computation of the euler number using the contact perimeter we present the computation of the euler number of shapes using the contact perimeter the contact perimeter was initially defined in e bribiesca measuring 2d shape compactness using the contact perimeter comput math appl 33 1997 1 9 in this reference the contact perimeter was used to define a measure of compactness for 2d shapes now in this paper we use the contact perimeter to compute the euler number of unit width objects composed of different side connected cells and face connected polyhedrons in two and three dimensions respectively finally we present some applications of this computation in knot and graph theory

active contours without edges we propose a new model for active contours to detect objects in a given image based on techniques of curve evolution mumford shah 1989 functional for segmentation and level sets our model can detect objects whose boundaries are not necessarily defined by the gradient we minimize an energy which can be seen as a particular case of the minimal partition problem in the level set formulation the problem becomes a mean curvature flow like evolving the active contour which will stop on the desired boundary however the stopping term does not depend on the gradient of the image as in the classical active contour models but is instead related to a particular segmentation of the image we give a numerical algorithm using finite differences finally we present various experimental results and in particular some examples for which the classical snakes methods based on the gradient are not applicable also the initial curve can be anywhere in the image and interior contours are automatically detected

geometrically accurate topology correction of cortical surfaces using nonseparating loops in this paper we focus on the retrospective topology correction of surfaces we propose a technique to accurately correct the spherical topology of cortical surfaces specifically we construct a mapping from the original surface onto the sphere to detect topological defects as minimal nonhomeomorphic regions the topology of each defect is then corrected by opening and sealing the surface along a set of nonseparating loops that are selected in a bayesian framework the proposed method is a wholly self contained topology correction algorithm which determines geometrically accurate topologically correct solutions based on the magnetic resonance imaging mri intensity profile and the expected local curvature applied to real data our method provides topological corrections similar to those made by a trained operator

a fast level set method for propagating interfaces a method is introduced to decrease the computational labor of the standard level set method for propagating interfaces the fast approach uses only points close to the curve at every time step we describe this new algorithm and compare its efficiency and accuracy with the standard level set approach

a geometric model for active contours in image processing we propose a new model for active contours based on a geometric partial differential equation our model is intrinsec stable satisfies the maximum principle and permits a rigorous mathematical analysis it enables us to extract smooth shapes we cannot retrieve angles and it can be adapted to find several contours simultaneously moreover as a consequence of the stability we can design robust algorithms which can be engineed with no parameters in applications numerical experiments are presented

automated 3 d extraction of inner and outer surfaces of cerebral cortex from mri automatic computer processing of large multidimensional images such as those produced by magnetic resonance imaging mri is greatly aided by deformable models which are used to extract identify and quantify specific neuroanatomic structures a general method of deforming polyhedra is presented here with two novel features first explicit prevention of self intersecting surface geometries is provided unlike conventional deformable models which use regularization constraints to discourage but not necessarily prevent such behavior second deformation of multiple surfaces with intersurface proximity constraints allows each surface to help guide other surfaces into place using model based constraints such as expected thickness of an anatomic surface these two features are used advantageously to identify automatically the total surface of the outer and inner boundaries of cerebral cortical gray matter from normal human mr images accurately locating the depths of the sulci even where noise and partial volume artifacts in the image obscure the visibility of sulci the extracted surfaces are enforced to be simple two dimensional manifolds having the topology of a sphere even though the data may have topological holes this automatic 3 d cortex segmentation technique has been applied to 150 normal subjects simultaneously extracting both the gray white and gray cerebrospinal fluid interface from each individual the collection of surfaces has been used to create a spatial map of the mean and standard deviation for the location and the thickness of cortical gray matter three alternative criteria for defining cortical thickness at each cortical location were developed and compared these results are shown to corroborate published postmortem and in vivo measurements of cortical thickness

strongly normal sets of contractible tiles in n dimensions the second and third authors and others have studied collections of usually convex tiles a generalization of pixels or voxels in r 2 and r 3 that have a property called strong normality sn for any tile p only finitely many tiles intersect p and any nonempty intersection of those tiles also intersects p this paper extends basic results about strong normality to collections of contractible polyhedra in r n whose nonempty intersections are contractible we also give sufficient and trivially necessary conditions on a locally finite collection of contractible polyhedra in r 2 or r 3 for their nonempty intersections to be contractible

multiscale opening of conjoined fuzzy objects theory and applications theoretical properties of a multiscale opening algorithm for two conjoined fuzzy objects are established and its extension to separating two conjoined fuzzy objects with different intensity properties is introduced in addition its applications to artery vein separation in pulmonary ct imaging and carotid vessel segmentation in ct angiograms ctas of patients with intracranial aneurysms are presented the new algorithm accounts for distinct intensity properties of individual conjoined objects by combining fuzzy distance transform a morphologic feature with fuzzy connectivity a topologic feature the algorithm iteratively opens the two conjoined objects starting at large scales and progressing toward finer scales results of application of the method in separating arteries and veins in a physical cast phantom of a pig lung are presented accuracy of the algorithm is quantitatively evaluated in terms of sensitivity and specificity on patients cta datasets and its performance is compared with existing methods reproducibility of the algorithm is examined in terms of volumetric agreement between two users carotid vessel segmentation results experimental results using this algorithm on patients cta data demonstrate a high average accuracy of 96 3 with 95 1 sensitivity and 97 5 specificity and a high reproducibility of 94 2 average agreement between segmentation results from two mutually independent users approximately 25 35 user specified seeds separators are needed for each cta data through a custom designed graphical interface requiring an average of 30 min to complete carotid vascular segmentation in a patient s cta dataset

data driven model reduction of monotone systems by nonlinear dc gains in this paper we develop data driven model reduction methods for monotone nonlinear control systems based on a nonlinear version of the dc gain the nonlinear dc gain is a function of the amplitude of the input and can be used to evaluate the importance of each state variable in fact the nonlinear dc gain is directly related to the infinity induced norm of the system as well as a notion of output reachability given the dc gain model reduction is performed by either truncating not so important state variables or aggregating state variables having similar importance under such truncation and clustering monotonicity and boundedness of the nonlinear dc gain are preserved moreover these two operations can be approximately performed based on simulation or experimental data alone this empirical model reduction approach is illustrated by an example of a gene regulatory network

minimax optimal level set estimation this paper describes a new methodology and associated theoretical analysis for rapid and accurate extraction of level sets of a multivariate function from noisy data the identification of the boundaries of such sets is an important theoretical problem with applications for digital elevation maps medical imaging and pattern recognition this problem is significantly different from classical segmentation because level set boundaries may not correspond to singularities or edges in the underlying function as a result segmentation methods which rely upon detecting boundaries would be potentially ineffective in this regime this issue is addressed in this paper through a novel error metric sensitive to both the error in the location of the level set estimate and the deviation of the function from the critical level hoeffding s inequality is used to derive a novel regularization term that is distinctly different from regularization methods used in conventional image denoising settings building upon this foundation it is possible to derive error performance bounds for the proposed estimator and demonstrate that it exhibits near minimax optimal error decay rates for large classes of level set problems the proposed method automatically adapts to the spatially varying regularity of both the boundary of the level set and the underlying function

