boundary behavior of solutions to some singular elliptic boundary value problems abstract let be a bounded domain with smooth boundary in r n n 1 for the more general weight b some nonlinearities f and singularities g by two kinds of nonlinear transformations a new perturbation method which was introduced by garcia melian in j garcia melian boundary behavior of large solutions to elliptic equations with singular weights nonlinear anal 67 2007 818 826 and comparison principles we show that the boundary behavior of solutions to a boundary blow up elliptic problem w b x f w w 0 x w and a singular dirichlet problem u b x g u u 0 x u 0 has the same form under the nonlinear transformations which can be determined in terms of the inverses of the transformations

realigning 2d and 3d object fragments without correspondences this paper addresses the problem of simultaneous estimation of different linear deformations resulting in a global non linear transformation between an original object and its broken fragments a general framework is proposed without using correspondences where the solution of a polynomial system of equations directly provides the parameters of the alignment we quantitatively evaluate the proposed algorithm on a large synthetic dataset containing 2d and 3d images where linear rigid body and affine transformations are considered we also conduct an exhaustive analysis of the robustness against segmentation errors and the numerical stability of the proposed method moreover we present experiments on 2d real images as well as on volumetric medical images

uncertainty characterization of the orthogonal procrustes problem with arbitrary covariance matrices abstract this paper addresses the weighted orthogonal procrustes problem of matching stochastically perturbed point clouds formulated as an optimization problem with a closed form solution a novel uncertainty characterization of the solution of this problem is proposed resorting to perturbation theory concepts which admits arbitrary transformations between point clouds and individual covariance and cross covariance matrices for the points of each cloud the method is thoroughly validated through extensive monte carlo simulations and particularly interesting cases where nonlinearities may arise are further analyzed

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

smoothing and matching of 3 d space curves we present a new approach to the problem of matching 3 d curves the approach has a low algorithmic complexity in the number of models and can operate in the presence of noise and partial occlusions our method builds upon the seminal work of kishon et al 1990 where curves are first smoothed using b splines with matching based on hashing using curvature and torsion measures however we introduce two enhancements we present experimental results using synthetic data and also using characteristic curves extracted from 3 d medical images an earlier version of this article was presented at the 2nd european conference on computer vision in italy

the relationship between breaking the diffie hellman protocol and computing discrete logarithms both uniform and nonuniform results concerning the security of the diffie hellman key exchange protocol are proved first it is shown that in a cyclic group g of order g prod p i e i where all the multiple prime factors of g are polynomial in log g there exists an algorithm that reduces the computation of discrete logarithms in g to breaking the diffie hellman protocol in g and has complexity sqrt max nu p i cdot log g o 1 where nu p stands for the minimum of the set of largest prime factors of all the numbers d in the interval p 2 sqrt p 1 p 2 sqrt p 1 under the unproven but plausible assumption that nu p is polynomial in log p this reduction implies that the diffie hellman problem and the discrete logarithm problem are polynomial time equivalent in g second it is proved that the diffie hellman problem and the discrete logarithm problem are equivalent in a uniform sense for groups whose orders belong to certain classes there exists a polynomial time reduction algorithm that works for all those groups moreover it is shown that breaking the diffie hellman protocol for a small but nonnegligible fraction of the instances is equally difficult as breaking it for all instances finally efficient constructions of groups are described for which the algorithm reducing the discrete logarithm problem to the diffie hellman problem is efficiently constructible

nonlinear elliptic equations with singular boundary conditions and stochastic control with state constraints hamiltoniens sousquadratiques conditions aux limites infinies et donnees d explosion hamiltoniens superquadratiques formulation viscosite des conditions aux limites le probleme ergodique commande stochastique optimale avec contraintes d etat

a second order estimate for blow up solutions of elliptic equations abstract we investigate second term asymptotic behavior of boundary blow up solutions to the problems u b x f u x subject to the singular boundary condition u x in a bounded smooth domain r n b x is a non negative weight function the nonlinearly f is regularly varying at infinity with index 1 that is lim u f u f u for every 0 and the mapping f u u is increasing on 0 the main results show how the mean curvature of the boundary appears in the asymptotic expansion of the solution u x our analysis relies on suitable upper and lower solutions and the karamata regular variation theory

