regularity preserving image interpolation assumptions about image continuity lead to oversmoothed edges in common image interpolation algorithms a wavelet based interpolation method that imposes no continuity constraints is introduced the algorithm estimates the regularity of edges by measuring the decay of wavelet transform coefficients across scales and preserves the underlying regularity by extrapolating a new subband to be used in image resynthesis the algorithm produces visibly sharper edges than traditional techniques and exhibits an average peak signal to noise ratio psnr improvement of 2 5 db over bilinear and bicubic techniques

higher order approximation of analytic sets by topologically equivalent algebraic sets it is known that every germ of an analytic set is homeomorphic to the germ of an algebraic set in this paper we show that the homeomorphism can be chosen in such a way that the analytic and algebraic germs are tangent with any prescribed order of tangency moreover the space of arcs contained in the algebraic germ approximates the space of arcs contained in the analytic one in the sense that they are identical up to a prescribed truncation order

on the role of exponential splines in image interpolation a sobolev reproducing kernel hilbert space approach to image interpolation is introduced the underlying kernels are exponential functions and are related to stochastic autoregressive image modeling the corresponding image interpolants can be implemented effectively using compactly supported exponential b splines a tight l2 upper bound on the interpolation error is then derived suggesting that the proposed exponential functions are optimal in this regard experimental results indicate that the proposed interpolation approach with properly tuned signal dependent weights outperforms currently available polynomial b spline models of comparable order furthermore a unified approach to image interpolation by ideal and nonideal sampling procedures is derived suggesting that the proposed exponential kernels may have a significant role in image modeling as well our conclusion is that the proposed sobolev based approach could be instrumental and a preferred alternative in many interpolation tasks

approximation of analytic sets by nash tangents of higher order the aim of this paper is to show that for every locally analytic subset x of cm and every a in x there exist a neighborhood v of a in cm and a sequence x nu of nash subsets of v converging to x cap v such that x and x satisfy a certain condition for tangency of order next it is shown that this condition implies that for sufficiently large the multiplicities of x and x at a are equal

isogeometric overlapping schwarz preconditioners for the bidomain reaction diffusion system abstract we present and study an overlapping additive schwarz preconditioner for the isogeometric discretization of a reaction diffusion system modeling the heart bioelectrical activity known as the bidomain model consisting of a degenerate system of parabolic and elliptic pde this model includes intramural fiber rotation anisotropic conductivity coefficients and is coupled through the reaction term with a system of odes which models the ionic currents of the cellular membrane the overlapping schwarz preconditioner is applied with a pcg accelerator to solve the linear system arising at each time step from the isogeometric discretization in space and a semi implicit adaptive method in time a theoretical convergence rate analysis shows that the resulting solver is scalable optimal in the ratio of subdomain element size and the convergence rate improves with increasing overlap size numerical tests in three dimensional ellipsoidal domains confirm the theoretical estimates and additionally show the robustness with respect to jump discontinuities of the orthotropic conductivity coefficients

strongly pseudoconvex domains as subvarieties of complex manifolds in this paper we obtain existence and approximation results for closed complex subvarieties that are normalized by strongly pseudoconvex stein domains our sufficient condition for the existence of such subvarieties in a complex manifold x is expressed in terms of the morse indices and the number of positive levi eigenvalues of an exhaustion function on x examples show that our conditions cannot be weakened in general we obtain optimal results for subvarieties of this type in complements of compact complex submanifolds with griffiths positive normal bundle in the projective case these generalize classical theorems of remmert bishop and narasimhan concerning proper holomorphic maps and embeddings to bbb c n bbb p n backslash bbb p n 1

on nash approximation of complex analytic sets in runge domains abstract we prove that every complex analytic set x in a runge domain can be approximated by nash sets on any relatively compact subdomain 0 of moreover for every nash subset y of with y x the approximating sets can be chosen so that they contain y 0 as a consequence we derive a necessary and sufficient condition for a complex analytic set x to admit a nash approximation which coincides with x along its arbitrary given subset

scaling theorems for zero crossings we characterize some properties of the zero crossings of the laplacian of signals in particular images filtered with linear filters as a function of the scale of the filter extending recent work by witkin 16 we prove that in any dimension the only filter that does not create generic zero crossings as the scale increases is the gaussian this result can be generalized to apply to level crossings of any linear differential operator it applies in particular to ridges and ravines in the image intensity in the case of the second derivative along the gradient there is no filter that avoids creation of zero crossings unless the filtering is performed after the derivative is applied