a comparison of three error estimation techniques for finite volume solutions of compressible flows three techniques to obtain error estimates for finite volume solutions on unstructured grids are compared in this study the first estimation technique uses richardson extrapolation involving three flow solutions on different grids error estimates on these grids are computed simultaneously with the order of convergence the second technique is based on the difference between the computed solution and a higher order reconstruction obtained using the least squares method finally a third technique solves an error equation driven by source terms computed from the flux jump at cell interfaces the flows solved as test cases are governed by the two dimensional euler equations and the discretization employs roe s flux difference splitting scheme comparisons with exact errors allow the efficiency of each error estimation technique to be assessed for various types of flows

tracking using motion estimation with physically motivated inter region constraints we propose a method for tracking structures e g ventricles and myocardium in cardiac images e g magnetic resonance by propagating forward in time a previous estimate of the structures using a new physically motivated motion estimation scheme our method estimates motion by regularizing only within structures so that differing motions among different structures are not mixed it simultaneously satisfies the physical constraints at the interface between a fluid and a medium that the normal component of the fluid s motion must match the normal component of the medium s motion and the no slip condition which states that the tangential velocity approaches zero near the interface we show that these conditions lead to partial differential equations with robin boundary conditions at the interface which couple the motion between structures we show that propagating a segmentation across frames using our motion estimation scheme leads to more accurate segmentation than traditional motion estimation that does not use physical constraints our method is suited to interactive segmentation prominently used in commercial applications for cardiac analysis where segmentation propagation is used to predict a segmentation in the next frame we show that our method leads to more accurate predictions than a popular and recent interactive method used in cardiac segmentation

digital topology and geometry in medical imaging a survey digital topology and geometry refers to the use of topologic and geometric properties and features for images defined in digital grids such methods have been widely used in many medical imaging applications including image segmentation visualization manipulation interpolation registration surface tracking object representation correction quantitative morphometry etc digital topology and geometry play important roles in medical imaging research by enriching the scope of target outcomes and by adding strong theoretical foundations with enhanced stability fidelity and efficiency this paper presents a comprehensive yet compact survey on results principles and insights of methods related to digital topology and geometry with strong emphasis on understanding their roles in various medical imaging applications specifically this paper reviews methods related to distance analysis and path propagation connectivity surface tracking image segmentation boundary and centerline detection topology preservation and local topological properties skeletonization and object representation correction and quantitative morphometry a common thread among the topics reviewed in this paper is that their theory and algorithms use the principle of digital path connectivity path propagation and neighborhood analysis

a topology preserving level set method for geometric deformable models active contour and surface models also known as deformable models are powerful image segmentation techniques geometric deformable models implemented using level set methods have advantages over parametric models due to their intrinsic behavior parameterization independence and ease of implementation however a long claimed advantage of geometric deformable models the ability to automatically handle topology changes turns out to be a liability in applications where the object to be segmented has a known topology that must be preserved we present a new class of geometric deformable models designed using a novel topology preserving level set method which achieves topology preservation by applying the simple point concept from digital topology these new models maintain the other advantages of standard geometric deformable models including subpixel accuracy and production of nonintersecting curves or surfaces moreover since the topology preserving constraint is enforced efficiently through local computations the resulting algorithm incurs only nominal computational overhead over standard geometric deformable models several experiments on simulated and real data are provided to demonstrate the performance of this new deformable model algorithm

variational segmentation of vector valued images with gradient vector flow in this paper we extend the gradient vector flow field for robust variational segmentation of vector valued images rather than using scalar edge information we define a vectorial edge map derived from a weighted local structure tensor of the image that enables the diffusion of the gradient vectors in accurate directions through the 4d gradient vector flow equation to reduce the contribution of noise in the structure tensor image channels are weighted according to a blind estimator of contrast the method is applied to biological volume delineation in dynamic pet imaging and validated on realistic monte carlo simulations of numerical phantoms as well as on real images

a dual graph norm refinement indicator for finite volume approximations of the euler equations we generalise and apply a refinement indicator of the type originally designed by mackenzie suli and warnecke in 15 and 16 for linear friedrichs systems to the euler equations of inviscid compressible fluid flow the euler equations are symmetrized by means of entropy variables and locally linearized about a constant state to obtain a symmetric hyperbolic system to which an a posteriori error analysis of the type introduced in 15 can be applied we discuss the details of the implementation of the refinement indicator into the dlr tau code which is based on a finite volume method of box type on an unstructured grid and present numerical results

efficient methods for implicit geometrical representation of complex material microstructures summary we present two methods for initializing distance functions on adaptively refined finite element meshes to represent complex material microstructures from segmented x ray tomographic data implicit microstructure representation combined with the extended fem allows modelers to represent complex material microstructures with consistent mesh quality and accuracy in the first method a level set evolution equation is formulated and solved by the galerkin method on an adaptively refined mesh we show that the convergence and stability of this method is optimal for the order of elements used in the second approach we initialize the distance field by the fast marching method on a uniform grid and then project the solution onto the finite element mesh by least squares we show that this latter approach is superior in speed and accuracy as an example problem both methods are demonstrated in the initialization of distance fields for two inclusion phases within a al 7075 alloy copyright 2014 john wiley sons ltd

area and length minimizing flows for shape segmentation a number of active contour models have been proposed that unify the curve evolution framework with classical energy minimization techniques for segmentation such as snakes the essential idea is to evolve a curve in two dimensions or a surface in three dimensions under constraints from image forces so that it clings to features of interest in an intensity image the evolution equation has been derived from first principles as the gradient flow that minimizes a modified length functional tailored to features such as edges however because the flow may be slow to converge in practice a constant hyperbolic term is added to keep the curve surface moving in the desired direction we derive a modification of this term based on the gradient flow derived from a weighted area functional with image dependent weighting factor when combined with the earlier modified length gradient flow we obtain a partial differential equation pde that offers a number of advantages as illustrated by several examples of shape segmentation on medical images in many cases the weighted area flow may be used on its own with significant computational savings

