on pro p analogues of limit groups via extensions of centralizers we begin a study of a pro p analogue of limit groups via extensions of centralizers and call mathcal l this new class of pro p groups we show that the pro p groups of mathcal l have finite cohomological dimension type fp and non positive euler characteristic among the group theoretic properties it is proved that they are free by torsion free nilpotent and if non abelian do not have a finitely generated non trivial normal subgroup of infinite index furthermore it is shown that every 2 generated pro p group in the class mathcal l is either free pro p or abelian

the hanna neumann conjecture for demushkin groups abstract we confirm the hanna neumann conjecture for topologically finitely generated closed subgroups u and w of a nonsolvable demushkin group g namely we show that g u g w d u g w g 1 d u d w where d k max d k 1 0 and d k is the least cardinality of a topological generating set for the group k

practical global optimization for multiview geometry this paper presents a practical method for finding the provably globally optimal solution to numerous problems in projective geometry including multiview triangulation camera resectioning and homography estimation unlike traditional methods which may get trapped in local minima due to the non convex nature of these problems this approach provides a theoretical guarantee of global optimality the formulation relies on recent developments in fractional programming and the theory of convex underestimators and allows a unified framework for minimizing the standard l 2 norm of reprojection errors which is optimal under gaussian noise as well as the more robust l 1 norm which is less sensitive to outliers even though the worst case complexity of our algorithm is exponential the practical efficacy is empirically demonstrated by good performance on experiments for both synthetic and real data an open source matlab toolbox that implements the algorithm is also made available to facilitate further research

branch and bound methods for euclidean registration problems in this paper we propose a practical and efficient method for finding the globally optimal solution to the problem of determining the pose of an object we present a framework that allows us to use point to point point to line and point to plane correspondences for solving various types of pose and registration problems involving euclidean or similarity transformations traditional methods such as the iterative closest point algorithm or bundle adjustment methods for camera pose may get trapped in local minima due to the nonconvexity of the corresponding optimization problem our approach of solving the mathematical optimization problems guarantees global optimality the optimization scheme is based on ideas from global optimization theory in particular convex underestimators in combination with branch and bound methods we provide a provably optimal algorithm and demonstrate good performance on both synthetic and real data we also give examples of where traditional methods fail due to the local minima problem

go icp a globally optimal solution to 3d icp point set registration the iterative closest point icp algorithm is one of the most widely used methods for point set registration however being based on local iterative optimization icp is known to be susceptible to local minima its performance critically relies on the quality of the initialization and only local optimality is guaranteed this paper presents the first globally optimal algorithm named go icp for euclidean rigid registration of two 3d point sets under the l 2 error metric defined in icp the go icp method is based on a branch and bound scheme that searches the entire 3d motion space se 3 by exploiting the special structure of se 3 geometry we derive novel upper and lower bounds for the registration error function local icp is integrated into the bnb scheme which speeds up the new method while guaranteeing global optimality we also discuss extensions addressing the issue of outlier robustness the evaluation demonstrates that the proposed method is able to produce reliable registration results regardless of the initialization go icp can be applied in scenarios where an optimal solution is desirable or where a good initialization is not always available

a method for registration of 3 d shapes the authors describe a general purpose representation independent method for the accurate and computationally efficient registration of 3 d shapes including free form curves and surfaces the method handles the full six degrees of freedom and is based on the iterative closest point icp algorithm which requires only a procedure to find the closest point on a geometric entity to a given point the icp algorithm always converges monotonically to the nearest local minimum of a mean square distance metric and the rate of convergence is rapid during the first few iterations therefore given an adequate set of initial rotations and translations for a particular class of objects with a certain level of shape complexity one can globally minimize the mean square distance metric over all six degrees of freedom by testing each initial registration one important application of this method is to register sensed data from unfixtured rigid objects with an ideal geometric model prior to shape inspection experimental results show the capabilities of the registration algorithm on point sets curves and surfaces

