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

using points at infinity for parameter decoupling in camera calibration the majority of camera calibration methods including the gold standard algorithm use point based information and simultaneously estimate all calibration parameters in contrast we propose a novel calibration method that exploits line orientation information and decouples the problem into two simpler stages we formulate the problem as minimization of the lateral displacement between single projected image lines and their vanishing points unlike previous vanishing point methods parallel line pairs are not required additionally the invariance properties of vanishing points mean that multiple images related by pure translation can be used to increase the calibration data set size without increasing the number of estimated parameters we compare this method with vanishing point methods and the gold standard algorithm and demonstrate that it has comparable performance

medical image segmentation volume representation and registration using spheres in the geometric algebra framework this paper presents an algorithm to model volumetric data and other one for non rigid registration of such models using spheres formulated in the geometric algebra framework the proposed algorithm for modeling as opposite to the union of spheres method reduces the number of entities spheres used to model 3d data our proposal is based in marching cubes idea using however spheres while the union of spheres uses delaunay tetrahedrization the non rigid registration is accomplished in a deterministic annealing scheme at the preprocessing stage we segment the objects of interest by a segmentation method based on texture information this method is embedded in a region growing scheme as our final application we present a scheme for surgical object tracking using again geometric algebra techniques

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

information theoretic matching of two point sets this paper describes the theoretic roadmap of least relative entropy matching of two point sets the novel feature is to align two point sets without needing to establish explicit point correspondences the recovery of transformational geometry is achieved using a mixture of principal axes registrations whose parameters are estimated by minimizing the relative entropy between the two point distributions and using the expectation maximization algorithm we give evidence of the optimality of the method and we then evaluate the algorithm s performance in both rigid and nonrigid image registration cases

a quantization property for static ginzburg landau vortices for any critical point of the complex ginzburg landau functional in dimension 3 we prove that for large coupling constants if the energy of this critical point on a ball of a given radius r is relatively small compared to r log then the ball of half radius contains no vortex the modulus of the solution is larger than we then show how this property can be applied to describe limiting vortices as e 0 2001 john wiley sons inc

rigid body constrained noisy point pattern matching noisy pattern matching problems arise in many areas e g computational vision robotics guidance and control stereophotogrammetry astronomy genetics and high energy physics least squares pattern matching over the euclidean space e sup n for unordered sets of cardinalities p and q is commonly formulated as a combinatorial optimization problem having complexity p p 1 spl middot spl middot spl middot p q 1 q spl les p since p and q may be 10 sup 3 or larger in typical applications less than satisfactory suboptimal methods are usually employed a hybrid approach is described for solving the pattern matching problem under rigid motion constraints which often apply the method reduces the complexity to l sub 21 spl middot n sup 4 l sub 12 spl middot p sup 3 where l sub 12 and l sub 21 are the number of iterations required by steepest ascent and singular value decomposition svd based procedures respectively

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

vortex filaments pinning for inhomogeneous ginzburg landau equations abstract in this paper the structure of vortices of the ginzburg landau system with impurity in higher dimensions was studied this functional has been proposed as a model for vortex pinning we show that vortices are localized near the set of minimum of impurity this is the pinning phenomenon predicted in the physics literature it was also proven that the limiting vortices is n 2 dimensional rectifiable set