closed form solutions for physically based shape modeling and recognition the authors present a closed form physically based solution for recovering a three dimensional 3 d solid model from collections of 3 d surface measurements given a sufficient number of independent measurements the solution is overconstrained and unique except for rotational symmetries the proposed approach is based on the finite element method fem and parametric solid modeling using implicit functions this approach provides both the convenience of parametric modeling and the expressiveness of the physically based mesh formulation and in addition can provide great accuracy at physical simulation a physically based object recognition method that allows simple closed form comparisons of recovered 3 d solid models is presented the performance of these methods is evaluated using both synthetic range data with various signal to noise ratios and using laser rangefinder data

boundary blow up in nonlinear elliptic equations of bieberbach rademacher type the research of the first author was carried out at victoria university melbourne with the support of the australian government through detya the second author has been supported by grant 2 cex06 11 18 2006

registering multiview range data to create 3d computer objects concerns the problem of range image registration for the purpose of building surface models of 3d objects the registration task involves finding the translation and rotation parameters which properly align overlapping views of the object so as to reconstruct from these partial surfaces an integrated surface representation of the object the registration task is expressed as an optimization problem we define a function which measures the quality of the alignment between the partial surfaces contained in two range images as produced by a set of motion parameters this function computes a sum of euclidean distances from control points on one surfaces to corresponding points on the other the strength of this approach is in the method used to determine point correspondences it reverses the rangefinder calibration process resulting in equations which can be used to directly compute the location of a point in a range image corresponding to an arbitrary point in 3d space a stochastic optimization technique very fast simulated reannealing vfsr is used to minimize the cost function dual view registration experiments yielded excellent results in very reasonable time a multiview registration experiment took a long time a complete surface model was then constructed from the integration of multiple partial views the effectiveness with which registration of range images can be accomplished makes this method attractive for many practical applications where surface models of 3d objects must be constructed

boundary blow up elliptic problems with nonlinear gradient terms by karamata regular variation theory and perturbation method we show the exact asymptotical behaviour of solutions near the boundary to nonlinear elliptic problems u u q b x g u u 0 in u where is a bounded domain with smooth boundary in rn q 0 g c1 0 g 0 0 g is regularly varying at infinity with index with 0 and b is nonnegative nontrivial in which may be vanishing on the boundary

asymptotic estimates of boundary blow up solutions to the infinity laplace equations abstract in this paper we study the asymptotic behavior of boundary blow up solutions to the equation u b x f u in where is the laplacian the nonlinearity f is a positive increasing function in 0 and the weighted function b c is positive in and may vanish on the boundary we first establish the exact boundary blow up estimates with the first expansion when f is regularly varying at infinity with index p 3 and the weighted function b is controlled on the boundary in some manner furthermore for the case of f s s p 1 c g s with the function g normalized regularly varying with index q 0 we obtain the second expansion of solutions near the boundary it is interesting that the second term in the asymptotic expansion of boundary blow up solutions to the infinity laplace equation is independent of the geometry of the domain quite different from the boundary blow up problems involving the classical laplacian

boundary blow up solutions in the unit ball asymptotics uniqueness and symmetry abstract we calculate the full asymptotic expansion of boundary blow up solutions see eq 1 below for any nonlinearity f our approach enables us to state sharp qualitative results regarding uniqueness and radial symmetry of solutions as well as a characterization of nonlinearities for which the blow up rate is universal lastly we study in more detail the standard nonlinearities f u u p p 1

optimal uniqueness theorems and exact blow up rates of large solutions in this paper we prove some optimal uniqueness results for large solutions of a canonical class of semilinear equations under minimal regularity conditions on the weight function in front of the non linearity and combine these results with the localization method introduced in lopez gomez the boundary blow up rate of large solutions j differential equations 195 2003 25 45 to prove that any large solution l of u a x up p 1 a 0 must satisfy limx x0l x fx0 dist x i0 pp 1p 1p 1p 1p 1foreachx0 where fx0 t t 0sfx01p 1 p 1p 1ds i0 limt 0fx0 t fx0 t fx0 t 2 and fx0 is any smooth extension of the boundary normal section of a at x0 i e fx0 t a x0 tnx0 t 0 t 0 subsequently nx0 stands for the outward unit normal at x0 therefore the theory can be extended to cover the general case when fx0 l1p 1