a branch and bound approach to correspondence and grouping problems data correspondence grouping under an unknown parametric model is a fundamental topic in computer vision finding feature correspondences between two images is probably the most popular application of this research field and is the main motivation of our work it is a key ingredient for a wide range of vision tasks including three dimensional reconstruction and object recognition existing feature correspondence methods are based on either local appearance similarity or global geometric consistency or a combination of both in some heuristic manner none of these methods is fully satisfactory especially in the presence of repetitive image textures or mismatches in this paper we present a new algorithm that combines the benefits of both appearance based and geometry based methods and mathematically guarantees a global optimization our algorithm accepts the two sets of features extracted from two images as input and outputs the feature correspondences with the largest number of inliers which verify both the appearance similarity and geometric constraints specifically we formulate the problem as a mixed integer program and solve it efficiently by a series of linear programs via a branch and bound procedure we subsequently generalize our framework in the context of data correspondence grouping under an unknown parametric model and show it can be applied to certain classes of computer vision problems our algorithm has been validated successfully on synthesized data and challenging real images

singular limits for the compressible euler equation in an exterior domain justification des phenomenes lies au passage des equations des fluides parfaits compressibles a celles des fluides parfaits incompressibles limites singulieres de l equation d euler des fluides compressibles dans un domaine exterieur

on subdirect products of free pro p groups and demushkin groups of infinite depth abstract we study subdirect products of free and demushkin pro p groups of depth developing theory similar to the abstract case see bridson et al 2002 4 furthermore we classify when a subdirect product has homological type fp m for some m 2 a problem still open for abstract groups for m 3

geometry and convergence analysis of algorithms for registration of 3d shapes the computation of a rigid body transformation which optimally aligns a set of measurement points with a surface and related registration problems are studied from the viewpoint of geometry and optimization we provide a convergence analysis for widely used registration algorithms such as icp using either closest points besl and mckay 1992 or tangent planes at closest points chen and medioni 1991 and for a recently developed approach based on quadratic approximants of the squared distance function pottmann et al 2004 icp based on closest points exhibits local linear convergence only its counterpart which minimizes squared distances to the tangent planes at closest points is a gauss newton iteration it achieves local quadratic convergence for a zero residual problem and if enhanced by regularization and step size control comes close to quadratic convergence in many realistic scenarios quadratically convergent algorithms are based on the approach in pottmann et al 2004 the theoretical results are supported by a number of experiments there we also compare the algorithms with respect to global convergence behavior stability and running time

fast rotation search with stereographic projections for 3d registration registering two 3d point clouds involves estimating the rigid transform that brings the two point clouds into alignment recently there has been a surge of interest in using branch and bound bnb optimisation for point cloud registration while bnb guarantees globally optimal solutions it is usually too slow to be practical a fundamental source of difficulty lies in the search for the rotational parameters in this work first by assuming that the translation is known we focus on constructing a fast rotation search algorithm with respect to an inherently robust geometric matching criterion we propose a novel bounding function for bnb that is provably tighter than previously proposed bounds further we also propose a fast algorithm to evaluate our bounding function our idea is based on using stereographic projections to precompute and index all possible point matches in spatial r trees for rapid evaluations the result is a fast and globally optimal rotation search algorithm to conduct full 3d registration we co optimise the translation by embedding our rotation search kernel in a nested bnb algorithm since the inner rotation search is very efficient the overall 6dof optimisation is speeded up significantly without losing global optimality on various challenging point clouds including those taken out of lab settings our approach demonstrates superior efficiency

global optimization through rotation space search this paper introduces a new algorithmic technique for solving certain problems in geometric computer vision the main novelty of the method is a branch and bound search over rotation space which is used in this paper to determine camera orientation by searching over all possible rotations problems can be reduced to known fixed rotation problems for which optimal solutions have been previously given in particular a method is developed for the estimation of the essential matrix giving the first guaranteed optimal algorithm for estimating the relative pose using a cost function based on reprojection errors recently convex optimization techniques have been shown to provide optimal solutions to many of the common problems in structure from motion however they do not apply to problems involving rotations the search method described in this paper allows such problems to be solved optimally apart from the essential matrix the algorithm is applied to the camera pose problem providing an optimal algorithm the approach has been implemented and tested on a number of both synthetically generated and real data sets with good performance