automatic segmentation and reconstruction of the cortex from neonatal mri abstract segmentation and reconstruction of cortical surfaces from magnetic resonance mr images are more challenging for developing neonates than adults this is mainly due to the dynamic changes in the contrast between gray matter gm and white matter wm in both t1 and t2 weighted images t1w and t2w during brain maturation in particular in neonatal t2w images wm typically has higher signal intensity than gm this causes mislabeled voxels during cortical segmentation especially in the cortical regions of the brain and in particular at the interface between gm and cerebrospinal fluid csf we propose an automatic segmentation algorithm detecting these mislabeled voxels and correcting errors caused by partial volume effects our results show that the proposed algorithm corrects errors in the segmentation of both gm and wm compared to the classic expectation maximization em scheme quantitative validation against manual segmentation demonstrates good performance the mean dice value 0 758 0 037 for gm and 0 794 0 078 for wm the inner central and outer cortical surfaces are then reconstructed using implicit surface evolution a landmark study is performed to verify the accuracy of the reconstructed cortex the mean surface reconstruction error 0 73 mm for inner surface and 0 63 mm for the outer both segmentation and reconstruction have been tested on 25 neonates with the gestational ages ranging from 27 to 45 weeks this preliminary analysis confirms previous findings that cortical surface area and curvature increase with age and that surface area scales to cerebral volume according to a power law while cortical thickness is not related to age or brain growth

structure preserving truncation of nonlinear port hamiltonian systems in this paper we present a novel balancing method for nonlinear port hamiltonian systems based on the hamiltonian and the controllability function this corresponding balanced truncation method results in a reduced order model that is still in port hamiltonian form in contrast to the traditional balanced truncation method based on the controllability and observability functions

interconnection and damping assignment passivity based control of port controlled hamiltonian systems passivity based control pbc is a well established technique that has shown to be very powerful to design robust controllers for physical systems described by euler lagrange el equations of motion for regulation problems of mechanical systems which can be stabilized shaping only the potential energy pbc preserves the el structure and furthermore assigns a closed loop energy function equal to the difference between the energy of the system and the energy supplied by the controller thus we say that stabilization is achieved via energy balancing unfortunately these nice properties of el pbc are lost when used in other applications which require shaping of the total energy for instance in electrical or electromechanical systems or even some underactuated mechanical devices our main objective in this paper is to develop a new pbc theory which extends to a broader class of systems the aforementioned energy balancing stabilization mechanism and the structure invariance towards this end we depart from the el description of the systems and consider instead port controlled hamiltonian models which result from the network modelling of energy conserving lumped parameter physical systems with independent storage elements and strictly contain the class of el models

a cellular model for multi objects multi dimensional homotopic deformations abstract we deal in this paper with complex three dimensional scenes partitioned into several objects of any shape and with varying local dimensions we propose a consistent topological modeling of such scenes based on a cellular model we introduce a definition of simple elements for any adjacency graph based geometrical structure then we prove a local characterization of simple cells of a cellular model in the case of two objects and of any number of objects this characterization allows to define homotopic deformations of a complex scene

deformable shape finding with models based on kernel methods in this paper a new kernel based deformable model is proposed for detecting deformable shapes to incorporate valuable information for shape detection such as edge orientations into the shape representation a novel scheme based on kernel methods has been utilized the variation model of a deformable shape is established by a set of training samples of the shape represented in a kernel feature space the proposed deformable model consists of two parts a set of basis vectors describing the sample subspace including the shape representations of the training samples and a feasibility constraint generated by the one class support vector machine to describe the feasible region of the training samples in the sample subspace the aim of the proposed feasibility constraint is to avoid finding some invalid shapes by using the proposed deformable model an efficient algorithm without initial solutions is developed for shape detection the proposed approach was tested against real images experimental results show the effectiveness of the proposed deformable model and prove the feasibility of the proposed approach

robust surface reconstruction via laplace beltrami eigen projection and boundary deformation in medical shape analysis a critical problem is reconstructing a smooth surface of correct topology from a binary mask that typically has spurious features due to segmentation artifacts the challenge is the robust removal of these outliers without affecting the accuracy of other parts of the boundary in this paper we propose a novel approach for this problem based on the laplace beltrami lb eigen projection and properly designed boundary deformations using the metric distortion during the lb eigen projection our method automatically detects the location of outliers and feeds this information to a well composed and topology preserving deformation by iterating between these two steps of outlier detection and boundary deformation we can robustly filter out the outliers without moving the smooth part of the boundary the final surface is the eigen projection of the filtered mask boundary that has the correct topology desired accuracy and smoothness in our experiments we illustrate the robustness of our method on different input masks of the same structure and compare with the popular spharm tool and the topology preserving level set method to show that our method can reconstruct accurate surface representations without introducing artificial oscillations we also successfully validate our method on a large data set of more than 900 hippocampal masks and demonstrate that the reconstructed surfaces retain volume information accurately

riemannian optimal model reduction of linear port hamiltonian systems abstract in this paper we describe the development of a riemannian optimal model reduction method for linear stable port hamiltonian systems this development is motivated by the fact that there remains room for improvement in existing methods the model reduction problem is formulated as an optimization problem on the product manifold of the set of skew symmetric matrices the manifold of the symmetric positive definite matrices and euclidean space the reduced systems constructed using the optimal solutions to the problem preserve the original structure i e stability passivity and the port hamiltonian form the riemannian gradient is derived to relate our problem to another problem in some studies and the hessian is also derived to solve our problem using a riemannian trust region method the initial point in the proposed method is chosen by using the output of the iterative rational krylov algorithm for linear port hamiltonian systems irka ph a numerical experiment illustrates that the proposed method considerably improves the results of irka ph when the reduced model dimension is small

improving level set method for fast auroral oval segmentation auroral oval segmentation from ultraviolet imager images is of significance in the field of spatial physics compared with various existing image segmentation methods level set is a promising auroral oval segmentation method with satisfactory precision however the traditional level set methods are time consuming which is not suitable for the processing of large aurora image database for this purpose an improving level set method is proposed for fast auroral oval segmentation the proposed algorithm combines four strategies to solve the four problems leading to the high time complexity the first two strategies including our shape knowledge based initial evolving curve and neighbor embedded level set formulation can not only accelerate the segmentation process but also improve the segmentation accuracy and then the latter two strategies including the universal lattice boltzmann method and sparse field method can further reduce the time cost with an unlimited time step and narrow band computation experimental results illustrate that the proposed algorithm achieves satisfactory performance for auroral oval segmentation within a very short processing time

anatomical labeling of the circle of willis using maximum a posteriori probability estimation anatomical labeling of the cerebral arteries forming the circle of willis cow enables inter subject comparison which is required for geometric characterization and discovering risk factors associated with cerebrovascular pathologies we present a method for automated anatomical labeling of the cow by detecting its main bifurcations the cow is modeled as rooted attributed relational graph with bifurcations as its vertices whose attributes are characterized as points on a riemannian manifold the method is first trained on a set of pre labeled examples where it learns the variability of local bifurcation features as well as the variability in the topology then the labeling of the target vasculature is obtained as maximum a posteriori probability map estimate where the likelihood of labeling individual bifurcations is regularized by the prior structural knowledge of the graph they span the method was evaluated by cross validation on 50 subjects imaged with magnetic resonance angiography and showed a mean detection accuracy of 95 in addition besides providing the map the method can rank the labelings the proposed method naturally handles anatomical structural variability and is demonstrated to be suitable for labeling arterial segments of the cow