3d free form surface registration and object recognition a new technique to recognise 3d free form objects via registration is proposed this technique attempts to register a free form surface represented by a set of mathtype mtef 2 1 feaafeart1ev1aaatcvaufebsjuyzl2yd9gzlbvynv2caerbulwbln hiov2dgi1btfmbaexatlxbi9gbaerbd9wdylwzybitldharqqtubsr 4rnchbgeagqivu0je9sqqrpepc0xbbl8f4rqqrffpeea0xe9lq jc9 vqaqpepm0xbba9pwe9q8fs0 yqaqpepae9pg0firpepekkfr0xfr x fr xb9adbaqaaegacigaaiaabeqaamaabaabaagcbagaagomamaala aabagaagymaaqaaiaaikdaaagaamiraaaa 38f8 2 frac 1 2 d sensed data points to the model surface represented by another set of mathtype mtef 2 1 feaafeart1ev1aaatcvaufebsjuyzl2yd9gzlbvynv2caerbulwbln hiov2dgi1btfmbaexatlxbi9gbaerbd9wdylwzybitldharqqtubsr 4rnchbgeagqivu0je9sqqrpepc0xbbl8f4rqqrffpeea0xe9lq jc9 vqaqpepm0xbba9pwe9q8fs0 yqaqpepae9pg0firpepekkfr0xfr x fr xb9adbaqaaegacigaaiaabeqaamaabaabaagcbagaagomamaala aabagaagymaaqaaiaaikdaaagaamiraaaa 38f8 2 frac 1 2 d model data points without prior knowledge of correspondence or view points between the two point sets with an initial assumption that the sensed surface be part of a more complete model surface the algorithm begins by selecting three dispersed reliable points on the sensed surface to find the three corresponding model points the method uses the principal curvatures and the darboux frames to restrict the search over the model space invariably many possible model 3 typles will be found for each hypothesized model 3 tuple the transformation to match the sensed 3 tuple to the model 3 tuple can be determined a heuristic search is proposed to single out the optimal transformation in low order time for realistic object recognition or registration where the two range images are often extracted from different view points of the model the earlier assumption that the sensed surface be part of a more complete model surface cannot be relied on with this the sensed 3 tuple must be chosen such that the three sensed points lie on the common region visible to both the sensed and model views we propose an algorithm to select a minimal non redundant set of 3 tuples such that at least one of the 3 tuples will lie on the overlap applying the previous algorithm to each 3 tuple within this set the optimal transformation can be determined experiments using data obtained from a range finder have indicated fast registration for relatively complex test cases if the optimal registrations between the sensed data candidate and each of a set of model data are found then for 3d object recognition purposes the minimal best fit error can be used as the decision rule

a framework for uncertainty and validation of 3 d registrationmethods based on points and frames in this paper we propose and analyze several methods to estimate a rigid transformation from a set of 3 d matched points or matched frames which are important features in geometric algorithms we also develop tools to predict and verify the accuracy of these estimations the theoretical contributions are an intrinsic model of noise for transformations based on composition rather than addition a unified formalism for the estimation of both the rigid transformation and its covariance matrix for points or frames correspondences and a statistical validation method to verify the error estimation which applies even when no ground truth is available we analyze and demonstrate on synthetic data that our scheme is well behaved the practical contribution of the paper is the validation of our transformation estimation method in the case of 3 d medical images which shows that an accuracy of the registration far below the size of a voxel can be achieved and in the case of protein substructure matching where frame features drastically improve both selectivity and complexity

matching sets of 3d line segments with application to polygonal arc matching in this paper we consider two sets of corresponding 3d line segments of equal length we derive a closed form solution for the coordinate transform rotation and translation that gives the best match between the two sets best in the sense of a least squares distance measure between the sets we use these results as the basis to construct efficient algorithms for solving other problems in computer vision specifically we address the problem of matching polygonal arcs that is the problem of finding a match between a short arc and a piece of long arc

new geometric methods for computer vision an application tostructure and motion estimation we discuss a coordinate free approach to the geometry of computer vision problems the technique we use to analyse the three dimensional transformations involved will be that of geometric algebra a framework based on the algebras of clifford and grassmann this is not a system designed specifically for the task in hand but rather a framework for all mathematical physics central to the power of this approach is the way in which the formalism deals with rotations for example if we have two arbitrary sets of vectors known to be related via a 3d rotation the rotation is easily recoverable if the vectors are given extracting the rotation by conventional means is not as straightforward the calculus associated with geometric algebra is particularly powerful enabling one in a very natural way to take derivatives with respect to any multivector general element of the algebra what this means in practice is that we can minimize with respect to rotors representing rotations vectors representing translations or any other relevant geometric quantity this has important implications for many of the least squares problems in computer vision where one attempts to find optimal rotations translations etc given observed vector quantities we will illustrate this by analysing the problem of estimating motion from a pair of images looking particularly at the more difficult case in which we have available only 2d information and no information on range while this problem has already been much discussed in the literature we believe the present formulation to be the only one in which least squares estimates of the motion and structure are derived simultaneously using analytic derivatives

