonstrated in detailed calculations on the square lattice they calculate the number of excess perimeter sites as a function of time and find that its asymptotic value decays with a power law as a function of increasing hitting number substrate effects and anisotropy become more apparent if noise reduction is applied

remarks on singularities dimension and energy dissipation for ideal hydrodynamics and mhd for weak solutions of the incompressible euler equations there is energy conservation if the velocity is in the besov space b 3 s with s greater than 1 3 b 3 s consists of functions that are lip s i e holder continuous with exponent s measured in the l p norm here this result is applied to a velocity field that is lip 0 except on a set of co dimension on which it is lip agr 1 with uniformity that will be made precise below we show that the frisch parisi multifractal formalism is valid at least in one direction for such a function and that there is energy conservation if analogous conservation results are derived for the equations of incompressible ideal mhd i e zero viscosity and resistivity for both energy and helicity in addition a necessary condition is derived for singularity development in ideal mhd generalizing the beale kato majda condition for ideal hydrodynamics

anomalous interface roughening in 3d porous media experiment and model abstract we report the first imbibition experiments in 2 1 dimensions using simple materials as the random media and various aqueous suspensions as wetting fluids we measure the width w l t of the resulting interface and find it to scale with length l as w l l with 0 50 0 05 this value of is larger than the value of 0 40 found for the kpz universality class in 2 1 dimensions we develop a new imbibition model that describes quantitatively our experiments for d 1 1 the model can be mapped to directed percolation for d 2 1 it corresponds to a new anisotropic surface percolation problem our model leads to the exponent 0 5 0 05 in excellent agreement with the experiment

growth properties of eden model with acceleration sites one plus one dimensional growth of an eden model with acceleration sites is investigated by simulations where the acceleration sites which are distributed at random before the process starts become immediately eden cells if the surface of eden cluster touches them the critical concentration of acceleration sites where the growth rate of the average cluster height diverges is found as pc 0 5920 005 corresponding to the site percolation threshold of the square lattice the exponent which characterizes this divergence near the percolation threshold have been found as 1 330 08 an eective roughness exponent which characterizes the surface morphology is found to belong to the same universality class as the eden model for p pc at the critical concentration the present system changes to hold a self similar surface c 1998 elsevier science b v all rights reserved

regularity criteria in terms of the pressure for the three dimensional mhd equations in this paper we consider the cauchy problem for the 3d incompressible mhd equations a regularity criterion by providing sufficient condition in terms of the pressure is established more precisely we show that if p l 0 t l r 3 with 3 2 7 4 and 12 5 4 then any weak solutions u b of the 3d mhd equations is regular on 0 t

a new regularity criterion for the 3d incompressible mhd equations in terms of one component of the gradient of pressure abstract in this paper we study the global regularity issue for the 3d incompressible mhd equations it is proved that if the pressure p satisfies 3 p l 0 t l r 3 with 2 3 2 3 and 1 then the corresponding weak solution u b is regular on 0 t

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

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

automatic panoramic image stitching using invariant features this paper concerns the problem of fully automated panoramic image stitching though the 1d problem single axis of rotation is well studied 2d or multi row stitching is more difficult previous approaches have used human input or restrictions on the image sequence in order to establish matching images in this work we formulate stitching as a multi image matching problem and use invariant local features to find matches between all of the images because of this our method is insensitive to the ordering orientation scale and illumination of the input images it is also insensitive to noise images that are not part of a panorama and can recognise multiple panoramas in an unordered image dataset in addition to providing more detail this paper extends our previous work in the area brown and lowe 2003 by introducing gain compensation and automatic straightening steps

projective reconstruction of all visual primitives we present a method to simultaneously reconstruct cameras points lines degenerate quadrics and full rank quadrics from a set of n uncalibrated views of a static scene our method is based on the use of bundle adjustment to refine an initial reconstruction during the initialization stage a novel algorithm was proposed for the conic outline correction in n views constrains derived from this algorithm were also integrated in the cost function of bundle adjustment to help preserve the right topology of the reconstructed quadrics

a multi frame structure from motion algorithm under perspective projection we present a fast robust algorithm for multi frame structure from motion from point features which works for general motion and large perspective effects the algorithm is for point features but easily extends to a direct method based on image intensities experiments on synthetic and real sequences show that the algorithm gives results nearly as accurate as the maximum likelihood estimate in a couple of seconds on an iris 10000 the results are significantly better than those of an optimal two image estimate when the camera projection is close to scaled orthographic the accuracy is comparable to that of the tomasi kanade algorithm and the algorithms are comparably fast the algorithm incorporates a quantitative theoretical analysis of the bas relief ambiguity and exemplifies how such an analysis can be exploited to improve reconstruction also we demonstrate a structure from motion algorithm for partially calibrated cameras with unknown focal length varying from image to image unlike the projective approach this algorithm fully exploits the partial knowledge of the calibration it is given by a simple modification of our algorithm for calibrated sequences and is insensitive to errors in calibrating the camera center theoretically we show that unknown focal length variations strengthen the effects of the bas relief ambiguity this paper includes extensive experimental studies of two frame reconstruction and the tomasi kanade approach in comparison to our algorithm we find that two frame algorithms are surprisingly robust and accurate despite some problems with local minima we demonstrate experimentally that a nearly optimal two frame reconstruction can be computed quickly by a minimization in the motion parameters alone lastly we show that a well known problem with the tomasi kanade algorithm is often not a significant one