a multilevel hybrid newton krylov schwarz method for the bidomain model of electrocardiology abstract a multilevel hybrid newton krylov schwarz nks method is constructed and studied numerically for implicit time discretizations of the bidomain reaction diffusion system in three dimensions this model describes the bioelectrical activity of the heart by coupling two degenerate parabolic equations with a stiff system of ordinary differential equations the nks bidomain solver employs an outer inexact newton iteration to solve the nonlinear finite element system originating at each time step of the implicit discretization the jacobian update during the newton iteration is solved by a krylov method employing a multilevel hybrid overlapping schwarz preconditioner additive within the levels and multiplicative among the levels several parallel tests on linux clusters are performed showing that the convergence of the method is independent of the number of subdomains scalability the discretization parameters and the number of levels optimality

addendum to subelliptic spin c dirac operators iii we prove the relative index conjecture which in turn implies that the set of embeddable deformations of a strictly pseudoconvex cr structure on a compact 3 manifold is closed in the c 1 topology

a histogram modification framework and its application for image contrast enhancement a general framework based on histogram equalization for image contrast enhancement is presented in this framework contrast enhancement is posed as an optimization problem that minimizes a cost function histogram equalization is an effective technique for contrast enhancement however a conventional histogram equalization he usually results in excessive contrast enhancement which in turn gives the processed image an unnatural look and creates visual artifacts by introducing specifically designed penalty terms the level of contrast enhancement can be adjusted noise robustness white black stretching and mean brightness preservation may easily be incorporated into the optimization analytic solutions for some of the important criteria are presented finally a low complexity algorithm for contrast enhancement is presented and its performance is demonstrated against a recently proposed method

k3 surfaces with involution equivariant analytic torsion and automorphic forms on the moduli space in this paper we introduce an invariant of a k3 surface with 2 action equipped with a 2 invariant kahler metric which we obtain using the equivariant analytic torsion of the trivial line bundle this invariant is shown to be independent of the choice of the kahler metric it can be viewed as a function on the moduli space of k3 surfaces with involution the main result of this paper is that this function can be identified with an automorphic form which characterizes the discriminant locus in particular we show that the ray singer analytic torsion of the trivial line bundle on an enriques surface with ricci flat kahler metric is given by the value of the norm of the borcherds function at its period point

multilevel schwarz methods for elliptic partial differential equations we investigate multilevel schwarz domain decomposition preconditioners to efficiently solve linear systems arising from numerical discretizations of elliptic partial differential equations by the finite element method in our analysis we deal with unstructured mesh partitions and with subdomain boundaries resulting from using the mesh partitioner we start from two level preconditioners with either aggregative or interpolative coarse level components then we focus on a strategy to increase the number of levels for all preconditioners we consider the additive residual update and its multiplicative variants within and between levels moreover we compare the preconditioners behaviour regarding scalability and rate of convergence numerical results are provided for elliptic boundary value problems including a convection diffusion problem when suitable stabilization becomes necessary c 2011 elsevier b v all rights reserved

a general framework for quadratic volterra filters for edge enhancement an inherent problem in most image enhancement schemes is the amplification of noise which due to weber s law is mostly visible in the darker portions of an image using a special class of quadratic volterra filters we can adapt the enhancement process in a computationally efficient way to the local image brightness because these filters are approximately equivalent to the product of a local mean estimator and a highpass filter we analyze and derive this subclass of quadratic volterra filters by investigating the 1 d case first and then we generalize the results to two dimensions an important property of these filters is that they map sinusoidal inputs to constant outputs which allows us to develop a new filter characterization that is more intuitive for our application than the 4 d frequency response this description finally leads to a novel least squares design methodology image enhancement results using our volterra filters are superior to those obtained with standard linear filters which we demonstrate both quantitatively and qualitatively

fractional differential mask a fractional differential based approach for multiscale texture enhancement in this paper we intend to implement a class of fractional differential masks with high precision thanks to two commonly used definitions of fractional differential for what are known as grumwald letnikov and riemann liouville we propose six fractional differential masks and present the structures and parameters of each mask respectively on the direction of negative x coordinate positive x coordinate negative y coordinate positive y coordinate left downward diagonal left upward diagonal right downward diagonal and right upward diagonal moreover by theoretical and experimental analyzing we demonstrate the second is the best performance fractional differential mask of the proposed six ones finally we discuss further the capability of multiscale fractional differential masks for texture enhancement experiments show that for rich grained digital image the capability of nonlinearly enhancing complex texture details in smooth area by fractional differential based approach appears obvious better than by traditional integral based algorithms