hamilton jacobi skeleton on cortical surfaces in this paper we propose a new method to construct graphical representations of cortical folding patterns by computing skeletons on triangulated cortical surfaces in our approach a cortical surface is first partitioned into sulcal and gyral regions via the solution of a variational problem using graph cuts which can guarantee global optimality after that we extend the method of hamilton jacobi skeleton to subsets of triangulated surfaces together with a geometrically intuitive pruning process that can trade off between skeleton complexity and the completeness of representing folding patterns compared with previous work that uses skeletons of 3 d volumes to represent sulcal patterns the skeletons on cortical surfaces can be easily decomposed into branches and provide a simpler way to construct graphical representations of cortical morphometry in our experiments we demonstrate our method on two different cortical surface models its ability of capturing major sulcal patterns and its application to compute skeletons of gyral regions

nonlinear moment matching based model order reduction in this paper we present a time domain notion of moments for a class of single input single output nonlinear systems in terms of the evolution of the output of a generalized signal generator driven by the nonlinear system we also define a new notion of moment matching and present a family of nonlinear parametrized reduced order models that achieve moment matching we establish relations with existing notions of moment for nonlinear systems showing that the newly derived and the existing families of reduced order models that achieve nonlinear moment matching respectively are equivalent furthermore we compute the reduced order model that matches the moments at two chosen signal generators one exciting the input of the system and another driven by the system simultaneously we also present a family of models computed on the basis of a nonlinear extension of the petrov galerkin projection that achieve moment matching finally we specialize the results to the case of nonlinear input affine systems

snakes shapes and gradient vector flow snakes or active contours are used extensively in computer vision and image processing applications particularly to locate object boundaries problems associated with initialization and poor convergence to boundary concavities however have limited their utility this paper presents a new external force for active contours largely solving both problems this external force which we call gradient vector flow gvf is computed as a diffusion of the gradient vectors of a gray level or binary edge map derived from the image it differs fundamentally from traditional snake external forces in that it cannot be written as the negative gradient of a potential function and the corresponding snake is formulated directly from a force balance condition rather than a variational formulation using several two dimensional 2 d examples and one three dimensional 3 d example we show that gvf has a large capture range and is able to move snakes into boundary concavities

geodesic active contours and level sets for the detection and tracking of moving objects this paper presents a new variational framework for detecting and tracking multiple moving objects in image sequences motion detection is performed using a statistical framework for which the observed interframe difference density function is approximated using a mixture model this model is composed of two components namely the static background and the mobile moving objects one both components are zero mean and obey laplacian or gaussian law this statistical framework is used to provide the motion detection boundaries additionally the original frame is used to provide the moving object boundaries then the detection and the tracking problem are addressed in a common framework that employs a geodesic active contour objective function this function is minimized using a gradient descent method a new approach named hermes is proposed which exploits aspects from the well known front propagation algorithms and compares favorably to them very promising experimental results are provided using real video sequences

minimal non deletable sets and minimal non codeletable sets in binary images the concepts of strongly 8 deletable and strongly 4 deletable sets of 1s in binary images on the 2d cartesian grid were introduced by ronse in the mid 1980s to formalize the connectivity preservation conditions that parallel thinning algorithms are required to satisfy in this paper we call these sets deletable and codeletable respectively to establish that a proposed parallel thinning algorithm for binary images on the 2d cartesian grid preserves 8 4 connected foreground components and 4 8 connected background components it is enough to prove that the set of 1s which are changed to 0s at each pass of the algorithm is always a deletable codeletable set ronse established results that are very useful in this context for proving that a finite set d of 1s is deletable or codeletable in particular he showed that d and its proper subsets are all codeletable in a binary image if each singleton and each pair of 8 adjacent pixels in d is codeletable he further showed that d and its proper subsets are all deletable in a binary image if 1 each singleton and each pair of 4 adjacent pixels in d is deletable and 2 no set of 2 3 or 4 pairwise 8 adjacent pixels that is an 8 connected foreground component of the image is entirely contained in d in the 1990s and early 2000s analogous results were obtained by hall ma gau and the author for binary images on the 2d hexagonal grid the 3d cartesian and face centered cubic grids and the 4d cartesian grid this paper extends the above mentioned work to binary images on almost any polytopal complex whose union is n dimensional euclidean space for n 4 our main results generalize and unify the corresponding results of the earlier work

the solution of the matrix equations axb cxd e and ya dz yc bz e f the conditions for the existence of a unique solution of the matrix equation axb cxd e are proved to be that i the pencils a c and d b are regular and ii the spectra of the pencils have an empty intersection a numerical algorithm for solving the equation is proposed the possibility of a least squares type solution is briefly discussed the set of equations ya dz yc bz e f is proved to be equivalent to the aforementioned equation and its solution is also investigated a numerical algorithm is proposed

adaptive finite element methods for conservation laws based on a posteriori error estimates we prove a posteriori error estimates for a finite element method for systems of strictly hyperbolic conservation laws in one space dimension and design corresponding adaptive methods the proof of the a posteriori error estimates is based on a strong stability estimate for an associated dual problem together with the galerkin orthogonality of the finite element method the strong stability estimate uses the entropy condition for the system in an essential way 1995 john wiley sons inc

adaptive reproducing kernel particle method for extraction of the cortical surface we propose a novel adaptive approach based on the reproducing kernel particle method rkpm to extract the cortical surfaces of the brain from three dimensional 3 d magnetic resonance images mris to formulate the discrete equations of the deformable model a flexible particle shape function is employed in the galerkin approximation of the weak form of the equilibrium equations the proposed support generation method ensures that support of all particles cover the entire computational domains the deformable model is adaptively adjusted by dilating the shape function and by inserting or merging particles in the high curvature regions or regions stopped by the target boundary the shape function of the particle with a dilation parameter is adaptively constructed in response to particle insertion or merging the proposed method offers flexibility in representing highly convolved structures and in refining the deformable models self intersection of the surface during evolution is prevented by tracing backward along gradient descent direction from the crest interface of the distance field which is computed by fast marching these operations involve a significant computational cost the initial model for the deformable surface is simple and requires no prior knowledge of the segmented structure no specific template is required e g an average cortical surface obtained from many subjects the extracted cortical surface efficiently localizes the depths of the cerebral sulci unlike some other active surface approaches that penalize regions of high curvature comparisons with manually segmented landmark data are provided to demonstrate the high accuracy of the proposed method we also compare the proposed method to the finite element method and to a commonly used cortical surface extraction approach the cruise method we also show that the independence of the shape functions of the rkpm from the underlying mesh enhances the convergence speed of the deformable model