dual computation of projective shape and camera positions from multiple images given multiple image data from a set of points in 3d there are two fundamental questions that can be addressed what is the structure of the set of points in 3d what are the positions of the cameras relative to the points in this paper we show that for projective views and with structure and position defined projectively these problems are dual because they can be solved using constraint equations where space points and camera positions occur in a reciprocal way more specifically by using canonical projective reference frames for all points in space and images the imaging of point sets in space by multiple cameras can be captured by constraint relations involving three different kinds of parameters only coordinates of 1 space points 2 camera positions 3 image points the duality implies that the problem of computing camera positions fromp points in q views can be solved with the same algorithm as the problem of directly reconstructing q 4 points in p 4 views this unifies different approaches to projective reconstruction methods based on external calibration and direct methods exploiting constraints that exist between shape and image invariants

linear multi view reconstruction and camera recovery using a reference plane this paper presents a linear algorithm for simultaneous computation of 3d points and camera positions from multiple perspective views based on having a reference plane visible in all views the reconstruction and camera recovery is achieved in a single step by finding the null space of a matrix built from image data using singular value decomposition contrary to factorization algorithms this approach does not need to have all points visible in all views this paper investigates two reference plane configurations finite reference planes defined by four coplanar points and infinite reference planes defined by vanishing points a further contribution of this paper is the study of critical configurations for configurations with four coplanar points by simultaneously reconstructing points and views we can exploit the numerical stabilizing effect of having wide spread cameras with large mutual baselines this is demonstrated by reconstructing the outside and inside courtyard of a building on the basis of 35 views in one single singular value decomposition

shape and motion from image streams under orthography a factorization method inferring scene geometry and camera motion from a stream of images is possible in principle but is an ill conditioned problem when the objects are distant with respect to their size we have developed a factorization method that can overcome this difficulty by recovering shape and motion under orthography without computing depth as an intermediate step an image stream can be represented by the 2fxp measurement matrix of the image coordinates of p points tracked through f frames we show that under orthographic projection this matrix is of rank 3 based on this observation the factorization method uses the singular value decomposition technique to factor the measurement matrix into two matrices which represent object shape and camera rotation respectively two of the three translation components are computed in a preprocessing stage the method can also handle and obtain a full solution from a partially filled in measurement matrix that may result from occlusions or tracking failures the method gives accurate results and does not introduce smoothing in either shape or motion we demonstrate this with a series of experiments on laboratory and outdoor image streams with and without occlusions

verifying global minima for l2 minimization problems in multiple view geometry we consider the least squares l2 minimization problems in multiple view geometry for triangulation homography camera resectioning and structure and motion with known rotation or known plane although optimal algorithms have been given for these problems under an l infinity cost function finding optimal least squares solutions to these problems is difficult since the cost functions are not convex and in the worst case may have multiple minima iterative methods can be used to find a good solution but this may be a local minimum this paper provides a method for verifying whether a local minimum solution is globally optimal by providing a simple and rapid test involving the hessian of the cost function the basic idea is that by showing that the cost function is convex in a restricted but large enough neighbourhood a sufficient condition for global optimality is obtained the method is tested on numerous problem instances of real data sets in the vast majority of cases we are able to verify that the solutions are optimal in particular for small to medium scale problems

some mathematical questions related to the mhd equations some questions relating to the large time behavior of the solutions of mhd equations for a viscous incompressible resistive fluid are investigated the physical system is briefly described and the functional setting of the equations a flow in a bounded domain or in whole space with a space periodicity property in all directions the main existence and uniqueness results for weak and strong solutions of the mhd equations are recalled regularity properties and bounds on the solutions to the equations which are valid for all time are established and the concept of functional invariant sets is introduced which is contained in the space of smooth functions if the data are sufficiently regular the squeezing property of the trajectories are stated and it is shown that any functional invariant set for the mhd equations and in particular any attractor has a finite haussdorf dimension the flow is found to be totally determined for large dimensions by a finite number of parameters 26 references

reduced multilinear constraints theory and experiments this paper deals with the problem of reconstructing the locations of n points in space from m different images without camera calibration we will show how these reconstruction problems for different n and m can be put into a similar theoretical framework this will be done using a special choice of coordinates both in the object and in the images called reduced affine coordinates this choice of coordinates simplifies the analysis of the multilinear geometry and gives simpler forms of the multilinear tensors in particular we will investigate the cases which can be solved by linear methods i e 8 points in 2 images 7 points in 3 images and 6 points in 4 images a new concept the reduced fundamental matrix is introduced which gives bilinear expressions in the image coordinates it has six nonzero elements which depend on just four parameters and can be used to make reconstruction from 2 images we also introduce the concept of the reduced trifocal tensor which gives trilinear expressions in the image coordinates in 3 images it has 15 nonzero elements and depends on nine parameters and can be used to make reconstruction from 3 images finally the reduced quadfocal tensor is introduced which describes the relations between points in 4 images and gives quadlinear expressions in the image coordinates this tensor has 36 nonzero elements which depend on 14 independent parameters and can be used to make reconstruction from 4 images these tensors give the possibility to calculate linear solutions from 8 points in 2 images 7 points in 3 images and also from 6 points in 4 images furthermore a canonical form of the camera matrices in a sequence is presented and it is shown that the quadlinear constraints can be calculated from the trilinear ones and that in general the trilinear constraints can be calculated from the bilinear ones