cohomology of q convex spaces in top degrees it is shown that every strongly q complete subvariety of a complex analytic space has a fundamental system of strongly q complete neighborhoods as a consequence we find a simple proof of ohsawa s result that every non compact irreducible n dimensional analytic space is strongly n complete finally it is shown that l cohomology theory readily implies ohsawa s hodge decomposition and lefschetz isomorphism theorems for absolutely q convex manifolds

multilevel additive schwarz preconditioners for the bidomain reaction diffusion system multilevel additive schwarz methods are analyzed and studied numerically for the anisotropic cardiac bidomain model in three dimensions this is the most complete model to date of the bioelectrical activity of the heart tissue consisting of a degenerate parabolic system of nonlinear reaction diffusion equations coupled with a stiff system of several ordinary differential equations describing the ionic currents through the cellular membrane due to the presence of very different scales in both space and time the numerical discretization of this system by finite elements in space and semi implicit methods in time produces very ill conditioned linear systems that must be solved at each time step the proposed multilevel algorithm employs a hierarchy of nested meshes with overlapping schwarz preconditioners on each level and is fully additive hence parallel within and among levels convergence estimates are proved for the resulting multilevel algorithm showing that its convergence rate is independent of the number of subdomains scalability of the mesh sizes of each level and of the number of levels optimality several parallel tests on a linux cluster confirm the scalability and optimality of the method as well as its parallel efficiency on both cartesian and deformed domains in three dimensions

the method weak lefschetz theorems and the topology of kahler manifolds in no nori studied the fundamental group of complements of nodal curves with ample normal bundle in smooth projective surfaces the main tool was the following weak lefschetz theorem theorem nori suppose u x is a local biholomorphism from a connected complex manifold u into a connected smooth projective variety x of dimension at least 2 and u contains a connected effective divisor y with compact support and ample normal bundle then for every zariski open subset z of x the image of 1 1 z in 1 z is of finite index

some l2 results for overline partial on projective varieties with general singularities let x be an irreducible n dimensional projective variety in bbb c p n with arbitrary singular locus we prove that the l 2 overline partial p 1 cohomology groups with respect to the fubini study metric of the regular part of x are finite dimensional

a model based block triangular preconditioner for the bidomain system in electrocardiology we introduce a preconditioner for the solution of the bidomain system governing the propagation of action potentials in the myocardial tissue the bidomain model is a degenerate parabolic set of nonlinear reaction diffusion equations the nonlinear term describes the ion flux at the cellular level the degenerate nature of the problem results in a severe ill conditioning of its discretization our preconditioning strategy is based on a suitable adaptation of the monodomain model a simplified version of the bidomain one which is by far simpler to solve nevertheless is unable to capture significant features of the action potential propagation the monodomain preconditioner application to a non symmetric formulation of the bidomain system results at the algebraic level in a lower block triangular preconditioner we prove optimality of the preconditioner with respect to the mesh size and corroborate our theoretical results with 3d numerical simulations both on idealized and real ventricle geometries

renormalized chern gauss bonnet formula for complete kahler einstein metrics we present a renormalized gauss bonnet formula for a strictly pseudoconvex manifold with a complete k a hler metric given by a globally defined potential function near the boundary when the metric is asymptotically einstein the boundary contribution in the formula is explicitly written down in terms of the pseudo hermitian geometry of the boundary and is shown to be a global cr invariant the cr invariant generalizes the burns epstein invariant on 3 dimensional cr manifolds

preconditioning the bidomain model with almost linear complexity the bidomain model is widely used in electro cardiology to simulate spreading of excitation in the myocardium and electrocardiograms it consists of a system of two parabolic reaction diffusion equations coupled with an ode system its discretisation displays an ill conditioned system matrix to be inverted at each time step simulations based on the bidomain model therefore are associated with high computational costs in this paper we propose a preconditioning for the bidomain model either for an isolated heart or in an extended framework including a coupling with the surrounding tissues the torso the preconditioning is based on a formulation of the discrete problem that is shown to be symmetric positive semi definite a block lu decomposition of the system together with a heuristic approximation referred to as the monodomain approximation are the key ingredients for the preconditioning definition numerical results are provided for two test cases a 2d test case on a realistic slice of the thorax based on a segmented heart medical image geometry a 3d test case involving a small cubic slab of tissue with orthotropic anisotropy the analysis of the resulting computational cost both in terms of cpu time and of iteration number shows an almost linear complexity with the problem size i e of type nlog a n for some constant a which is optimal complexity for such problems