a model of the soft tissue artefact rigid component when using stereophotogrammetry and skin markers the reconstruction of skeletal movement is affected by soft tissue artefact sta this may be described by considering a marker cluster as a deformable shape undergoing a geometric transformation formed by a non rigid change in size and shape and a rigid component translation and rotation displacements a modal decomposition of the sta relative to an appropriately identified basis allows the separation of these components this study proposes a mathematical model of the sta that embeds only its rigid component and estimates the relevant six mode amplitudes as linear functions of selected proximal and distal joint rotations during the analysed task this model was successfully calibrated for thigh and shank using simultaneously recorded pin and skin marker data of running volunteers the root mean square difference between measured and model estimated sta rigid component was 1 1 0 8 mm median inter quartile range over 3 subjects 5 trials 33 markers coordinates and it was mostly due to the wobbling not included in the model knee joint kinematics was estimated using reference pin marker data and skin marker data both raw and compensated with the model estimated sta sta compensation decreased inaccuracy on average from 6 to 1 for flexion extension from 43 to 18 for the other two rotations and from 69 to 25 for the linear displacements thus the proposed mathematical model provides an sta estimate which can be effectively used within optimal bone pose and joint kinematics estimators for artefact compensation and for simulations aimed at their comparative assessments

analysis and approximation of the ginzburg landau model of superconductivity the authors consider the ginzburg landau model for superconductivity first some well known features of superconducting materials are reviewed and then various results concerning the model the resultant differential equations and their solution on bounded domains are derived then finite element approximations of the solutions of the ginzburg landau equations are considered and error estimates of optimal order are derived

registration of translated and rotated images using finite fourier transforms a well known method for image registration is based on a conventional correlation between phase only or whitened versions of the two images to be realigned the method covering rigid translational movements is characterized by an outstanding robustness against correlated noise and disturbances such as those encountered with nonuniform time varying illumination this correspondence discusses an extension of the method to cover both translational and rotational movements

stereo matching using epipolar distance transform in this paper we propose a simple but effective image transform called the epipolar distance transform for matching low texture regions it converts image intensity values to a relative location inside a planar segment along the epipolar line such that pixels in the low texture regions become distinguishable we theoretically prove that the transform is affine invariant thus the transformed images can be directly used for stereo matching any existing stereo algorithms can be directly used with the transformed images to improve reconstruction accuracy for low texture regions results on real indoor and outdoor images demonstrate the effectiveness of the proposed transform for matching low texture regions keypoint detection and description for low texture scenes our experimental results on middlebury images also demonstrate the robustness of our transform for highly textured scenes the proposed transform has a great advantage its low computational complexity it was tested on a macbook air laptop computer with a 1 8 ghz core i7 processor with a speed of about 9 frames per second for a video graphics array sized image

motion analysis of a homogeneously deformable object using subset correspondences abstract analysis of generalized motion parameters involves the estimation of translation rotation and the deformation parameters for a non rigid object most motion analysis methods require a preprocessing step of establishing the feature point correspondence between subsequent time frames such a preprocessing of data is computationally demanding and very often leads to erroneous results we explore the possibility of relaxing the above requirements for a homogeneously deformable object a computationally efficient method is proposed here that needs only subset correspondences between 3d feature points on the object at two different time instants instead of having explicit point correspondence the deformation parameters are obtained utilizing the changes in the euclidean distance for individual feature points belonging to different subsets under the proposed model the object may now be transformed into a rigid one utilizing the estimated deformation parameters the rotation parameters are estimated by considering the invariance properties of the principal moments simulation experiments are carried out to evaluate the performance of the proposed method the applicability of the method is also tested on a real data set

stratified generalized procrustes analysis generalized procrustes analysis computes the best set of transformations that relate matched shape data in shape analysis the transformations are usually chosen as similarities while in general statistical data analysis other types of transformation groups such as the affine group may be used generalized procrustes analysis has a nonlinear and nonconvex formulation the classical approach alternates the computation of a so called reference shape and the computation of transformations relating this reference shape to each shape datum in turn we propose the stratified approach to generalized procrustes analysis it first uses the affine transformation group to analyze the data and then upgrades the solution to the sought after group whether euclidean or similarity we derive a convex formulation for each of these two steps and efficient practical algorithms that gracefully handle missing data incomplete shapes extensive experimental results show that our approaches perform well on simulated and real data in particular our closed form solution gives very accurate results for generalized procrustes analysis of euclidean data

asymptotics for the ginzburg landau equation in arbitrary dimensions let be a bounded simply connected regular domain of rn n 2 for 0 e 1 let ue c be a smooth solution of the ginzburg landau equation in with dirichlet boundary condition ge i e formula we are interested in the asymptotic behavior of ue as e goes to zero under the assumption that ee ue m0 log e and some conditions on ge which allow singularities of dimension n 3 on