surface fluid registration of conformal representation application to detect disease burden and genetic influence on hippocampus in this paper we develop a new automated surface registration system based on surface conformal parameterization by holomorphic 1 forms inverse consistent surface fluid registration and multivariate tensor based morphometry mtbm first we conformally map a surface onto a planar rectangle space with holomorphic 1 forms second we compute surface conformal representation by combining its local conformal factor and mean curvature and linearly scale the dynamic range of the conformal representation to form the feature image of the surface third we align the feature image with a chosen template image via the fluid image registration algorithm which has been extended into the curvilinear coordinates to adjust for the distortion introduced by surface parameterization the inverse consistent image registration algorithm is also incorporated in the system to jointly estimate the forward and inverse transformations between the study and template images this alignment induces a corresponding deformation on the surface we tested the system on alzheimer s disease neuroimaging initiative adni baseline dataset to study ad symptoms on hippocampus in our system by modeling a hippocampus as a 3d parametric surface we nonlinearly registered each surface with a selected template surface then we used mtbm to analyze the morphometry difference between diagnostic groups experimental results show that the new system has better performance than two publicly available subcortical surface registration tools first and spharm we also analyzed the genetic influence of the apolipoprotein e 4 allele apoe4 which is considered as the most prevalent risk factor for ad our work successfully detected statistically significant difference between apoe4 carriers and non carriers in both patients of mild cognitive impairment mci and healthy control subjects the results show evidence that the apoe genotype may be associated with accelerated brain atrophy so that our work provides a new mri analysis tool that may help presymptomatic ad research

numerical simulation of the gas flow in a circuit breaker a computational methodology for the solution of unsteady two dimensional axisymmetric euler equations within geometries with moving boundaries is presented the flow simulation is carried out by applying a finite volume method which makes use of a lagrangian eulerian version of roe s approximate riemann solver the domain discretization is handled via unstructured triangular grids grid adaptation is applied on the basis of geometric and physical requirements the importance of the implicit treatment of the space conservation laws based on geometric analysis is evoked the procedure for reconstructing roe s method for moving meshes is described and validated finally the ability of the method for the prediction of the transient flow in a circuit breaker during its opening phase is illustrated

a posteriori error estimation the relationship between different procedures to address the issue of accurate and efficient estimation of the discretization error of the finite element solution the relationship between different types of error estimators is investigated we found that some of the widely used error estimators are in fact related although they were originally derived from different methodologies the recognition of the relation between these error estimators provides a different viewpoint on the theory of a posteriori error estimation and a guidance in the development of the error estimators

two symmetrical thinning algorithms for 3d binary images based on p simple points in this paper we propose two 3d symmetrical thinning algorithms based on the parallel deletion of p simple points the first one permits surface skeletons to be obtained the second one permits curve skeletons to be extracted and as far as we know this is the only symmetrical curve thinning algorithm which preserves topology these algorithms have been conceived in order to obtain precise results on simple specific objects parallelepipeds consequently we can predict the number of deletion iterations the number of deleted points and the skeleton of these objects obtained by the two algorithms which is hardly ever possible to assess with other algorithms even on these simple objects

magnification of label maps with a topology preserving level set method image segmentation aims at partitioning an image into multiple segments the application of this procedure produces a label map also referred to as segmentation map that classifies the pixels of the original image in contrast to natural images label maps are nominal scale images typically represented as integer valued images nominal scaled label maps can also appear as a representation of the raw data in areas such as in geostatistics in some applications the original resolution of a label map does not suffice and a larger size map has to be generated in this paper we present a magnification algorithm for label maps and nominal images the main property of our method is that it preserves the topology during the magnification process which means that no isolated pixel vanishes to the best of our knowledge apart from nearest neighbor interpolation the problem of label map magnification has not previously been addressed in the literature the main idea of the proposed method is to accomplish a boundary refinement by smoothing the regions boundaries on a finer grid the method relies on well known methods namely the fundamental operations of morphological image processing erosion and dilation and the level set method the level set method is well suited for our purposes since it does not depend on a parametrization and it is numerically stable the topological flexibility of the level set method often found to be an advantage in applications is a drawback here since the topology of the original label map should be preserved however using the so called simple point criterion from digital topology one can adapt the conventional level set method so that the topology will not be modified throughout the magnification procedure

important moments in systems and control the moment problem matured from its various special forms in the late 19th and early 20th centuries to a general class of problems that continues to exert profound influence on the development of analysis and its applications to a wide variety of fields in particular the theory of systems and control is no exception where the applications have historically been to circuit theory optimal control robust control signal processing spectral estimation stochastic realization theory and the use of the moments of a probability density many of these applications are also still works in progress in this paper we consider the generalized moment problem expressed in terms of a basis of a finite dimensional subspace p of the banach space c a b and a positive sequence c but with a new wrinkle inspired by the applications to systems and control we seek to parameterize solutions which are positive rational measures in a suitably generalized sense our parameterization is given in terms of smooth objects in particular the desired solution space arises naturally as a manifold which can be shown to be diffeomorphic to a euclidean space and which is the domain of some canonically defined functions the analysis of these functions and related maps yields interesting corollaries for the moment problem and its applications which we compare to those in the recent literature and which play a crucial role in part of our proof

joint sulcal detection on cortical surfaces with graphical models and boosted priors in this paper we propose an automated approach for the joint detection of major sulci on cortical surfaces by representing sulci as nodes in a graphical model we incorporate markovian relations between sulci and formulate their detection as a maximum a posteriori map estimation problem over the joint space of major sulci to make the inference tractable a sample space with a finite number of candidate curves is automatically generated at each node based on the hamilton jacobi skeleton of sulcal regions using the adaboost algorithm we learn both individual and pairwise shape priors of sulcal curves from training data which are then used to define potential functions in the graphical model based on the connection between adaboost and logistic regression finally belief propagation is used to perform the map inference and select the joint detection results from the sample spaces of candidate curves in our experiments we quantitatively validate our algorithm with manually traced curves and demonstrate the automatically detected curves can capture the main body of sulci very accurately a comparison with independently detected results is also conducted to illustrate the advantage of the joint detection approach

