on second order weakly hyperbolic equations and the ultradifferentiable classes abstract we consider second order weakly hyperbolic equations with time dependent coefficients in the ultradifferentiable classes our main purpose of the present paper is an investigation the relation between the classes of the functions to be well posed and the following properties of the coefficients the order of degeneration stabilization to a monotonic function and their smoothness in the ultradifferentiable classes

finite element methods for active contour models and balloons for 2 d and 3 d images the use of energy minimizing curves known as snakes to extract features of interest in images has been introduced by kass witkin and terzopoulos 1987 a balloon model was introduced by cohen 1991 as a way to generalize and solve some of the problems encountered with the original method a 3 d generalization of the balloon model as a 3 d deformable surface which evolves in 3 d images is presented it is deformed under the action of internal and external forces attracting the surface toward detected edgels by means of an attraction potential we also show properties of energy minimizing surfaces concerning their relationship with 3 d edge points to solve the minimization problem for a surface two simplified approaches are shown first defining a 3 d surface as a series of 2 d planar curves then after comparing finite element method and finite difference method in the 2 d problem we solve the 3 d model using the finite element method yielding greater stability and faster convergence this model is applied for segmenting magnetic resonance images

on the asymptotic behavior of the energy for the wave equations with time depending coefficients we consider the asymptotic behavior of the total energy of solutions to the cauchy problem for wave equations with time dependent propagation speed the main purpose of this paper is that the asymptotic behavior of the total energy is dominated by the following properties of the coefficient order of the differentiability behavior of the derivatives as t and stabilization of the amplitude described by an integral moreover the optimality of these properties are ensured by actual examples

spectral gap global solutions for degenerate kirchhoff equations abstract we consider the second order cauchy problem u m a 1 2 u 2 a u 0 u 0 u 0 u 0 u 1 where m 0 0 is a continuous function and a is a self adjoint nonnegative operator with dense domain on a hilbert space it is well known that this problem admits local in time solutions provided that u 0 and u 1 are regular enough depending on the continuity modulus of m and on the strict weak hyperbolicity of the equation we prove that for such initial data u 0 u 1 there exist two pairs of initial data u 0 u 1 u 0 u 1 for which the solution is global and such that u 0 u 0 u 0 u 1 u 1 u 1 this is a byproduct of a global existence result for initial data with a suitable spectral gap which extends previous results obtained in the strictly hyperbolic case with a smooth nonlinearity m

scale space and edge detection using anisotropic diffusion a new definition of scale space is suggested and a class of algorithms used to realize a diffusion process is introduced the diffusion coefficient is chosen to vary spatially in such a way as to encourage intraregion smoothing rather than interregion smoothing it is shown that the no new maxima should be generated at coarse scales property of conventional scale space is preserved as the region boundaries in the approach remain sharp a high quality edge detector which successfully exploits global information is obtained experimental results are shown on a number of images parallel hardware implementations are made feasible because the algorithm involves elementary local operations replicated over the image

crystal growth and dendritic solidification we present a numerical method which computes the motion of complex solid liquid boundaries in crystal growth the model we solve includes physical effects such as crystalline anisotropy surface tension molecular kinetics and undercooling the method is based on two ideas first the equations of motion are recast as a single history dependent boundary integral equation on the solid liquid boundary a fast algorithm is used to solve the integral equation efficiently second the boundary is moved by solving a hamiltonjacobi type equation on a fixed domain formulated by osher and sethian for a function in which the boundary is a particular level set this equation is solved by finite difference schemes borrowed from the technology of hyperbolic conservation laws the two ideas are combined by constructing a smooth extension of the normal velocity off the moving boundary in a way suggested by the physics of the problem our numerical experiments show the evolution of complex crystalline shapes development of large spikes and corners dendrite formation and side branching and pieces of solid merging and breaking off freely

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

global solvability for kirchhoff equation in special classes of non analytic functions abstract in this paper we derive the following two properties the first one is a precise representation of wkb solution to the cauchy problem of a linear wave equation with a variable coefficient with respect to time and the second one is the global solvability for kirchhoff equation in some special classes of nonreal analytic functions which is proved by grace of the first property

constraints on deformable models recovering 3d shape and nongrid motion abstract inferring the 3d structures of nonrigidly moving objects from images is a difficult yet basic problem in computational vision our approach makes use of dynamic elastically deformable object models that offer the geometric flexibility to satisfy a diversity of real world visual constraints we specialize these models to include intrinsic forces inducing a preference for axisymmetry image based constraints are applied as extrinsic forces that mold the symmetry seeking model into shapes consistent with image data we describe an extrinsic force that applies constraints derived from profiles of monocularly viewed objects we generalize this constraint force to incorporate profile information from multiple views and use it to exploit binocular image data for time varying images the force becomes dynamic and the model is able to infer not only depth but nonrigid motion as well we demonstrate the recovery of 3d shape and nonrigid motion from natural imagery