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

boundary holder estimates for nonlinear singular elliptic equations abstract in this paper we study the dirichlet problem of a class of nonlinear elliptic equations which includes monge ampere equation k hessian equation and the usual linear elliptic equation this problem becomes singular near the boundary of the domain by carefully constructing sub solutions we obtain the boundary holder estimate for the convex solution to the problem when the domain satisfies exterior sphere condition

a geometric approach for the analysis and computation of the intrinsic camera parameters the authors of this paper adopted the projected characteristics of the absolute conic in terms of the pascal s theorem to propose an entirely new camera calibration method based on purely geometric thoughts the use of this theorem in the geometric algebra framework allows us to compute a projective invariant using the conics of only two images which expressed using brackets helps us to set enough equations to solve the calibration problem the method requires restricted controlled camera movements our method is less sensitive to noise as the kruppa s equation based methods experiments with simulated and real images con rm that the performance of the algorithm is reliable 2001pattern recognition society published by elsevier science ltd all rights reserved

pose estimation by fusing noisy data of different dimensions a method for fusing and integrating different 2d and 3d measurements for pose estimation is proposed the 2d measured data is viewed as 3d data with infinite uncertainty in particular directions the method is implemented using kalman filtering it is robust and easily parallelizable

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

the generalized ginzburg landau equation posed in a quarter plane this paper is concerned with a generalized 1d ginzburg landau equation involving a fifth order term and two nonlinear terms containing spatial derivatives the equation is posed in a quarter plane 0

local minimizers with vortices to the ginzburg landau system in three dimensions we construct local minimizers to the ginzburg landau energy in certain three dimensional domains based on the asymptotic connection between the energy and the total length of vortices using the theory of weak jacobians whenever there exists a collection of locally minimal line segments spanning the domain we can find local minimizers with arbitrarily assigned degrees with respect to each segment 2003 wiley periodicals inc

optimal boundary regularity for a singular monge ampere equation abstract in this paper we study the optimal global regularity for a singular monge ampere type equation which arises from a few geometric problems we find that the global regularity does not depend on the smoothness of domain but it does depend on the convexity of the domain we introduce a type to describe the convexity as a result we show that the more convex is the domain the better is the regularity of the solution in particular the regularity is the best near angular points

on a registration based approach to sensor network localization we consider a registration based approach for localizing sensor networks from range measurements this is based on the assumption that one can find overlapping cliques spanning the network that is for each sensor one can identify geometric neighbors for which all inter sensor ranges are known such cliques can be efficiently localized using multidimensional scaling however since each clique is localized in some local coordinate system we are required to register them in a global coordinate system in other words our approach is based on transforming the localization problem into a problem of registration in this context the main contributions are as follows first we describe an efficient method for partitioning the network into overlapping cliques second we study the problem of registering the localized cliques and formulate a necessary rigidity condition for uniquely recovering the global sensor coordinates in particular we present a method for efficiently testing rigidity and a proposal for augmenting the partitioned network to enforce rigidity a recently proposed semidefinite relaxation of global registration is used for registering the cliques we present simulation results on random and structured sensor networks to demonstrate that the proposed method compares favourably with state of the art methods in terms of run time accuracy and scalability

approximate geometric pattern matching under rigid motions we present techniques for matching point sets in two and three dimensions under rigid body transformations we prove bounds on the worst case performance of these algorithms to be within a small constant factor of optimal and conduct experiments to show that the average performance of these matching algorithms is often better than that predicted by the worst case bounds

image registration using the walsh transform this paper presents a new algorithm which can be used to register images of the same or different modalities e g images with multiple channels such as x rays temperature or elevation or simply images of different spectral bands in particular a correlation based scheme is used but instead of gray values it correlates numbers formulated by different combinations of the extracted local walsh coefficients of the images each image patch is expanded in terms of walsh basis functions each walsh basis function can be thought of as measuring a different aspect of local structure e g horizontal edge corner etc the coefficients of the expansion therefore can be thought of as dense local features estimating at each point the degree of presence of for example a horizontal edge a corner with contrast of a certain type etc these coefficients are normalized and used as digits in a chosen number system which allows one to create a unique number for each type of local structure the choice of the basis of the number system allows one to give different emphasis to different types of local feature e g corners versus edges and thus the method we present forms a unified framework in terms of which several feature matching methods may be interpreted the algorithm is compared with wavelet and contour based approaches using simulated and real images the two images are assumed to differ from each other by a rotation and a translation only