the second order expansion of boundary blow up solutions for infinity laplacian equations abstract in this paper by using karamata regular variation theory and a perturbed argument we study the second order expansion of viscosity solutions to boundary blow up elliptic problem u b x f u x u where is a bounded domain with c 2 boundary in r n b c is non negative and non trivial in f c 1 0 is a normalized regularly varying function at infinity with index 3

a frequency domain technique for range data registration this work introduces an original method for registering pairs of 3d views consisting of range data sets which operates in the frequency domain the fourier transform allows the decoupling of the estimate of the rotation parameters from the estimate of the translation parameters our algorithm exploits this well known property by suggesting a three step procedure the rotation parameters are estimated by the first two steps through convenient representations and projections of the fourier transforms magnitudes and the translational displacement is recovered by the third step by means of a standard phase correlation technique after compensating one of the two views for rotation the performance of the algorithm which is well suited for unsupervised registration is clearly assessed through extensive testing with several objects and shows that good and robust estimates of 3d rigid motion are achievable our algorithm can be used as a prealignment tool for more accurate space domain registration techniques like the icp algorithm

general approach to first order error prediction in rigid point registration a general approach to the first order analysis of error in rigid point registration is presented that accommodates fiducial localization error fle that may be inhomogeneous varying from point to point and anisotropic varying with direction and also accommodates arbitrary weighting that may also be inhomogeneous and anisotropic covariances are derived for target registration error tre and for weighted fiducial registration error fre in terms of covariances of fle culminating in a simple implementation that encompasses all combinations of weightings and anisotropy furthermore it is shown that for ideal weighting in which the weighting matrix for each fiducial equals the inverse of the square root of the cross covariance of its two space fle fluctuations of fre and tre are mutually independent these results are validated by comparison with previously published expressions and by simulation furthermore simulations for randomly generated fiducial positions and fles are presented that show that correlation is negligible in the exact case for both ideal and uniform weighting i e no weighting the latter of which is employed in commercial surgical guidance systems from these results we conclude that for these weighting schemes while valid expressions exist relating the covariance of fre to the covariance of tre there are no measures of the goodness of fit of the fiducials for a given registration that give to first order any information about the fluctuation of tre from its expected value and none that give useful information in the exact case therefore as estimators of registration accuracy such measures should be approached with extreme caution both by the purveyors of guidance systems and by the practitioners who use them

comprehensive use of curvature for robust and accurate online surface reconstruction interactive real time scene acquisition from hand held depth cameras has recently developed much momentum enabling applications in ad hoc object acquisition augmented reality and other fields a key challenge to online reconstruction remains error accumulation in the reconstructed camera trajectory due to drift inducing instabilities in the range scan alignments of the underlying iterative closest point icp algorithm various strategies have been proposed to mitigate that drift including sift based pre alignment color based weighting of icp pairs stronger weighting of edge features and so on in our work we focus on surface curvature as a feature that is detectable on range scans alone and hence does not depend on accurate multi sensor alignment in contrast to previous work that took curvature into consideration however we treat curvature as an independent quantity that we consistently incorporate into every stage of the real time reconstruction pipeline including densely curvature weighted icp range image fusion local surface reconstruction and rendering using multiple benchmark sequences and in direct comparison to other state of the art online acquisition systems we show that our approach significantly reduces drift both when analyzing individual pipeline stages in isolation as well as seen across the online reconstruction pipeline as a whole

symmetry of large solutions of nonlinear elliptic equations in a ball let g be a locally lipschitz continuous real valued function which satisfies the keller osserman condition and is convex at infinity then any large solution of u g u 0 in a ball is radially symmetric

robust matching of 3d contours using iterative closest point algorithm improved by m estimation abstract an extension of the iterative closest point matching by m estimation is proposed for realization of robustness to non overlapping data or outlying data in two sets of contour data or depth images for rigid bodies an objective function which includes independent residual components for each of x y and z coordinates is originally defined and proposed to evaluate the fitness simultaneously dealing with a distribution of outlying gross noise the proposed procedure is based on modified m estimation iterations with bi weighting coefficients for selecting corresponding points for optimization of estimating the transforms for matching the transforms can be represented by quaternions in the procedure to eliminate redundancy in representation of rotational degree of freedom by linear matrices optimization steps are performed by the simplex method because it does not need computation of differentiation some fundamental experiments utilizing real data of 2d and 3d measurement show effectiveness of the proposed method when reasonable initial positions are given the unique solution of position could be provided in spite of surplus point data in the objects and then the outlying data could be filtered out from the normal ones by the proposed method