an efficient globally optimal algorithm for asymmetric point matching although the robust point matching algorithm has been demonstrated to be effective for non rigid registration there are several issues with the adopted deterministic annealing optimization technique first it is not globally optimal and regularization on the spatial transformation is needed for good matching results second it tends to align the mass centers of two point sets to address these issues we propose a globally optimal algorithm for the robust point matching problem in the case that each model point has a counterpart in scene set by eliminating the transformation variables we show that the original matching problem is reduced to a concave quadratic assignment problem where the objective function has a low rank hessian matrix this facilitates the use of large scale global optimization techniques we propose a modified normal rectangular branch and bound algorithm to solve the resulting problem where multiple rectangles are simultaneously subdivided to increase the chance of shrinking the rectangle containing the global optimal solution in addition we present an efficient lower bounding scheme which has a linear assignment formulation and can be efficiently solved extensive experiments on synthetic and real datasets demonstrate the proposed algorithm performs favorably against the state of the art methods in terms of robustness to outliers matching accuracy and run time

linear n point camera pose determination the determination of camera position and orientation from known correspondences of 3d reference points and their images is known as pose estimation in computer vision and space resection in photogrammetry it is well known that from three corresponding points there are at most four algebraic solutions less appears to be known about the cases of four and five corresponding points we propose a family of linear methods that yield a unique solution to 4 and 5 point pose determination for generic reference points we first review the 3 point algebraic method then we present our two step 4 point and one step 5 point linear algorithms the 5 point method can also be extended to handle more than five points finally we demonstrate our methods on both simulated and real images we show that they do not degenerate for coplanar configurations and even outperform the special linear algorithm for coplanar configurations in practice

problems with different time scales for nonlinear partial differential equations consider a system of partial differential equations u t varepsilon 1 p 0 p 1 u here 0 varepsilon ll 1 is a small constant p 0 p 0 partial partial x is a differential operator with constant coefficients and p 1 p 1 x t u partial partial x is a quasilinear operator the coefficients of p 0 p 1 are of order o 1 it is shown how to prepare the initial data such that the solutions u x t and their derivatives can be bounded independently of varepsilon applications are discussed

globally optimal algorithms for stratified autocalibration we present practical algorithms for stratified autocalibration with theoretical guarantees of global optimality given a projective reconstruction we first upgrade it to affine by estimating the position of the plane at infinity the plane at infinity is computed by globally minimizing a least squares formulation of the modulus constraints in the second stage this affine reconstruction is upgraded to a metric one by globally minimizing the infinite homography relation to compute the dual image of the absolute conic diac the positive semidefiniteness of the diac is explicitly enforced as part of the optimization process rather than as a post processing step for each stage we construct and minimize tight convex relaxations of the highly non convex objective functions in a branch and bound optimization framework we exploit the inherent problem structure to restrict the search space for the diac and the plane at infinity to a small fixed number of branching dimensions independent of the number of views chirality constraints are incorporated into our convex relaxations to automatically select an initial region which is guaranteed to contain the global minimum experimental evidence of the accuracy speed and scalability of our algorithm is presented on synthetic and real data

demuskin fields with valuations we study the arithmetic structure of fields f of characteristic neq p containing a primitive pth root of unity for which the maximal pro p galois group of f is a finitely generated demuskin group

demuskin groups galois modules and the elementary type conjecture abstract let p be a prime and f p the maximal p extension of a field f containing a primitive pth root of unity we give a new characterization of demuskin groups among galois groups gal f p f when p 2 and assuming the elementary type conjecture when p 2 as well this characterization is in terms of the structure as galois modules of the galois cohomology of index p subgroups of gal f p f

unbiased estimation and statistical analysis of 3 d rigid motion from two views the problem of estimating 3d rigid motion from point correspondences over two views is formulated as nonlinear least squares ls optimization and the statistical behaviors of the errors in the solution are analyzed by introducing a realistic model of noise described in terms of the covariance matrices of n vectors it is shown that the ls solution based on the epipolar constraint is statistically biased the geometry of this bias is described in both quantitative and qualitative terms finally an unbiased estimation scheme is presented and random number simulations are conducted to observe its effectiveness