dead beat control of linear periodic discrete time systems in this paper the dead beat control of linear periodic discrete time systems subject to periodic disturbances is studied necessary and sufficient conditions are given for the existence of a linear periodic controller such that both output dead beat control under periodic disturbances and state dead beat control under no disturbance are performed moreover synthesis procedures of the controller as well as of state dead beat observers are given which can be applied also to a class of bilinear systems

disturbance localization by measurement feedback for linear periodic discrete time systems abstract the recent notions of inner controllable outer controllable and outer reconstructible subspaces together with the extension of the notion of c a b pair of subspaces to the class of linear periodic discrete time systems are the main tools used in this paper in order to study the disturbance localization problem by measurement feedback for the same class of systems by means of these concepts the necessary and sufficient solvability conditions of such a problem and synthesis procedures of the solutions are found for three different cases i e with and without an additional requirement of output or state dead beat control

computing interface motion in compressible gas dynamics a hamilton jacobi level set formulation of the equations of motion for propagating interfaces has been introduced recently by osher and sethian this formulation allows fronts to self intersect develop singularities and change topology the numerical algorithms based on this approach handle topological merging and breaking naturally work in any number of space dimensions and do not require that the moving front be written as a function instead the moving front is embedded as a particular level set in a fixed domain partial differential equation numerical techniques borrowed from hyperbolic conservation laws are then used to accurately capture the complicated surface motion that satisfies the global entropy condition for propagating fronts given by sethian in this paper we analyze the coupling of this level set formulation to a system of conservation laws for compressible gas dynamics we study both conservative and non conservative differencing of the level set function and compare the two approaches to illustrate the capability of the method we study the compressible rayleigh taylor and kelvin helmholtz instabilities for air air and air helium boundaries we perform numerical convergence studies of the method over a range of parameters and analyze the accuracy of this approach applied to these problems

dead beat observers of reduced order for linear periodic discrete time systems with inaccessible inputs in this paper necessary and sufficient conditions are given for the existence of a dead beat observer for a linear periodic discrete time system subject to immeasurable periodic disturbances the conditions express in terms of the disturbed system the reconstructibility of the augmented system obtained by connecting the former with the disturbance generator a synthesis procedure of the observer is also provided

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

nonlinear multiscale analysis of three dimensional echocardiographic sequences introduces a new model for multiscale analysis of space time echocardiographic sequences the proposed nonlinear partial differential equation representing the multiscale analysis filters the sequence while keeping the space time coherent structures it combines the ideas of regularized perona malik anisotropic diffusion and the galilean invariant movie multiscale analysis of alvarez et al arch rat mech anal vol 123 p 200 57 1993 a numerical method for solving the proposed partial differential equation is suggested and its stability is shown computational results on synthesized and real sequences are provided a qualitative and quantitative evaluation of the accuracy of the method is presented

motion of multiple junctions a level set approach abstract a coupled level set method for the motion of multiple junctions is proposed the new method extends the hamilton jacobi level set formulation of osher and sethian it retains the feature of tracking fronts by following level sets and allows the specification of arbitrary velocities on each front the diffusion equation is shown to generate curvature dependent motion and this is used to develop an algorithm to move multiple junctions with curvature dependent speed systems of reaction diffusion equations are shown to possess inherent properties which prohibit efficient numerical solutions when applied to curvature dependent motion

on the global solvability of kirchhoff equation for non analytic initial data abstract we give sufficient conditions for the global solvability of kirchhoff equation in terms of the spectral resolutions of the initial data u 0 x u t 0 x we assume no smallness conditions and only sobolev type regularity

hyperbolic parabolic singular perturbation for mildly degenerate kirchhoff equations time decay estimates we consider degenerate kirchhoff equations with a small parameter e in front of the second order time derivative it is well known that these equations admit global solutions when e is small enough and that these solutions decay as t with the same rate of solutions of the limit problem of parabolic type in this paper we prove decay error estimates for the difference between a solution of the hyperbolic problem and the solution of the corresponding parabolic problem these estimates show in the same time that the difference tends to zero both as e 0 and as t concerning the decay rates it turns out that the difference decays faster than the two terms separately as t proofs involve a nonlinear step where we separate fourier components with respect to the lowest frequency followed by a linear step where we exploit weighted versions of classical energies

