an inverse boundary value problem for schrodinger operators with vector potentials we consider the schrodinger operator for a magnetic potential a and an electric potential q which are supported in a bounded domain in r n with n 3 we prove that knowledge of the dirichlet to neumann map associated to the schrodinger operator determines the magnetic field rot a and the electric potential 4 simultaneously provided rot a is small in the l topology

the lagrange multiplier rule in set valued optimization the known lagrange multiplier rule is extended to set valued constrained optimization problems using the contingent epiderivative as differentiability notion a necessary optimality condition for weak minimizers is derived which is also a sufficient condition under generalized convexity assumptions

interactive image segmentation based on synthetic graph coordinates in this paper we propose a framework for interactive image segmentation the goal of interactive image segmentation is to classify the image pixels into foreground and background classes when some foreground and background markers are given the proposed method minimizes a min max bayesian criterion that has been successfully used on image segmentation problem and it consists of several steps in order to take into account visual information as well as the given markers without any requirement of training first we partition the image into contiguous and perceptually similar regions superpixels then we construct a weighted graph that represents the superpixels and the connections between them an efficient algorithm for graph clustering based on synthetic coordinates is used yielding an initial map of classified pixels this method reduces the problem of graph clustering to the simpler problem of point clustering instead of solving the problem on the graph data structure as most of the known algorithms from literature do finally having available the data modeling and the initial map of classified pixels we use a markov random field mrf model or a flooding algorithm to get the image segmentation by minimizing a min max bayesian criterion experimental results and comparisons with other methods from the literature are presented on lhi gulshan and zhao datasets demonstrating the high performance and accuracy of the proposed scheme

set relations and optimality conditions in set valued maps abstract problems in set valued optimization can be solved via set optimization in this paper properties of set optimization are investigated conditions for existence of solutions are established directional derivatives are studied for set valued mappings necessary and sufficient conditions in the existence of solutions are showed with directional derivatives

interactive image segmentation via kernel propagation abstract in this paper we propose a new approach to interactive image segmentation via kernel propagation kp called kp cut the key to success in interactive image segmentation is to preserve characteristics of the user s interactive input and maintain data coherence effectively to achieve this we employ kp which is very effective in propagating the given supervised information into the entire data set kp first learns a small size seed kernel matrix and then propagates it into a large size full kernel matrix it is based on a learned kernel and thus can fit the given data better than a predefined kernel based on kp we first generate a small size seed kernel matrix from the user s interactive input then the seed kernel matrix is propagated into the full kernel matrix of the entire image during the propagation foreground objects are effectively segmented from background experimental results demonstrate that kp cut effectively extracts foreground objects from background and outperforms the state of the art methods for interactive image segmentation

interactive image segmentation using probabilistic hypergraphs this paper introduces a novel interactive framework for segmenting images using probabilistic hypergraphs which model the spatial and appearance relations among image pixels the probabilistic hypergraph provides us a means to pose image segmentation as a machine learning problem in particular we assume that a small set of pixels which are referred to as seed pixels are labeled as the object and background the seed pixels are used to estimate the labels of the unlabeled pixels by learning on a hypergraph via minimizing a quadratic smoothness term formed by a hypergraph laplacian matrix subject to the known label constraints we derive a natural probabilistic interpretation of this smoothness term and provide a detailed discussion on the relation of our method to other hypergraph and graph based learning methods we also present a front to end image segmentation system based on the proposed method which is shown to achieve promising quantitative and qualitative results on the commonly used grabcut dataset

on approximate solutions in set valued optimization problems in this paper we introduce several concepts of approximate solutions of set valued optimization problems with vector and set optimization we prove existence results and necessary and sufficient conditions by using limit sets

determining anisotropic real analytic conductivities by boundary measurements if an electrical potential is applied to the surface of a solid body the current flux across the surface depends on the conductivity in the interior of the body we want to consider the inverse problem of determining the conductivity by these boundary measurements

inverse problems for the anisotropic maxwell equations we prove that the electromagnetic material parameters are uniquely determined by boundary measurements for the time harmonic maxwell equations in certain anisotropic settings we give a uniqueness result in the inverse problem for maxwell equations on an admissible riemannian manifold and a uniqueness result for maxwell equations in euclidean space with admissible matrix coefficients the proofs are based on a new fourier analytic construction of complex geometrical optics solutions on admissible manifolds and involve a proper notion of uniqueness for such solutions