newton krylov bddc solvers for nonlinear cardiac mechanics abstract the aim of this work is to design and study a balancing domain decomposition by constraints bddc solver for the nonlinear elasticity system modeling the mechanical deformation of cardiac tissue the contraction relaxation process in the myocardium is induced by the generation and spread of the bioelectrical excitation throughout the tissue and it is mathematically described by the coupling of cardiac electro mechanical models consisting of systems of partial and ordinary differential equations in this study the discretization of the electro mechanical models is performed by q1 finite elements in space and semi implicit finite difference schemes in time leading to the solution of a large scale linear system for the bioelectrical potentials and a nonlinear system for the mechanical deformation at each time step of the simulation the parallel mechanical solver proposed in this paper consists in solving the nonlinear system with a newton krylov bddc method based on the parallel solution of local mechanical problems and a coarse problem for the so called primal unknowns three dimensional parallel numerical tests on different machines show that the proposed parallel solver is scalable in the number of subdomains quasi optimal in the ratio of subdomain to mesh sizes and robust with respect to tissue anisotropy

image enhancement by nonlinear extrapolation in frequency space a technique for enhancing the perceptual sharpness of an image is described the enhancement algorithm augments the frequency content of the image using shape invariant properties of edges across scale by using a nonlinearity that generates phase coherent higher harmonics the procedure utilizes the laplacian transform and the laplacian pyramid image representation results are presented depicting the power spectra augmentation and the visual enhancement of several images simplicity of computations and ease of implementation allow for real time applications such as high definition television hdtv

embeddability of some strongly pseudoconvex cr manifolds we obtain an embedding theorem for compact strongly pseudoconvex cr manifolds which are boundaries of some complete hermitian manifolds we use this to compactify some negatively curved kahler manifolds with compact strongly pseudoconvex boundary an embedding theorem for sasakian manifolds is also derived

k3 surfaces with involution equivariant analytic torsion and automorphic forms on the moduli space iii the case r m 18 we prove the automorphic property of the invariant of k3 surfaces with involution which we obtained using equivariant analytic torsion in the case where the dimension of the moduli space is less than or equal to 2

the laplacian pyramid as a compact image code we describe a technique for image encoding in which local operators of many scales but identical shape serve as the basis functions the representation differs from established techniques in that the code elements are localized in spatial frequency as well as in space pixel to pixel correlations are first removed by subtracting a lowpass filtered copy of the image from the image itself the result is a net data compression since the difference or error image has low variance and entropy and the low pass filtered image may represented at reduced sample density further data compression is achieved by quantizing the difference image these steps are then repeated to compress the low pass image iteration of the process at appropriately expanded scales generates a pyramid data structure the encoding process is equivalent to sampling the image with laplacian operators of many scales thus the code tends to enhance salient image features a further advantage of the present code is that it is well suited for many image analysis tasks as well as for image compression fast algorithms are described for coding and decoding

holomorphic flexibility properties of complex manifolds we obtain results on approximation of holomorphic maps by algebraic maps the jet transversality theorem for holomorphic and algebraic maps between certain classes of manifolds and the homotopy principle for holomorphic submersions of stein manifolds to certain algebraic manifolds

balancing neumann neumann methods for the cardiac bidomain model balancing neumann neumann preconditioners are constructed analyzed and numerically studied for the cardiac bidomain model in three dimensions this reaction diffusion system is discretized by low order finite elements in space and implicit explicit methods in time yielding very ill conditioned linear systems that must be solved at each time step the proposed algorithm is based on decomposing the domain into nonoverlapping subdomains and on solving iteratively the bidomain schur complement obtained by implicitly eliminating the degrees of freedom interior to each subdomain the iteration is preconditioned by a balancing neumann neumann method employing local neumann solves on each subdomain and a coarse bidomain solve a novel approach for the estimation of the average operator of the nonoverlapping decomposition provides a framework for designing coarse spaces for balancing neumann neumann methods the theoretical estimates obtained show that the proposed method is scalable quasi optimal and robust with respect to possible coefficient discontinuities of the bidomain operator the results of extensive parallel numerical tests in three dimensions confirm the convergence rates predicted by the theory