curvature based algorithms for nonrigid motion and correspondence estimation we present a novel technique for utilizing the gaussian curvature information in 3d nonrigid motion estimation in the absence of known correspondence differential geometric constraints derived in the paper allow one to estimate parameters of the local affine motion model given the values of gaussian curvature before and after motion these constraints can be further combined with the previously known constraints based on the unit normals before and after motion our experiments demonstrate that the resulting hybrid algorithm is more accurate than each of its constituents and more accurate than the classical icp algorithm we also present a technique for curvilinear orthogonalization of quadratic monge patches that is essential in our derivation and useful in other applications

icp registration using invariant features investigates the use of euclidean invariant features in a generalization of iterative closest point icp registration of range images pointwise correspondences are chosen as the closest point with respect to a weighted linear combination of positional and feature distances it is shown that under ideal noise free conditions correspondences formed using this distance function are correct more often than correspondences formed using the positional distance alone in addition monotonic convergence to at least a local minimum is shown to hold for this method when noise is present a method that automatically sets the optimal relative contribution of features and positions is described this method trades off the error in feature values due to noise against the error in positions due to misalignment experimental results suggest that using invariant features decreases the probability of being trapped in a local minimum and may be an effective solution for difficult range image registration problems where the scene is very small compared to the model

blow up rates of large solutions for elliptic equations in this paper we mainly study the boundary behavior of solutions to boundary blow up elliptic problems for more general nonlinearities f which may be rapidly varying at infinity u b x f u x u where is a bounded domain with smooth boundary in rn and b c which is positive in and may be vanishing on the boundary and rapidly varying near the boundary further when f s sp f1 s for s sufficiently large where p 1 and f1 is normalized regularly varying at infinity with index p1 0 p we show the influence of the geometry of on the boundary behavior for solutions to the problem we also give the existence and uniqueness of solutions

factoring polynomials with rational coefficients in this paper we present a polynomial time algorithm to solve the following problem given a non zero polynomial fe q x in one variable with rational coefficients find the decomposition of f into irreducible factors in q x it is well known that this is equivalent to factoring primitive polynomials fez x into irreducible factors in z x here we call f z x primitive if the greatest common divisor of its coefficients the content of f is 1 our algorithm performs well in practice cf 8 its running time measured in bit operations is o nl2 n9 log fd3

a necessary and sufficient condition for existence of large solutions to semilinear elliptic equations we consider the semilinear equation u p x f u on a domain rn n 3 where f is a nonnegative nondecreasing continuous function which vanishes at the origin and p is a nonnegative continuous function with the property that any zero of p is contained in a bounded domain in such that p is positive on its boundary for bounded we show that a nonnegative solution u satisfying u x as x exists if and only if the function s s0 f t dt satisfies 1 s 1 2 ds for unbounded including rn we show that a similar result holds where u x as x within and u x as x if p x decays to zero rapidly as x

surface bounded growth modeling applied to human mandibles from a set of longitudinal three dimensional scans of the same anatomical structure the authors have accurately modeled the temporal shape and size changes using a linear shape model on a total of 31 computed tomography scans of the mandible from six patients 14 851 semilandmarks are found automatically using shape features and a new algorithm called geometry constrained diffusion the semilandmarks are mapped into procrustes space principal component analysis extracts a one dimensional subspace which is used to construct a linear growth model the worst case mean modeling error in a cross validation study is 3 7 mm