random walks for image segmentation a novel method is proposed for performing multilabel interactive image segmentation given a small number of pixels with user defined or predefined labels one can analytically and quickly determine the probability that a random walker starting at each unlabeled pixel will first reach one of the prelabeled pixels by assigning each pixel to the label for which the greatest probability is calculated a high quality image segmentation may be obtained theoretical properties of this algorithm are developed along with the corresponding connections to discrete potential theory and electrical circuits this algorithm is formulated in discrete space i e on a graph using combinatorial analogues of standard operators and principles from continuous potential theory allowing it to be applied in arbitrary dimension on arbitrary graphs

determining conductivity by boundary measurements a p calderon pose la question est il possible de determiner la conductivite thermique d un objet a partir de mesures statiques de la temperature et du flux de chaleur a la limite on demontre que ces mesures determinent de facon unique la conductivite thermique et toutes ses derivees a la limite

an inverse source problem for maxwell s equations in magnetoencephalography consider an inverse source problem for maxwell s equations which arises in determining locations of epileptic foci in the living human brain the human brain is modeled as a heterogeneous medium where the electric permittivity magnetic permeability and conductivity may all be functions a current dipole is used to model the epilepsy the inverse source problem in this context is to determine the current dipole from boundary measurements of the fields in this paper a new computational method is introduced for solving the inverse problem the method is based on a low frequency asymptotic analysis of maxwell s equations our method is constructive and has good convergence properties a crucial step of the method is to construct special test functions uniqueness and stability results for the inverse problem are also established the method and results are expected to find applications particularly in magnetoencephalography

nonconvex scalarization in set optimization with set valued maps abstract the aim of this work is to obtain scalar representations of set valued optimization problems without any convexity assumption using a criterion of solution introduced by kuroiwa d kuroiwa some duality theorems of set valued optimization with natural criteria in proceedings of the international conference on nonlinear analysis and convex analysis world scientific river edge nj 1999 pp 221 228 which is based on ordered relations between sets we characterize this type of solutions by means of nonlinear scalarization the scalarizing function is a generalization of the gerstewitz s nonconvex separation function as applications of our results we give two existence theorems for set valued optimization problems

fast approximate energy minimization via graph cuts many tasks in computer vision involve assigning a label such as disparity to every pixel a common constraint is that the labels should vary smoothly almost everywhere while preserving sharp discontinuities that may exist e g at object boundaries these tasks are naturally stated in terms of energy minimization the authors consider a wide class of energies with various smoothness constraints global minimization of these energy functions is np hard even in the simplest discontinuity preserving case therefore our focus is on efficient approximation algorithms we present two algorithms based on graph cuts that efficiently find a local minimum with respect to two types of large moves namely expansion moves and swap moves these moves can simultaneously change the labels of arbitrarily large sets of pixels in contrast many standard algorithms including simulated annealing use small moves where only one pixel changes its label at a time our expansion algorithm finds a labeling within a known factor of the global minimum while our swap algorithm handles more general energy functions both of these algorithms allow important cases of discontinuity preserving energies we experimentally demonstrate the effectiveness of our approach for image restoration stereo and motion on real data with ground truth we achieve 98 percent accuracy

fine structured object segmentation via neighborhood propagation this paper presents a novel method for the challenging task of fine structured fs object segmentation the task is formulated as a label propagation problem on an affinity graph the proposed method has mainly three advantages first to enhance the completeness and connectivity of fs objects we introduce a novel neighborhood system combining both local and nonlocal connections with a robust scheme for edge weight calculation second appearance models are explicitly incorporated into the energy function as a term of region cost this helps to further preserve the connectivity of the fine parts for which the label information is hard to propagate correctly via neighboring pixels alone third the resulting energy minimization problem has a closed form solution with global optimum guaranteed showing an advantage over the fs object segmentation methods that suffer from np hardness to enrich the evaluation of fs object segmentation methods we created a new challenging data set it consists of 100 natural images involving diverse fs objects with accurately hand labeled ground truth extensive experimental results demonstrate that our method is effective in handling fs objects and achieves the state of the art performance highlightswe propose a method for fine structured object segmentation via label propagation a novel affinity graph combining local and nonlocal connections is constructed we incorporate appearance models as labeling preference for the label propagation the energy minimization is achieved with a globally optimal closed form solution extensive experimental results demonstrate the effectiveness of our method

stability estimates for the radon transform with restricted data and applications in this article we prove a stability estimate going from the radon transform of a function with limited angle distance data to the l p norm of the function itself under some conditions on the support of the function we apply this theorem to obtain stability estimates for an inverse boundary value problem with partial data