on three dimensional cauchy riemann manifolds of the almost complex tensor of c2 multiplication by i the collection of these subspaces hp m forms a bundle hm c tm called the horizontal or contact bundle indeed strict pseudoconvexity of m implies that the plane field hpm is nondegenerate i e defines a contact structure the almost complex tensor of c2 then restricts to a bundle endomorphism j hm hm such that j2 id the bundle hm c tm together with this endomorphism j defines the cr structure of m slightly more generally let d d u m be a four dimensional compact manifold with boundary m interior d endowed with a smooth almost complex tensor which is integrable on d if d is strictly pseudoconvex i e in a neighborhood of any p e m there is a smooth strictly plurisubharmonic function u negative on d 0 on m but du 0 on m then m inherits a strictly pseudoconvex cr structure from d in this case we shall say that m bounds a strictly pseudoconvex surface this leads us to the abstract definition a strictly pseudoconvex threedimensional cr manifold is a compact manifold m without boundary dim m 3 endowed with a contact structure hm hpm p e m c tm and an endomorphism j of hm such that j2 id throughout this paper unless otherwise stated we shall be working with infinitely differentiable objects thus m hm j are assumed to be smooth in this sense furthermore a differentiable function f m c is a cr function if for any p e m the restriction df ihm hpm tf p c

bpx preconditioners for the bidomain model of electrocardiology the aim of this work is to develop a bpx preconditioner for the bidomain model of electrocardiology this model describes the bioelectrical activity of the cardiac tissue and consists of a system of a non linear parabolic reaction diffusion partial differential equation pde and an elliptic linear pde modeling at macroscopic level the evolution of the transmembrane and extracellular electric potentials of the anisotropic cardiac tissue the evolution equation is coupled through the non linear reaction term with a stiff system of ordinary differential equations the so called membrane model describing the ionic currents through the cellular membrane the discretization of the coupled system by finite elements in space and semi implicit finite differences in time yields at each time step the solution of an ill conditioned linear system the goal of the present study is to construct analyze and numerically test a bpx preconditioner for the linear system arising from the discretization of the bidomain model optimal convergence rate estimates are established and verified by two and three dimensional numerical tests on both structured and unstructured meshes moreover in a full heartbeat simulation on a three dimensional wedge of ventricular tissue the bpx preconditioner is about 35 faster in terms of cpu times than ilu 0 and an algebraic multigrid preconditioner

a splitting preconditioner for a block two by two linear system with applications to the bidomain equations we construct an alternating splitting iteration scheme for solving and preconditioning a block two by two linear system arising from numerical discretizations of the bidomain equations the convergence theory of this class of splitting iteration methods is established and some useful properties of the preconditioned matrix are analyzed the potential of this approach is illustrated by numerical experiments

chromosome image enhancement using multiscale differential operators chromosome banding patterns are very important features for karyotyping based on which cytogenetic diagnosis procedures are conducted due to cell culture staining and imaging conditions image enhancement is a desirable preprocessing step before performing chromosome classification in this paper we apply a family of differential wavelet transforms wang and lee 1998 wang 1999 for this purpose the proposed differential filters facilitate the extraction of multiscale geometric features of chromosome images moreover desirable fast computation can be realized we study the behavior of both banding edge pattern and noise in the wavelet transform domain based on the fact that image geometrical features like edges are correlated across different scales in the wavelet representation a multiscale point wise product mpp is used to characterize the correlation of the image features in the scale space a novel algorithm is proposed for the enhancement of banding patterns in a chromosome image in order to compare objectively the performance of the proposed algorithm against several existing image enhancement techniques a quantitative criteria the contrast improvement ratio cir has been adopted to evaluate the enhancement results the experimental results indicate that the proposed method consistently outperforms existing techniques in terms of the cir measure as well as in visual effect the effect of enhancement on cytogenetic diagnosis is further investigated by classification tests conducted prior to and following the chromosome image enhancement in comparison with conventional techniques the proposed method leads to better classification results thereby benefiting the subsequent cytogenetic diagnosis