a robust method for rotation estimation using spherical harmonics representation this paper presents a robust method for 3d object rotation estimation using spherical harmonics representation and the unit quaternion vector the proposed method provides a closed form solution for rotation estimation without recurrence relations or searching for point correspondences between two objects the rotation estimation problem is casted as a minimization problem which finds the optimum rotation angles between two objects of interest in the frequency domain the optimum rotation angles are obtained by calculating the unit quaternion vector from a symmetric matrix which is constructed from the two sets of spherical harmonics coefficients using eigendecomposition technique our experimental results on hundreds of 3d objects show that our proposed method is very accurate in rotation estimation robust to noisy data missing surface points and can handle intra class variability between 3d objects

an efficient fuzzy algorithm for aligning shapes under affine transformations abstract a fuzzy algorithm for aligning object shapes under affine transformations is proposed in this paper the algorithm with the name of fuzzy alignment algorithm faa extends marques algorithm to affine transformations it can efficiently estimate the point correspondence and the relevant affine transformational parameters between the feature points of the object shape and the reference shape in this algorithm the fuzzy point correspondence degrees are used to describe an uncertainty point assignment then both the parameters of the affine transformation and the fuzzy correspondence degrees are iteratively calculated by minimizing a constrained fuzzy objective function to prevent faa from sinking into local minimum when the shapes are greatly deformed an initialization method based on affine invariants is designed comparing to the eigenvector method the effectiveness and robustness of the proposed algorithm is investigated with a sensitivity study based on randomly generated points at last good performance of faa is illustrated with several experiments on aligning digits and object shapes

continuity equations and ode flows with non smooth velocity in this paper we review many aspects of the well posedness theory for the cauchy problem for the continuity and transport equations and for the ordinary differential equation ode in this framework we deal with velocity fields that are not smooth but enjoy suitable weak differentiability assumptions we first explore the connection between the partial differential equation pde and the ode in a very general non smooth setting then we address the renormalization property for the pde and prove that such a property holds for sobolev velocity fields and for bounded variation velocity fields finally we present an approach to the ode theory based on quantitative estimates

spinal shape changes resulting from scoliotic spine surgical instrumentation expressed as intervertebral rotations and centers of rotation this paper reports the changes in spinal shape resulting from scoliotic spine surgical instrumentation expressed as intervertebral rotations and centers of rotation the objective is to test the hypothesis that the type of spinal instrumentation system cotrel dubousset versus colorado does not influence these motion parameters intervertebral rotations and centers of rotation of the scoliotic spines were computed from the pre and post operative radiographs of 82 patients undergoing spinal correction the three dimensional 3d reconstruction of six anatomical landmarks was achieved for each of the thoracic and lumbar vertebrae a least squares approach based on singular value decomposition was used to calculate the rigid body transformation parameters average centers of rotation for all intervertebral levels are located in the neural canal at the mid sagittal plane and approximately at the superior endplate level of the inferior vertebra intervertebral rotations have components in all planes 6 7 degrees frontal 5 5 degrees sagittal and 4 5 degrees transverse rms for all intervertebral levels nearly all intervertebral rotations and centers of rotation are not significantly different for the two instrumentation systems various intervertebral rotations and 3d reconstruction errors were simulated on a theoretical model of a lumbar functional unit to assess the proposed method intervertebral rotation errors were 1 7 degrees when simulating 3d errors of 3mm on the position of the landmarks maximum errors for the position of centers of rotation were below 1cm in the case of intervertebral rotations larger than 2 5 degrees most cases but were larger 38 mm for small intervertebral rotations 1 degrees the type of instrumentation system did not influence intervertebral rotations and centers of rotation these results provide valuable data for the development and validation of simulation models for surgical instrumentation of idiopathic scoliosis