3d topology preserving flows for viewpoint based cortical unfolding we present a variational method for unfolding of the cortex based on a user chosen point of view as an alternative to more traditional global flattening methods which incur more distortion around the region of interest our approach involves three novel contributions the first is an energy function and its corresponding gradient flow to measure the average visibility of a region of interest of a surface with respect to a given viewpoint the second is an additional energy function and flow designed to preserve the 3d topology of the evolving surface the third is a method that dramatically improves the computational speed of the 3d topology preservation approach by creating a tree structure of the 3d surface and using a recursion technique experiments results show that the proposed approach can successfully unfold highly convoluted surfaces such as the cortex while preserving their topology during the evolution

a new approach to computing the euler characteristic in this paper we describe a new approach to computing the euler characteristic of a three dimensional digital image our approach is based on computing the change in numbers of black components tunnels and cavities in 3 x 3 x 3 neighborhood of an object black point due to its deletion the existing algorithms to computing the euler characteristic of a 3d digital image are based on counting the numbers of all k dimensional elements 0 k 3 in a polyhedral representation of the image our approach can be modified for 6 26 18 6 6 18 and other connectivity relations of grid points a parallel implementation of the algorithm is described using the concept of sub fields

on the evolution of vector distance functions of closed curves inspired by the work by gomes et al we describe and analyze a vector distance function approach for the implicit evolution of closed curves of codimension larger than one the approach is set up in complete generality and then applied to the evolution of dynamic geometric active contours in mathbb r 4 codimension three case in order to carry this out one needs an explicit expression for the zero level set for which we propose a discrete connectivity method this leads us to make connections with the new theory of cubical homology we provide some explicit simulation results in order to illustrate the methodology

snakes active contour models a snake is an energy minimizing spline guided by external constraint forces and influenced by image forces that pull it toward features such as lines and edges snakes are active contour models they lock onto nearby edges localizing them accurately scale space continuation can be used to enlarge the capture region surrounding a feature snakes provide a unified account of a number of visual problems including detection of edges lines and subjective contours motion tracking and stereo matching we have used snakes successfully for interactive interpretation in which user imposed constraint forces guide the snake near features of interest

minimal surfaces based object segmentation a geometric approach for 3d object segmentation and representation is presented the segmentation is obtained by deformable surfaces moving towards the objects to be detected in the 3d image the model is based on curvature motion and the computation of surfaces with minimal areas better known as minimal surfaces the space where the surfaces are computed is induced from the 3d image volumetric data in which the objects are to be detected the model links between classical deformable surfaces obtained via energy minimization and intrinsic ones derived from curvature based flows the new approach is stable robust and automatically handles changes in the surface topology during the deformation

numerical assessment of error estimators for euler equations grid convergence studies are conducted to assess four error estimators for their asymptotic behavior explicit residual solution reconstruction richardson extrapolation and solution of the error equations their accuracy reliability and efficitivity to predict the true error are verified on the quasi one dimensional euler equations solved by a second order accurate finite volume method

generating cubical complexes from image data and computation of the euler number abstract a number of tasks in image processing and computer vision require the computation of certain topological characteristics of objects in a given image in this paper we introduce a new method based on the notion of the algebraic topology complex to compute the euler number of a given object first we attach a cubical complex to the object of interest then we associate an algebraic structure on which a number of simplifying operations preserving the topology but not necessarily the geometric nature of the complex are possible this is a unifying dimension independent approach we show that the euler number can be obtained directly from the cubical structure or one can perform a collapsing operation that allows to reduce the given image to a lower dimension structure with equivalent topological properties this reduced structure can be used in a further process in particular for the computation of the euler number

global regularizing flows with topology preservation for active contours and polygons active contour and active polygon models have been used widely for image segmentation in some applications the topology of the object s to be detected from an image is known a priori despite a complex unknown geometry and it is important that the active contour or polygon maintain the desired topology in this work we construct a novel geometric flow that can be added to image based evolutions of active contours and polygons in order to preserve the topology of the initial contour or polygon we emphasize that unlike other methods for topology preservation the proposed geometric flow continually adjusts the geometry of the original evolution in a gradual and graceful manner so as to prevent a topology change long before the curve or polygon becomes close to topology change the flow also serves as a global regularity term for the evolving contour and has smoothness properties similar to curvature flow these properties of gradually adjusting the original flow and global regularization prevent geometrical inaccuracies common with simple discrete topology preservation schemes the proposed topology preserving geometric flow is the gradient flow arising from an energy that is based on electrostatic principles the evolution of a single point on the contour depends on all other points of the contour which is different from traditional curve evolutions in the computer vision literature

statistical region snake based segmentation adapted to different physical noise models algorithms for object segmentation are crucial in many image processing applications during past years active contour models snakes have been widely used for finding the contours of objects this segmentation strategy is classically edge based in the sense that the snake is driven to fit the maximum of an edge map of the scene we propose a region snake approach and we determine fast algorithms for the segmentation of an object in an image the algorithms developed in a maximum likelihood approach are based on the calculation of the statistics of the inner and the outer regions defined by the snake it has thus been possible to develop optimal algorithms adapted to the random fields which describe the gray levels in the input image if we assume that their probability density function family are known we demonstrate that this approach is still efficient when no boundary s edge exists in the image we also show that one can obtain fast algorithms by transforming the summations over a region for the calculation of the statistics into summations along the boundary of the region finally we will provide numerical simulation results for different physical situations in order to illustrate the efficiency of this approach

computing skeletons in three dimensions skeletonization will probably become as valuable a tool for shape analysis in 3d as it is in 2d we present a topology preserving 3d skeletonization method which computes both surface and curve sk

efficient algorithms for globally optimal trajectories we present serial and parallel algorithms for solving a system of equations that arises from the discretization of the hamilton jacobi equation associated to a trajectory optimization problem of the following type a vehicle starts at a prespecified point x sub o and follows a unit speed trajectory x t inside a region in spl rscr sup m until an unspecified time t that the region is exited a trajectory minimizing a cost function of the form spl int sub 0 sup t r x t dt q x t is sought the discretized hamilton jacobi equation corresponding to this problem is usually solved using iterative methods nevertheless assuming that the function r is positive we are able to exploit the problem structure and develop one pass algorithms for the discretized problem the first algorithm resembles dijkstra s shortest path algorithm and runs in time o n log n where n is the number of grid points the second algorithm uses a somewhat different discretization and borrows some ideas from a variation of dial s shortest path algorithm 1969 that we develop here it runs in time o n which is the best possible under some fairly mild assumptions finally we show that the latter algorithm can be efficiently parallelized for two dimensional problems and with p processors its running time becomes o n p provided that p o spl radic n log n

the problem of the selection of an a posteriori error indicator based on smoothening techniques abstract this paper addresses the problem of assessing the quality of an a posteriori error estimate of a finite element solution an error estimate based on local l projections is analyzed in the case of translation invariant meshes it is shown that for general meshes this technique does not lead to an asymptotically exact estimator the problem is analyzed in detail in the one dimensional setting it is shown that an asymptotically exact estimator is not the optimal one when the solution is not sufficiently smooth an optimal estimator for adaptively constructed meshes is given finally a general mathematical framework for the quality assessment of estimators is introduced

distance driven skeletonization in voxel images a distance driven method to compute the surface and curve skeletons of 3d objects in voxel images is described the method is based on the use of the weighted distance transform on the detection of anchor points and on the application of topology preserving removal operations the obtained surface and curve skeletons are centered within the object have the same topology as the object and have unit thickness the object can be almost completely recovered from the surface skeleton since this includes almost all of the centers of maximal balls of the object hence the surface skeleton is a faithful representation in turn though only partial recovery is possible from the curve skeleton this still provides an appealing representation of the object