iterative point matching for registration of free form curves and surfaces a heuristic method has been developed for registering two sets of 3 d curves obtained by using an edge based stereo system or two dense 3 d maps obtained by using a correlation based stereo system geometric matching in general is a difficult unsolved problem in computer vision fortunately in many practical applications some a priori knowledge exists which considerably simplifies the problem in visual navigation for example the motion between successive positions is usually approximately known from this initial estimate our algorithm computes observer motion with very good precision which is required for environment modeling e g building a digital elevation map objects are represented by a set of 3 d points which are considered as the samples of a surface no constraint is imposed on the form of the objects the proposed algorithm is based on iteratively matching points in one set to the closest points in the other a statistical method based on the distance distribution is used to deal with outliers occlusion appearance and disappearance which allows us to do subset subset matching a least squares technique is used to estimate 3 d motion from the point correspondences which reduces the average distance between points in the two sets both synthetic and real data have been used to test the algorithm and the results show that it is efficient and robust and yields an accurate motion estimate

new feature points based on geometric invariants for 3d image registration we introduce in this paper a new type of feature points of 3d surfaces based on geometric invariants we call this new type of feature points the extremal points of the 3d surfaces and we show that the relative positions of those 3d points are invariant according to 3d rigid transforms rotation and translation we show also how to extract those points from 3d images such as magnetic resonance images mri or cat scan images and also how to use them to perform precise 3d registration previously we described a method called the marching lines algorithm which allow us to extract the extremal lines which are geometric invariant 3d curves as the intersection of two implicit surfaces the extremal points are the intersection of the extremal lines with a third implicit surface we present an application of the extremal points extraction to the fully automatic registration of two 3d images of the same patient taken in two different positions to show the accuracy and robustness of the extracted extremal points

blow up boundary solutions of semilinear elliptic problems we consider the following semilinear elliptic equation u p x f u in u 0 u 0 in 1 where rn n 3 is a smooth domain bounded or possibly unbounded with compact possibly empty boundary we assume throughout this paper that p is a non negative function such that p c0 if is bounded and p c loc otherwise the nonlinearity f is assumed to ful ll f 1 f c1 0 f 0 f 0 0 and f 0 on 0 and the keller osserman condition see 7 13

the second expansion of large solutions for semilinear elliptic equations abstract in this paper we analyze the influence of the domain geometry in the second expansion of solutions to the boundary blow up elliptic problem u b x f u u 0 x u where is a bounded domain with c 4 smooth boundary in r n b c which is positive in and may be vanishing on the boundary and f is normalized regularly varying at infinity with index p p 1

a novel dynamic multilevel technique for image registration we present a novel dynamic multilevel technique for solving image registration problems the development is carried out to construct a spatial transformation based on cubic b spline basis functions and determine the control points dynamically unlike fem based image registration methods we do not have the difficulty of solving a complicated matrix system in addition the presented method is enhanced by a multilevel technique which makes it more efficient and flexible the numerical results and several comparison studies on real bio medical images show our technique is stable accurate and fast especially for large deformation registration problems

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

expanding the asymptotic explosive boundary behavior of large solutions to a semilinear elliptic equation the main goal of this paper is to study the asymptotic expansion near the boundary of the large solutions of the equation delta u lambda u m f in omega where lambda 0 m 1 f is an element of c omega f 0 and omega is an open bounded set of r n n 1 with boundary smooth enough roughly speaking we show that the number of explosive terms in the asymptotic boundary expansion of the solution is finite but it goes to infinity as in goes to 1 we prove that the expansion consists in two eventual geometrical and non geometrical parts separated by a term independent on the geometry of partial derivative omega but dependent on the diffusion for low explosive sources the non geometrical part does not exist all coefficients depend on the diffusion and the geometry of the domain by means of well known properties of the distance function dist x partial derivative omega for high explosive sources the preliminary coefficients relative to the non geometrical part are independent on omega and the diffusion finally the geometrical part does not exist for very high explosive sources consists in two eventual geometrical and non geometrical parts separated by a term independent on the geometry of partial omega but dependent on the diffusion for low explosive sources the non geometrical part does not exist all coefficients depend on the diffusion and the geometry of the domain by means of well known properties of the distance function rm dist x partial omega dist x for high explosive sources the preliminary coefficients relative to the non geometrical part are independent on omega and the diffusion finally the geometrical part does not exist for very high explosive sources

boundary behaviour for solutions of boundary blow up problems in a borderline case we investigate boundary blow up solutions of the equation u f u in a bounded domain rn under the condition that f t has a relatively slow growth as t goes to infinity we show how the mean curvature of the boundary appears in the asymptotic expansion of the solution u x in terms of the distance of x from