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 spinor ginzburg landau model in dimension three abstract recent papers in physics literature have introduced spin coupled or spinor ginzburg landau models for complex vector valued order parameters in order to account for ferromagnetic or antiferromagnetic effects in high temperature superconductors in this paper we study the asymptotic behavior of solutions to this model in dimension 3 it was also proven that limit singularities set is one dimensional rectifiable which consists of one or more line segments

applications of tensor theory to object recognition and orientation determination a method is developed by which images resulting from orthogonal projection of rigid planar patch objects arbitrarily oriented in three dimensional 3 d space may be used to form systems of linear equations which are solved for the affine transform relating the images the technique is applicable to complete images and to unlabeled feature sets derived from images and with small modification may be used to transform images of unknown objects such that they represent images of those objects from a known orientation for use in object identification no knowledge of point correspondence between images is required theoretical development of the method and experimental results are presented the method is shown to be computationally efficient requiring o n multiplications and additions where depending on the computation algorithm n may equal the number of object or edge picture elements

point set registration coherent point drift point set registration is a key component in many computer vision tasks the goal of point set registration is to assign correspondences between two sets of points and to recover the transformation that maps one point set to the other multiple factors including an unknown nonrigid spatial transformation large dimensionality of point set noise and outliers make the point set registration a challenging problem we introduce a probabilistic method called the coherent point drift cpd algorithm for both rigid and nonrigid point set registration we consider the alignment of two point sets as a probability density estimation problem we fit the gaussian mixture model gmm centroids representing the first point set to the data the second point set by maximizing the likelihood we force the gmm centroids to move coherently as a group to preserve the topological structure of the point sets in the rigid case we impose the coherence constraint by reparameterization of gmm centroid locations with rigid parameters and derive a closed form solution of the maximization step of the em algorithm in arbitrary dimensions in the nonrigid case we impose the coherence constraint by regularizing the displacement field and using the variational calculus to derive the optimal transformation we also introduce a fast algorithm that reduces the method computation complexity to linear we test the cpd algorithm for both rigid and nonrigid transformations in the presence of noise outliers and missing points where cpd shows accurate results and outperforms current state of the art methods

registration of mr mr and mr spect brain images by fast stochastic optimization of robust voxel similarity measures abstract this paper describes a robust fully automated algorithm to register intrasubject 3d single and multimodal images of the human brain the proposed technique accounts for the major limitations of the existing voxel similarity based methods sensitivity of the registration to local minima of the similarity function and inability to cope with gross dissimilarities in the two images to be registered local minima are avoided by the implementation of a stochastic iterative optimization technique fast simulated annealing in addition robust estimation is applied to reject outliers in case the images show significant differences due to lesion evolution incomplete acquisition non gaussian noise etc in order to evaluate the performance of this technique 2d and 3d mr and spect human brain images were artificially rotated translated and corrupted by noise a test object was acquired under different angles and positions for evaluating the accuracy of the registration the approach has also been validated on real multiple sclerosis mr images of the same patient taken at different times furthermore robust mr spect image registration has permitted the representation of functional features for patients with partially complex seizures the fast simulated annealing algorithm combined with robust estimation yields registration errors that are less than 1 in rotation and less than 1 voxel in translation image dimensions of 128 3 it compares favorably with other standard voxel similarity based approaches

a maximum likelihood approach to joint image registration and fusion both image registration and fusion can be formulated as estimation problems instead of estimating the registration parameters and the true scene separately as in the conventional way we propose a maximum likelihood approach for joint image registration and fusion in this paper more precisely the fusion performance is used as the criteria to evaluate the registration accuracy hence the registration parameters can be automatically tuned so that both fusion and registration can be optimized simultaneously the expectation maximization algorithm is employed to solve this joint optimization problem the cramer rao bound crb is then derived our experiments use several types of sensory images for performance evaluation such as visual images ir thermal images and hyperspectral images it is shown that the mean square error of estimating the registration parameters using the proposed method is close to the crbs at the mean time an improved fusion performance can be achieved in terms of the edge preservation measure qab f compared to the laplacian pyramid fusion approach

