dual hybrid trefftz element formulation based on independent boundary traction frame reference epfl article 102727view record in web of science record created on 2007 04 23 modified on 2016 08 08

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

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

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

least squares estimation of transformation parameters between two point patterns in many applications of computer vision the following problem is encountered two point patterns sets of points x sub i and x sub i i 1 2 n are given in m dimensional space and the similarity transformation parameters rotation translation and scaling that give the least mean squared error between these point patterns are needed recently k s arun et al 1987 and b k p horn et al 1987 presented a solution of this problem their solution however sometimes fails to give a correct rotation matrix and gives a reflection instead when the data is severely corrupted the proposed theorem is a strict solution of the problem and it always gives the correct transformation parameters even when the data is corrupted

vision based pose estimation from points with unknown correspondences pose estimation from points with unknown correspondences currently is still a difficult problem in the field of computer vision to solve this problem the softsi algorithm is proposed which can simultaneously obtain pose and correspondences the softsi algorithm is based on the combination of the proposed pnp algorithm the si algorithm and two singular value decomposition svd based shape description theorems other main contributions of this paper are 1 two svd based shape description theorems are proposed 2 by analyzing the calculation process of the si algorithm the method to avoid pose ambiguity is proposed and 3 an acceleration method to quickly eliminate bad initial values for the softsi algorithm is proposed the simulation results show that the si algorithm is accurate while the softsi algorithm is fast robust to noise and has large convergence radius

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

efficient hypersingular line and surface integrals direct evaluation by complex variable differentiation method abstract we present an efficient numerical scheme to evaluate hypersingular integrals appeared in boundary element methods the hypersingular integrals are first separated into regular and singular parts in which the singular integrals are defined as limits around the singularity and their values are determined analytically by taking the finite part values the remaining regular integrals can be evaluated using rational interpolatory quadrature or complex variable differentiation cvdm for the regular function when machine precision like accuracy is required the proposed method is then generalised for evaluating hypersingular surface integrals in which the inner integral is treated as the hypersingular line integral via coordinate transformations the procedure is implemented into 8 node rectangular boundary element and 6 node triangular element for numerical evaluation finally several numerical examples are presented to demonstrate the efficiency of the present method to the best of our knowledge the proposed method is more accurate faster and more generalised than other methods available in the literature to evaluate hypersingular integrals

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

second order symmetric duality in nondifferentiable multiobjective programming a pair of mond weir type second order symmetric nondifferentiable multiobjective programs is formulated weak strong and converse duality theorems are established under h pseudobonvexity assumptions special cases are discussed to show that this paper extends some work appeared in this area

variational formulations for tfem of piezoelectricity abstract the paper presents a family of variational formulations of trefftz finite elements wherein the assumed internal displacement and electric potential fields a priori fulfil the governing differential equations of the problem over the element sub domain while the inter element continuity and the boundary conditions are enforced using a modified variational principle together with an independent frame field defined on each element boundary it is based on four free energy densities each with two kinds of independent variables as basic independent variables i e d e e e d and e based on the assumed intra element and frame fields an element stiffness matrix equation is obtained which is implemented into computer programs for numerical analysis some numerical examples are considered to show the application of the proposed formulation

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

on second order symmetric duality in nondifferentiable programming this article is concerned with a pair of second order symmetric dual non differentiable programs and second order f pseudo convexity we establish the weak and the strong duality theorems for the new pair of dual models under the f pseudo convexity assumption several known results including mond and schechter as well as others are obtained as special cases

epnp an accurate o n solution to the pnp problem we propose a non iterative solution to the pnp problem the estimation of the pose of a calibrated camera from n 3d to 2d point correspondences whose computational complexity grows linearly with n this is in contrast to state of the art methods that are o n 5 or even o n 8 without being more accurate our method is applicable for all n 4 and handles properly both planar and non planar configurations our central idea is to express the n 3d points as a weighted sum of four virtual control points the problem then reduces to estimating the coordinates of these control points in the camera referential which can be done in o n time by expressing these coordinates as weighted sum of the eigenvectors of a 12 12 matrix and solving a small constant number of quadratic equations to pick the right weights furthermore if maximal precision is required the output of the closed form solution can be used to initialize a gauss newton scheme which improves accuracy with negligible amount of additional time the advantages of our method are demonstrated by thorough testing on both synthetic and real data

efficient linear solution of exterior orientation this paper concerns an efficient algorithm for the solution of the exterior orientation problem orthogonal decompositions are used to first isolate the unknown depths of feature points in the camera reference frame allowing the problem to be reduced to an absolute orientation with scale problem which is solved using the singular value decomposition svd the key feature of this approach is the low computational cost compared to existing approaches

pose estimation from line correspondences a complete analysis and a series of solutions in this paper we deal with the camera pose estimation problem from a set of 2d 3d line correspondences which is also known as pnl perspective n line problem we carry out our study by comparing pnl with the well studied pnp perspective n point problem and our contributions are three fold 1 we provide a complete 3d configuration analysis for p3l which includes the well known p3p problem as well as several existing analyses as special cases 2 by exploring the similarity between pnl and pnp we propose a new subset based pnl approach as well as a series of linear formulation based pnl approaches inspired by their pnp counterparts 3 the proposed linear formulation based methods can be easily extended to deal with the line and point features simultaneously