homology algorithm based on acyclic subspace we present a new reduction algorithm for the efficient computation of the homology of a cubical set the algorithm is based on constructing a possibly large acyclic subspace and then computing the relative homology instead of the plain homology we show that the construction of acyclic subspace may be performed in linear time this significantly reduces the amount of data that needs to be processed in the algebraic way and in practice it proves itself to be significantly more efficient than other available cubical homology algorithms

computing minimal surfaces via level set curvature flow given a fixed closed curve or curves in r sp3 there is an associated problem of finding a surface with mean curvature zero which has that curve or curves as its boundary in this paper a new approach to numerically solving the minimal surface problem is introduced the surface is represented as a level set of a global function phi r sp3 to r the family of surfaces evolve in time according to mean curvature flow a solution is found when a steady state condition is achieved a new system of interpolatory boundary conditions are used to maintain the connection between the surface and the fixed boundary contour several computer surfaces are shown including examples of topological changes

controllability observability and the solution of ax xb c a closed form finite series representation of the unique solution x of the matrix equation ax xb c is developed using this representation the image kernel and rank of x are related to the controllable and unobservable subspaces of the a c and c b pairs respectively bounds on the rank of x are obtainedin terms of the dimensions of these subspaces in the case that c has unitary rank an exact calculation of rank x is made the generic rank of x with a b fixed and c generic is evaluated

adaptive remeshing for compressible flow computations an adaptive mesh procedure for improving the quality of steady state solutions of the euler equations in two dimensions is described the procedure is implemented in conjunction with a finite element solution algorithm using linear triangular elements and an explicit time stepping scheme the mesh adaptation is accomplished by regeneration using information provided by the computed solution on the current mesh the meshes produced are characterised by the appearance of stretched elements in the vicinity of one dimensional flow features and can exhibit a large variation in element size this allows solutions of enhanced quality to be produced in a computationally efficient manner

variational geometric and statistical methods for modeling brain anatomy and function we survey the recent activities of the odyssee laboratory in the area of the application of mathematics to the design of models for studying brain anatomy and function we start with the problem of reconstructing sources in meg and eeg and discuss the variational approach we have developed for solving these inverse problems this motivates the need for geometric models of the head we present a method for automatically and accurately extracting surface meshes of several tissues of the head from anatomical magnetic resonance mr images anatomical connectivity can be extracted from diffusion tensor magnetic resonance images but in the current state of the technology it must be preceded by a robust estimation and regularization stage we discuss our work based on variational principles and show how the results can be used to track fibers in the white matter wm as geodesics in some riemannian space we then go to the statistical modeling of functional magnetic resonance imaging fmri signals from the viewpoint of their decomposition in a pseudo deterministic and stochastic part that we then use to perform clustering of voxels in a way that is inspired by the theory of support vector machines and in a way that is grounded in information theory multimodal image matching is discussed next in the framework of image statistics and partial differential equations pdes with an eye on registering fmri to the anatomy the paper ends with a discussion of a new theory of random shapes that may prove useful in building anatomical and functional atlases

on the detection of simple points in higher dimensions using cubical homology simple point detection is an important task for several problems in discrete geometry such as topology preserving thinning in image processing to compute discrete skeletons in this paper the approach to simple point detection is based on techniques from cubical homology a framework ideally suited for problems in image processing a d dimensional unitary cube for a d dimensional digital image is associated with every discrete picture element instead of a point in spl epsi sup d the d dimensional euclidean space as has been done previously a simple point in this setting then refers to the removal of a unitary cube without changing the topology of the cubical complex induced by the digital image the main result is a characterization of a simple point p i e simple unitary cube in terms of the homology groups of the 3 sup d 1 neighborhood of p for arbitrary finite dimensions d

homology computation by reduction of chain complexes abstract a new algorithm for computing the homology module of a finitely generated chain complex is given it is based on local one step reductions of the size of the initial chain complex and it has a clear geometrical interpretation the complexity of the algorithm is discussed in special cases

detection of 3 d simple points for topology preserving transformations with application to thinning the problems of 3 d digital topology preservation under binary transformations and 3 d object thinning are considered in this correspondence first the authors establish the conditions under which transformation of an object voxel to a non object voxel or its inverse does not affect the image topology an efficient algorithm to detect a simple point has been proposed on the basis of those conditions in this connection some other interesting properties of 3 d digital geometry are also discussed using these properties and the simple point detection algorithm the authors have proposed an algorithm to generate a surface skeleton so that the topology of the original image is preserved the shape of the image is maintained as much as possible and the results are less affected by noise

model reduction by moment matching for linear and nonlinear systems the model reduction problem for single input single output linear and nonlinear systems is addressed using the notion of moment a re visitation of the linear theory allows to obtain novel results for linear systems and to develop a nonlinear enhancement of the notion of moment this in turn is used to pose and solve the model reduction problem by moment matching for nonlinear systems to develop a notion of frequency response for nonlinear systems and to solve model reduction problems in the presence of constraints on the reduced model connections between the proposed results projection methods the covariance extension problem and interpolation theory are presented finally the theory is illustrated by means of simple worked out examples and case studies

homological methods for extraction and analysis of linear features in multidimensional images we show that the problem of extracting linear features from a noisy image and counting the number of branching points may be successfully solved by homological methods applied directly to the image without the need of skeletonization and the analysis of the resulting graph the method is based on the superimposition of a mask set over the original image and works even when the homology of the feature is trivial and in arbitrary dimension we tested the method on computer generated data 2d images of blood vessels 2d satellite images and 3d images of collagen fibers

a geometry driven optical flow warping for spatial normalization of cortical surfaces spatial normalization is frequently used to map data to a standard coordinate system by removing intersubject morphological differences thereby allowing for group analysis to be carried out the work presented in this paper is motivated by the need for an automated cortical surface normalization technique that will automatically identify homologous cortical landmarks and map them to the same coordinates on a standard manifold the geometry of a cortical surface is analyzed using two shape measures that distinguish the sulcal and gyral regions in a multiscale framework a multichannel optical flow warping procedure aligns these shape measures between a reference brain and a subject brain creating the desired normalization the partial differential equation that carries out the warping is implemented in a euclidean framework in order to facilitate a multiresolution strategy thereby permitting large deformations between the two surfaces the technique is demonstrated by aligning 33 normal cortical surfaces and showing both improved structural alignment in manually labeled sulci and improved functional alignment in positron emission tomography data mapped to the surfaces a quantitative comparison between our proposed surface based spatial normalization method and a leading volumetric spatial normalization method is included to show that the surface based spatial normalization performs better in matching homologous cortical anatomies

topology preservation in 3d digital space abstract in a 3d two tone digital space the conditions under which sequential transformation of an object point to a non object point or its inverse does not affect the image topology are investigated the concept of border connectivity is introduced and an efficient algorithm for checking a simple point is proposed in this connection some other interesting properties of 3d digital geometry are also discussed this investigation may be used in thinning and topology preserving morphological transformations in 3d digital space