iterative closest geometric objects registration abstract in this paper closed form solutions are obtained for registering two sets of line segments triangle patches or even general simple geometric objects that are defined by a set of ordered points based on these new registration approaches the iterative closest line segment registration icl algorithm and the iterative closest triangle patch registration ict algorithm are developed similar to the icp algorithm to simplify the mathematical representation the concept of matrix scalar product is defined and some of its properties are given the newly developed registration methods are tested the test shows that the icl algorithm and the ict algorithm work much better than the conventional icp algorithm considering that the icl and the ict algorithms are much less sensitive to the initial orientations of the object

grassmann calculus pseudoclassical mechanics and geometric algebra a reformulation of grassmann calculus is presented in terms of geometric algebra a unified language for physics based on clifford algebra in this reformulation grassmann generators are replaced by vectors so that every product of generators has a natural geometric interpretation the calculus introduced by berezin the method of second quantization academic new york 1966 is shown to be unnecessary amounting to no more than an algebraic contraction this approach is not only conceptually clearer but it is also computationally more efficient as demonstrated by treatments of the grauss integral and the grassmann fourier transform the reformulation is applied to pseudoclassical mechanics ann phys 104 336 1977 where it is shown to lead to a new concept the multivector lagrangian to illustrate this idea the three dimensional fermi oscillator is reformulated and solved and its symmetry properties discussed as a result a new and highly compact formula for generating super lie algebras is revealed the paper ends with a discussion of quantization outlining a new approach to fermionic path integrals

least squares fitting of two 3 d point sets two point sets pi and p i i 1 2 n are related by p i rpi t ni where r is a rotation matrix t a translation vector and ni a noise vector given pi and p i we present an algorithm for finding the least squares solution of r and t which is based on the singular value decomposition svd of a 3 3 matrix this new algorithm is compared to two earlier algorithms with respect to computer time requirements

global holder estimates for equations of monge ampere type we prove interior oscillation and global holder estimates independent of any boundary data for convex solutions of certain types of monge ampere equations under suitable conditions on the equation and the domain n we also deduce the existence uniqueness regularity and unboundedness under suitable conditions of convex extremal solutions of certain monge ampere equations

estimation of optimal fiducial target registration error in the presence of heteroscedastic noise we study the effect of point dependent heteroscedastic and identically distributed anisotropic fiducial localization noise on fiducial target registration error tre we derive an analytic expression based on the concept of mechanism spatial stiffness for predicting tre the accuracy of the predicted tre is compared to simulated values where the optimal registration transformation is computed using the heteroscedastic errors in variables algorithm the predicted values are shown to be contained by the 95 confidence intervals of the root mean square tre obtained from the simulations

moshfit algorithms for occlusion tolerant mean shape and rigid motion from 3d movement data this work addresses the use of 3d point data to measure rigid motions in the presence of occlusion and without reference to a prior model of relative point locations this is a problem where cluster based measurement techniques are used e g for measuring limb movements and no static calibration trial is available the same problem arises when performing the task known as roving capture in which a mobile 3d movement analysis system is moved through a volume with static markers in unknown locations and the ego motion of the system is required in order to understand biomechanical activity in the environment to provide a solution for both of these applications the new concept of a visibility graph is introduced and is combined with a generalised procrustes method adapted from ones used by the biological shape statistics and computer graphics communities recent results on shape space manifolds are applied to show sufficient conditions for convergence to unique solution algorithm source code is available and referenced here processing speed and rate of convergence are demonstrated using simulated data positional and angular accuracy are shown to be equivalent to approaches which require full calibration to within a small fraction of input resolution typical processing times for sub micron convergence are found to be fractions of a second so the method is suitable for workflows where there may be time pressure such as in sports science and clinical analysis

first order error propagation of the procrustes method for 3d attitude estimation the well known procrustes method determines the optimal rigid body motion that registers two point clouds by minimizing the square distances of the residuals in this paper we perform the first order error analysis of this method for the 3d case fully specifying how directional noise in the point clouds affects the estimated parameters of the rigid body motion these results are much more specific than the error bounds which have been established in numerical analysis we provide an intuitive understanding of the outcome to facilitate direct use in applications

estimation of nonlinear errors in variables models for computer vision applications in an errors in variables eiv model all the measurements are corrupted by noise the class of eiv models with constraints separable into the product of two nonlinear functions one solely in the variables and one solely in the parameters is general enough to represent most computer vision problems we show that the estimation of such nonlinear eiv models can be reduced to iteratively estimating a linear model having point dependent i e heteroscedastic noise process particular cases of the proposed heteroscedastic errors in variables heiv estimator are related to other techniques described in the vision literature the sampson method renormalization and the fundamental numerical scheme in a wide variety of tasks the heiv estimator exhibits the same or superior performance as these techniques and has a weaker dependence on the quality of the initial solution than the levenberg marquardt method the standard approach toward estimating nonlinear models