averaging theorems for conservative systems and the weakly compressible euler equations abstract a generic averaging theorem is proven for systems of odes with two time scales that cannot be globally transformed into the usual action angle variable normal form for such systems this theorem is shown to apply to certain fourier space truncations of the non isentropic slightly compressible euler equations of fluid mechanics for the full euler equations we derive formally the generic limit equations and analyze some of their properties in the one dimensional case we prove a generic converic convergence result for the full euler equations analogous to the result for odes by making use of special properties of the one dimensional equations we prove convergence to the solution of a more complicated set of averaged equations when the genericity assumptions fail

free by demushkin pro p groups we give an example of a short exact sequence 1 n g d 1 of pro p groups such that the cohomological dimension cd g 2 g is topologically finitely generated n is a free pro p group of infinite rank d is a demushkin group for every closed subgroup s of g containing n and any natural number n the inflation map open image in new window is an isomorphism but g is not a free pro p product of a free pro p group by a demushkin group this is a group theoretic version of a question raised by t wurfel for some special galois groups

the compressible euler equations in a bounded domain existence of solutions and the incompressible limit a short time existence theorem is proven for the euler equations for nonisentropic compressible fluid flow in a bounded domain and solutions with low mach number and almost incompressible initial data are shown to be close to corresponding solutions of the equations for incompressible flow

the kummerian property and maximal pro p galois groups abstract for a prime number p we give a new restriction on pro p groups g which are realizable as the maximal pro p galois group g f p for a field f containing a root of unity of order p this restriction arises from kummer theory and the structure of the maximal p radical extension of f we study it in the abstract context of pro p groups g with a continuous homomorphism g 1 p z p and characterize it cohomologically and in terms of 1 cocycles on g this is used to produce new examples of pro p groups which do not occur as maximal pro p galois groups of fields as above

the incompressible limit of the non isentropic euler equations we study the euler equations for slightly compressible fluids that is after rescaling the limits of the euler equations of fluid dynamics as the mach number tends to zero in this paper we consider the general non isentropic equations and general data we first prove the existence of classical solutions for a time independent of the small parameter then on the whole space d we prove that the solution converges to the solution of the incompressible euler equations

a minimal solution for the extrinsic calibration of a camera and a laser rangefinder this paper presents a new algorithm for the extrinsic calibration of a perspective camera and an invisible 2d laser rangefinder lrf the calibration is achieved by freely moving a checkerboard pattern in order to obtain plane poses in camera coordinates and depth readings in the lrf reference frame the problem of estimating the rigid displacement between the two sensors is formulated as one of registering a set of planes and lines in the 3d space it is proven for the first time that the alignment of three plane line correspondences has at most eight solutions that can be determined by solving a standard p3p problem and a linear system of equations this leads to a minimal closed form solution for the extrinsic calibration that can be used as hypothesis generator in a ransac paradigm our calibration approach is validated through simulation and real experiments that show the superiority with respect to the current state of the art method requiring a minimum of five input planes

centered potential regularization for the advection upstream splitting method this paper is devoted to a centered imex scheme in a multidimensional framework for a wide class of multicomponent and isentropic flows the proposed strategy is based on a regularized model where the advection velocity is modified by the gradient of the potential of the conservative forces in both mass and momentum equations the stability of the scheme is ensured by the dissipation of mechanic energy which stands for a mathematical entropy under an advective cfl condition the main physical properties such as positivity conservation of the total momentum and conservation of the steady state at rest are satisfied in addition asymptotic preserving properties in the regimes incompressible and acoustic are analyzed finally several simulations are presented to illustrate our results in a simplified context of oceanic flows in one dimension

review and analysis of solutions of the three point perspective pose estimation problem in this paper the major direct solutions to the three point perspective pose estimation problems are reviewed from a unified perspective beginning with the first solution which was published in 1841 by a german mathematician continuing through the solutions published in the german and then american photogrammetry literature and most recently in the current computer vision literature the numerical stability of these three point perspective solutions are also discussed we show that even in case where the solution is not near the geometric unstable region considerable care must be exercised in the calculation depending on the order of the substitutions utilized the relative error can change over a thousand to one this difference is due entirely to the way the calculations are performed and not due to any geometric structural instability of any problem instance we present an analysis method which produces a numerically stable calculation

wave operators and the incompressible limit of the compressible euler equation in an exterior domain in rn n 2 the solution of the compressible euler equation is shown to converge to that of the incompressible euler equation when the mach number tends to 0 the initial layer appears