inverse boundary value problems at the boundary continuous dependence we use the methods of microlocal analysis to give a new proof of a theorem of kohn and vogelius showing that the boundary values of a continuous isotropic conductivity can be recovered from voltage and current measurements at the boundary moreover we prove sharp estimates to establish the continuous dependence of the boundary values of the conductivity on the voltage to current maps

global uniqueness for an inverse boundary value problem arising in elasticity we prove that we can determine the lame parameters of an elastic isotropic inhomogeneous medium in dimensionsn 3 by making measurements of the displacements and corresponding stresses at the boundary of the medium

an inverse polynomial method for the identification of the leading coefficient in the sturm liouville operator from boundary measurements an inverse polynomial method of determining the unknown leading coefficient k k x of the linear sturm liouville operator au k x u x q x u x x 0 1 is presented as an additional condition only two measured data at the boundary x 0 x 1 are used in absence of a singular point u x 0 u x 0 x 0 1 the inverse problem is classified as a well conditioned if there exists at least one singular point then the inverse problem is classified as moderately ill conditioned u x 0 0 x 0 0 1 u x 0 x x 0 u x 0 x 0 1 and severely ill conditioned u x 0 u x 0 0 x 0 0 1 u x 0 u x 0 x x 0 for each of the cases direct problem solution is approximated by corresponding polynomials and the inverse problem is reformulated as a cauchy problem for to the first order differential equation with respect the unknown function k k x an approximate analytical solution of the each cauchy problems are derived in explicit form numerical simulations all the above cases are given for noise free and noisy data an accuracy of the presented approach is demonstrated on numerical test solutions

optimality conditions for set valued maps with set optimization abstract problems in set valued optimization can be solved via set optimization in this paper optimality conditions are studied for set valued maps with set optimization optimality requirements are established for continuous selections using directional derivatives necessary and sufficient conditions for the existence of solutions are shown for set valued maps under generalized convexity assumptions and with the notion of the contingent derivative

an inverse problem for maxwell s equations in a uniaxially anisotropic medium abstract we consider maxwell s equations for a uniaxially anisotropic and inhomogeneous medium we discuss an inverse problem of determining the permittivity tensor e 1 0 0 0 e 0 0 0 e and the permeability tensor 1 0 0 0 0 0 0 in the constitutive relations from a finite number of lateral boundary measurements applying a carleman estimate we prove a stability estimate of lipschitz type for the inverse problem provided that e 1 e 1 satisfy some a priori conditions

a linearized inverse boundary value problem for maxwell s equations abstract in this paper we consider the problem of determining the electromagnetic state of a body from measurements made on the surface of the body we study the full set of maxwell s equations that govern time harmonic electric and magnetic fields we seek to reconstruct the magnetic permeability the electric permitivity and the electric conductivity in the interior of the body from measurements made on the surface we exhibit appropriate boundary measurements in the form of a boundary mapping specifically the mapping from the tangential components of the electric field to the tangential components of the magnetic field this data can be used to reconstruct and approximately provided they deviate only slightly from known constants we also estimate the reconstruction errors

on the continuum limit of a discrete inverse spectral problem on optimal finite difference grids we consider finite difference approximations of solutions of inverse stur m liouville problems in bounded intervals using three point finite difference sc hemes we discretize the equations on so called optimal grids constructed as follow s for a staggered grid with 2k points we ask that the finite difference operator a k k jacobi matrix and the sturm liouville differential operator share the k lowest eigenvalues and the values of the orthonormal eigenfunctions at one end of the interval this requirement determines uniquely the entries in the jacobi matrix which are grid cell averages of the coefficients in the continuum problem if these coefficients are known we can find the grid which we call optimal becau se it gives by design a finite difference operator with a prescribed spectr al measure we focus attention on the inverse problem where neither the coefficients n or the grid are known a key question in inversion is how to parametrize the coefficients i e how to choose the grid it is clear that to be successful this grid must be close to the optimal one which is unknown fortunately as we show here the grid dependence on the unknown coefficients is weak so the inversion can be done on a pr ecomputed grid for an a priori guess of the unknown coefficients this obse rvation leads to a simple yet efficient inversion algorithm which gives coefficien ts that converge pointwise to the true solution as the number k of data points tends to infinity the cornerstone of our convergence proof is showing that op timal grids provide an implicit natural regularization of the inverse problem by givin g reconstructions with uniformly bounded total variation the analysis is based on a novel explicit perturbation analysis of lanczos recursions and on a discrete