boundary behavior for large solutions to elliptic equations with singular weights abstract in this paper we analyze the boundary behavior of large positive solutions to some semilinear elliptic equations which include a singular weight the most important point is that the growth of the solutions can be determined in terms of the solution to a one dimensional first order equation we also consider the questions of existence and uniqueness of positive solutions

boundary behavior of large solutions to semilinear elliptic equations with nonlinear gradient terms abstract in this paper we study the boundary behavior of solutions to boundary blow up elliptic problems u u q b x f u x u where is a bounded domain with smooth boundary in r n q 0 b c which is positive in and may be vanishing on the boundary and rapidly varying near the boundary and f is rapidly varying or normalized regularly varying at infinity

structural indexing efficient 3 d object recognition the authors present an approach for the recognition of multiple 3 d object models from three 3 d scene data the approach uses two different types of primitives for matching small surface patches where differential properties can be reliably computed and lines corresponding to depth or orientation discontinuities these are represented by splashes and 3 d curves respectively it is shown how both of these primitives can be encoded by a set of super segments consisting of connected linear segments these super segments are entered into a table and provide the essential mechanism for fast retrieval and matching the issues of robustness and stability of the features are addressed in detail the acquisition of the 3 d models is performed automatically by computing splashes in highly structured areas of the objects and by using boundary and surface edges for the generation of 3 d curves the authors present results with the current system 3 d object recognition based on super segments and discuss further extensions

convergent iterative closest point algorithm to accomodate anisotropic and inhomogenous localization error since its introduction in the early 1990s the iterative closest point icp algorithm has become one of the most well known methods for geometric alignment of 3d models given two roughly aligned shapes represented by two point sets the algorithm iteratively establishes point correspondences given the current alignment of the data and computes a rigid transformation accordingly from a statistical point of view however it implicitly assumes that the points are observed with isotropic gaussian noise in this paper we show that this assumption may lead to errors and generalize the icp such that it can account for anisotropic and inhomogenous localization errors we 1 provide a formal description of the algorithm 2 extend it to registration of partially overlapping surfaces 3 prove its convergence 4 derive the required covariance matrices for a set of selected applications and 5 present means for optimizing the runtime an evaluation on publicly available surface meshes as well as on a set of meshes extracted from medical imaging data shows a dramatic increase in accuracy compared to the original icp especially in the case of partial surface registration as point based surface registration is a central component in various applications the potential impact of the proposed method is high

uniqueness of positive solutions for a boundary blow up problem abstract in this paper we prove the uniqueness of the positive solution for the boundary blow up problem u f u in u on where is a c 2 bounded domain in r n under the hypotheses that f t is nondecreasing in t 0 and f t t p is increasing for large t and some p 1 we also consider the uniqueness of a related problem when the equation includes a nonnegative weight a x

second order expansion for blowup solutions of semilinear elliptic problems abstract in this paper we mainly study the second order expansion of solutions to the elliptic problems u b x f u u 0 x u where is a bounded domain with a smooth boundary in r n n 2 b c which is positive in and may be vanishing on the boundary and f is normalized regularly varying at infinity with index p 1 our analysis is based on the sub supersolution method and karamata regular variation theory

rigid affine and locally affine registration of free form surfaces in this paper we propose a new framework to perform nonrigid surface registration it is based on various extensions of an iterative algorithm recently presented by several researchers besl and mckay 1992 champleboux et al 1992 chen and medioni 1992 menq and lai 1992 zhang 1994 to rigidly register surfaces represented by a set of 3d points when a prior estimate of the displacement is available our framework consists of three stages first we search for the best rigid displacement to superpose the two surfaces we show how to efficiently use curvatures to superpose principal frames at possible corresponding points in order to find a prior rough estimate of the displacement and initialize the iterative algorithm second we search for the best affine transformation we introduce differential information in points coordinates this allows us to match locally similar points then we show how principal frames and curvatures are transformed by an affine transformation finally we introduce this differential information in a global criterion minimized by extended kalman filtering in order to ensure the convergence of the algorithm third we locally deform the surface instead of computing a global affine transformation we attach to each point a local affine transformation varying smoothly along the surface we call this deformation a locally affine deformation all these stages are illustrated with experiments on various real biomedical surfaces teeth faces skulls brains and hearts which demonstrate the validity of the approach