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

second order symmetric duality in non differentiable multiobjective programming with f convexity abstract this paper is concerned with a pair of mond weir type second order symmetric dual non differentiable multiobjective programming problems we establish the weak and strong duality theorems for the new pair of dual models under second order f convexity assumptions several results including many recent works are obtained as special cases

a boundary integral formulation and 2d fundamental solutions for piezoelectric media abstract first based on the basic equations of piezoelectricity the boundary integral formulation is derived by utilizing the reciprocal work theorem second for the plane problem of piezoelectric media one general solution in terms of harmonic functions is derived and the fundamental solutions are therefore obtained numerical calculations by boundary element method bem are performed to give the stress concentration coefficient of an infinite piezoelectric plane with a circular hole as well as the stress and electric intensity factors of a central crack locating on an infinite plate results are found to agree well with the exact solutions

second order symmetric duality in multiobjective programming abstract a pair of mond weir type multiobjective second order symmetric dual programs are formulated without non negativity constraints weak duality strong duality and converse duality theorems are established under bonvexity and pseudobonvexity assumptions a second order self duality theorem is given by assuming the functions involved to be skew symmetric

infinitesimal plane based pose estimation estimating the pose of a plane given a set of point correspondences is a core problem in computer vision with many applications including augmented reality ar camera calibration and 3d scene reconstruction and interpretation despite much progress over recent years there is still the need for a more efficient and more accurate solution particularly in mobile applications where the run time budget is critical we present a new analytic solution to the problem which is far faster than current methods based on solving pose from n n points pnp and is in most cases more accurate our approach involves a new way to exploit redundancy in the homography coefficients this uses the fact that when the homography is noisy it will estimate the true transform between the model plane and the image better at some regions on the plane than at others our method is based on locating a point where the transform is best estimated and using only the local transformation at that point to constrain pose this involves solving pose with a local non redundant 1st order pde we call this framework infinitesimal plane based pose estimation ippe because one can think of it as solving pose using the transform about an infinitesimally small region on the surface we show experimentally that ippe leads to very accurate pose estimates because ippe is analytic it is both extremely fast and allows us to fully characterise the method in terms of degeneracies number of returned solutions and the geometric relationship of these solutions this characterisation is not possible with state of the art pnp methods

second order global optimality conditions for convex composite optimization in recent years second order sufficient conditions of an isolated local minimizer for convex composite optimization problems have been established in this paper second order optimality conditions are obtained of aglobal minimizer for convex composite problems with a non finite valued convex function and a twice strictly differentiable function by introducing a generalized representation condition this result is applied to a minimization problem with a closed convex set constraint which is shown to satisfy the basic constraint qualification in particular second order necessary and sufficient conditions of a solution for a variational inequality problem with convex composite inequality constraints are obtained 1998 the mathematical programming society inc published by elsevier science b v

second order symmetric duality in mathematical programming with f convexity abstract under second order f convexity f concavity and second order f pseudoconvexity f pseudoconcavity appropriate second order duality results for pair of wolfe and mond weir type second order symmetric dual nonlinear programming problems are established these second order duality results are then used to formulate wolfe type and mond weir type second order minimax mixed integer dual programs and symmetric duality theorem is established under separability and second order f convexity f concavity of the kernel function f x y second order symmetric dual fractional mixed integer programs are studied using the above programs moreover second order self duality theorems for the above pairs are obtained assuming f x y to be skew symmetric

non differentiable second order symmetric duality in mathematical programming with f convexity abstract a pair of wolfe type non differentiable second order symmetric primal and dual problems in mathematical programming is formulated the weak and strong duality theorems are then established under second order f convexity assumptions symmetric minimax mixed integer primal and dual problems are also investigated

trefftz indirect methods for plane piezoelectricity in this paper a unified theory for the general solutions of three dimensional elasticity is employed to transform the governing equations of plane piezoelectricity into three generalized laplace equations the latter equations are uncoupled and can be pursued separately by introducing three generalized complex variables the complete solution sets for plane piezoelectricity are constructed by adopting the constituents in the solution sets as the trial functions the trefftz collocation and the trefftz galerkin methods are formulated both methods fall into the category of trefftz indirect methods as the coefficients of their trial functions are non physical numerical examples are presented to illustrate the efficacy of the formulations copyright 2005 john wiley sons ltd

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

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

trefftz solutions for piezoelectricity by lekhnitskii s formalism and boundary collocation method in this paper a solution procedure for plane piezoelectricity is developed by trefftz boundary collocation method starting with the general plane piezoelectricity solution derived by lekhnitskii s formalism the basic sets of trefftz functions which satisfy the homogeneous governing equations are derived moreover special sets of trefftz functions are derived for impermeable elliptical voids impermeable sharp cracks and permeable sharp cracks with arbitrary orientations with respect to the material poling direction the functions in the special sets satisfy not only the homogeneous governing equations but also the boundary conditions at the peripheries of the pertinent defects by adopting trefftz functions as the trial functions multi domain trefftz boundary collocation method is formulated numerical examples are presented to illustrate the efficacy of the formulation copyright 2005 john wiley sons ltd

object pose the link between weak perspective paraperspective and full perspective recently dementhon and davis 1992 1995 proposed a method for determining the pose of a 3 d object with respect to a camera from 3 d to 2 d point correspondences the method consists of iteratively improving the pose computed with a weak perspective camera model to converge at the limit to a pose estimation computed with a perspective camera model in this paper we give an algebraic derivation of dementhon and davis method and we show that it belongs to a larger class of methods where the perspective camera model is approximated either at zero order weak perspective or first order paraperspective we describe in detail an iterative paraperspective pose computation method for both non coplanar and coplanar object points we analyse the convergence of these methods and we conclude that the iterative paraperspective method proposed in this paper has better convergence properties than the iterative weak perspective method we introduce a simple way of taking into account the orthogonality constraint associated with the rotation matrix we analyse the sensitivity to camera calibration errors and we define the optimal experimental setup with respect to imprecise camera calibration we compare the results obtained with this method and with a non linear optimization method

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