lie groups as spin groups it is shown that every lie algebra can be represented as a bivector algebra hence every lie group can be represented as a spin group thus the computational power of geometric algebra is available to simplify the analysis and applications of lie groups and lie algebras the spin version of the general linear group is thoroughly analyzed and an invariant method for constructing real spin representations of other classical groups is developed moreover it is demonstrated that every linear transformation can be represented as a monomial of vectors in geometric algebra

distribution of fiducial registration error in rigid body point based registration rigid body point based registration is frequently used in computer assisted surgery to align corresponding points or fiducials in preoperative and intraoperative data this alignment is mostly achieved by assuming the same homogeneous error distribution for all the points however due to the properties of the medical instruments used in measuring the point coordinates the error distribution might be inhomogeneous and different for each point in this paper in an effort to understand the effect of error distribution in the localized points on the performed registration we derive a closed form solution relating the error distribution of each point with the performed registration accuracy the solution uses maximum likelihood estimation to calculate the probability density function of registration error at each fiducial point extensive numerical simulations are performed to validated the proposed solution

a physics based coordinate transformation for 3 d image matching many image matching schemes are based on mapping coordinate locations such as the locations of landmarks in one image to corresponding locations in a second image a new approach to this mapping coordinate transformation called the elastic body spline ebs is described the spline is based on a physical model of a homogeneous isotropic three dimensional 3 d elastic body the model can approximate the way that some physical objects deform the ebs as well as the affine transformation the thin plate spline and the volume spline are used to match 3 d magnetic resonance images mri s of the breast that are used in the diagnosis and evaluation of breast cancer these coordinate transformations are evaluated with different types of deformations and different numbers of corresponding paired coordinate locations in all but one of the cases considered using the ebs yields more similar images than the other methods

point based rigid body registration using an unscented kalman filter we present and validate a novel registration algorithm mapping two data sets generated from a rigid object in the presence of gaussian noise the proposed method is based on the unscented kalman filter ukf algorithm that is generally employed for analyzing nonlinear systems corrupted by additive gaussian noise first we employ our proposed registration algorithm to fit two randomly generated data sets in the presence of isotropic gaussian noise when the corresponding points between the two data sets are assumed to be known then we extend the registration method to the case where the data with known correspondences is stimulated by anisotropic gaussian noise the new registration method not only reliably converges to the correct registration solution but it also estimates the variance as a confidence measure for each of the estimated registration transformation parameters furthermore we employ the proposed registration algorithm for rigid body point based registration where corresponding points between two registering data sets are unknown the algorithm is tested on point data sets which are garnered from a pelvic cadaver and a scaphoid bone phantom by means of computed tomography ct and tracked free hand ultrasound imaging the collected 3 d points in the ultrasound frame are registered to the 3 d meshes in the ct frame by using the proposed and the standard iterative closest points icp registration algorithms experimental results demonstrate that our proposed method significantly outperforms the icp registration algorithm in the presence of additive gaussian noise it is also shown that the proposed registration algorithm is more robust than the icp registration algorithm in terms of outliers in data sets and initial misalignment between the two data sets

from image quadrilaterals to symmetrical trapezia abstract this paper concerns the 3 d interpretation of image quadrilaterals as the perspective projections of bilateral symmetric trapezia simple algorithms are described for reconstructing a symmetric trapezium from a given image quadrilateral and for determining the 3 d motion of a symmetric trapezium from two matched image quadrilaterals several results are established and or further verified including the necker reversal ambiguity in the interpretation of image quadrilaterals as the perspective projection of bilateral symmetric trapezia experiments with both synthetic and real images are included to demonstrate the validity of the theoretic results

convergence of the parabolic ginzburg landau equation to motion by mean curvature for the complex parabolic ginzburg landau equation we prove that asymptotically vorticity evolves according to motion by mean curvature in brakke s weak formulation the only assumption is a natural energy bound on the initial data in some cases we also prove convergence to enhanced motion in the sense of ilmanen