structure preserving tangential interpolation for model reduction of port hamiltonian systems port hamiltonian systems result from port based network modeling of physical systems and are an important example of passive state space systems in this paper we develop a framework for model reduction of large scale multi input multi output port hamiltonian systems via tangential rational interpolation the resulting reduced model is a rational tangential interpolant that retains the port hamiltonian structure hence it remains passive we introduce an h 2 inspired algorithm for effective choice of interpolation points and tangent directions and present several numerical examples illustrating its effectiveness

a topology preserving level set method for shape optimization the classical level set method which represents the boundary of the unknown geometry as the zero level set of a function has been shown to be very effective in solving shape optimization problems the present work addresses the issue of using a level set representation when there are simple geometrical and topological constraints we propose a logarithmic barrier penalty which acts to enforce the constraints leading to an approximate solution to shape design problems

structure preserving model reduction of port hamiltonian systems by moment matching at infinity model reduction of port hamiltonian systems by means of the krylov methods is considered aiming at port hamiltonian structure preservation it is shown how to employ the arnoldi method for model reduction in a particular coordinate system in order to preserve not only a specific number of the markov parameters but also the port hamiltonian structure for the reduced order model furthermore it is shown how the lanczos method can be applied in a structure preserving manner to a subclass of port hamiltonian systems which is characterized by an algebraic condition in fact for the same subclass of port hamiltonian systems the arnoldi method and the lanczos method turn out to be equivalent in the sense of producing reduced order port hamiltonian models with the same transfer function

fast geodesic active contours we use an unconditionally stable numerical scheme to implement a fast version of the geodesic active contour model the proposed scheme is useful for object segmentation in images like tracking moving objects in a sequence of images the method is based on the weickert romeney viergever additive operator splitting aos scheme it is applied at small regions motivated by the adalsteinsson sethian level set narrow band approach and uses sethian s 1996 fast marching method for re initialization experimental results demonstrate the power of the new method for tracking in color movies

families of moment matching based structure preserving approximations for linear port hamiltonian systems in this paper we propose a solution to the problem of moment matching with preservation of the port hamiltonian structure in the framework of time domain moment matching we characterize several families of parameterized port hamiltonian models that match the moments of a given port hamiltonian system at a set of finite interpolation points we also discuss the problem of markov parameters matching for linear systems as a moment matching problem for descriptor representations associated with the given system at zero interpolation points solving this problem yields families of parameterized reduced order models that achieve markov parameter matching finally we apply these results to the port hamiltonian case resulting in families of parameterized reduced order port hamiltonian approximations

model reduction of neutral linear and nonlinear time invariant time delay systems with discrete and distributed delays the problem of model reduction by moment matching for linear and nonlinear differential time delay systems is studied the class of models considered includes neutral differential time delay systems with discrete delays and distributed delays the description of moment is revisited by means of a sylvester like equation for linear time delay systems and by means of the center manifold theory for nonlinear time delay systems in addition the moments at infinity are characterized for both linear and nonlinear time delay systems parameterized families of models achieving moment matching are given the parameters can be exploited to derive delay free reduced order models or time delay reduced order models with additional properties e g interpolation at an arbitrary large number of points finally the problem of obtaining a reduced order model of an unstable system is discussed and solved

on the computation of the euler number of a binary object in this paper a new method to obtain the euler number of a binary object via its skeleton is presented the number of terminal points points with just one neighbor and the number of three edge points points with only three neighbors in the graph are used to obtain this important invariant as the proposed approach is inherently parallel the resulting algorithm is very fast

new characterizations of simple points in 2d 3d and 4d discrete spaces a point of a discrete object is called simple if it can be deleted from this object without altering topology in this article we present new characterizations of simple points which hold in dimensions 2 3 and 4 and which lead to efficient algorithms for detecting such points in order to prove these characterizations we establish two confluence properties of the collapse operation which hold in the neighborhood of a point in spaces of low dimension this work is settled in the framework of cubical complexes which provides a sound topological basis for image analysis and allows to retrieve the main notions and results of digital topology in particular the notion of simple point

extraction of the euclidean skeleton based on a connectivity criterion abstract the skeleton is essential for general shape representation the commonly required properties of a skeletonization algorithm are that the extracted skeleton should be accurate robust to noise position and rotation able to reconstruct the original object and able to produce a connected skeleton in order to preserve its topological and hierarchical properties however the use of a discrete image presents a lot of problems that may influence the extraction of the skeleton moreover most of the methods are memory intensive and computationally intensive and require a complex data structure in this paper we propose a fast efficient and accurate skeletonization method for the extraction of a well connected euclidean skeleton based on a signed sequential euclidean distance map a connectivity criterion is proposed which can be used to determine whether a given pixel is a skeleton point independently the criterion is based on a set of point pairs along the object boundary which are the nearest contour points to the pixel under consideration and its 8 neighbors our proposed method generates a connected euclidean skeleton with a single pixel width without requiring a linking algorithm or iteration process experiments show that the runtime of our algorithm is faster than the distance transformation and is linearly proportional to the number of pixels of an image

a new shape preserving parallel thinning algorithm for 3d digital images this paper is concerned with a new parallel thinning algorithm for three dimensional digital images that preserves the topology and maintains their shape we introduce an approach of selecting shape points and outer layer used for erosion during each iteration the approach produces good skeleton for different types of corners the concept of using two image versions in thinning is introduced and its necessity in parallel thinning is justified the robustness of the algorithm under pseudo random noise as well as rotation with respect to shape properties is studied and the results are found to be satisfactory

a variational level set approach to multiphase motion a coupled level set method for the motion of multiple junctions of e g solid liquid and grain boundaries which follows the gradient flow for an energy functional consisting of surface tension proportional to length and bulk energies proportional to area is developed the approach combines the level set method of s osher and j a sethian with a theoretical variational formulation of the motion by f reitich and h m soner the resulting method uses as many level set functions as there are regions and the energy functional is evaluated entirely in terms of level set functions the gradient projection method leads to a coupled system of perturbed by curvature terms hamilton jacobi equations the coupling is enforced using a single lagrange multiplier associated with a constraint which essentially prevents a regions from overlapping and b the development of a vacuum the numerical implementation is relatively simple and the results agree with and go beyond the theory as given in 12 other applications of this methodology including the decomposition of a domain into subregions with minimal interface length are discussed finally some new techniques and results in level set methodology are presented

discrete region competition for unknown numbers of connected regions we present a discrete unsupervised multiregion competition algorithm for image segmentation over different energy functionals the number of regions present in an image does not need to be known a priori nor their photometric properties the algorithm jointly estimates the number of regions their photometries and their contours the required regularization is provided by defining a region as a connected set of pixels the evolving contours in the image are represented by computational particles that move as driven by an energy minimization algorithm we present an efficient discrete algorithm that allows minimizing a range of well known energy functionals under the topological constraint of regions being connected components the presented framework and algorithms are implemented in the open source insight toolkit image processing library