recursive solutions to deadbeat observers for time varying multivariable systems this paper describes a new construction of the deadbeat observer for the state estimation of linear time varying multivariable systems the proposed design methods are computationally attractive because of their simplicity and recursive nature and are recommendable even for time invariant multivariable systems

parameterization of the class of deadbeat controllers this technical note deals with the problem of parameterizing the class of deadbeat controllers for a given system through the minimum of parameters it is shown that if n and m are dimensions of the state vector and control vector respectively and the i s are the controllability indexes then almost the whole class of deadbeat controllers is explicitly parameterizable through mn mu 1 3 mu 2 2m 1 mu m parameters

a class of non analytic functions for the global solvability of kirchhoff equation abstract we consider the global solvability to the cauchy problem of kirchhoff equation with generalized classes of manfrin s class manfrin s class is a subclass of sobolev space but we shall extend this class as a subclass of the ultradifferentiable class and we succeed to prove the global solvability of kirchhoff equation with large data in wider classes from the previous works

minimal time minimal order deadbeat regulator with internal stability this paper is concerned with the output deadbeat finite settling time regulation with internal stability for linear discrete time multivariable systems the two cases are treated separately the one is the regulation by state feedback and the other is the regulation through function observers for both cases the basic solvability conditions the minimal settling time and the characterizations of the minimal time regulators are derived throughout the paper the well posedness condition plays a fundamental role a deterministic version of the so called separation theorem in lqg problem is derived namely the minimal time state feedback regulator combined with the minimal time minimal order function observer yields the overall minimal time minimal order regulator by output feedback

a uniqueness result for kirchhoff equations with non lipschitz nonlinear term abstract we consider the second order cauchy problem u m a 1 2 u 2 a u 0 u 0 u 0 u 0 u 1 where m 0 0 is a continuous function and a is a self adjoint nonnegative operator with dense domain on a hilbert space it is well known that this problem admits local in time solutions provided that u 0 and u 1 are regular enough depending on the continuity modulus of m it is also well known that the solution is unique when m is locally lipschitz continuous in this paper we prove that if either a u 0 u 1 0 or a 1 2 u 1 2 m a 1 2 u 0 2 a u 0 2 then the local solution is unique even if m is not lipschitz continuous

cal h _ infty output feedback control based on an fir type quasi deadbeat observer this technical note proposes a novel output feedback control law based on a finite impulse response fir type quasi deadbeat observer for linear systems for nominal systems without disturbances this technical note first establishes the deadbeat condition that reduces the state estimation error to zero within a finite time and verifies that all the hidden poles of the closed loop system under the quasi deadbeat observer based control law are zero and that the separation principle holds true in order to enhance the disturbance rejection capability for systems with random work disturbances on the structural merit of the fir type observer we have proposed the conditions for an h infin quasi deadbeat observer and an h infin stabilizer based on the predetermined observer respectively

region tracking on level sets methods since the work by osher and sethian 1988 on level sets algorithms for numerical shape evolutions this technique has been used for a large number of applications in numerous fields in medical imaging this numerical technique has been successfully used for example in segmentation and cortex unfolding algorithms the migration from a lagrangian implementation to a eulerian one via implicit representations or level sets brought some of the main advantages of the technique i e topology independence and stability this migration means also that the evolution is parametrization free therefore the authors do not know exactly how each part of the shape is deforming and the point wise correspondence is lost in this note they present a technique to numerically track regions on surfaces that are being deformed using the level sets method the basic idea is to represent the region of interest as the intersection of two implicit surfaces and then track its deformation from the deformation of these surfaces this technique then solves one of the main shortcomings of the very useful level sets approach applications include lesion localization in medical images region tracking in functional mri fmri visualization and geometric surface mapping

combining multiple dynamic models and deep learning architectures for tracking the left ventricle endocardium in ultrasound data we present a new statistical pattern recognition approach for the problem of left ventricle endocardium tracking in ultrasound data the problem is formulated as a sequential importance resampling algorithm such that the expected segmentation of the current time step is estimated based on the appearance shape and motion models that take into account all previous and current images and previous segmentation contours produced by the method the new appearance and shape models decouple the affine and nonrigid segmentations of the left ventricle to reduce the running time complexity the proposed motion model combines the systole and diastole motion patterns and an observation distribution built by a deep neural network the functionality of our approach is evaluated using a dataset of diseased cases containing 16 sequences and another dataset of normal cases comprised of four sequences where both sets present long axis views of the left ventricle using a training set comprised of diseased and healthy cases we show that our approach produces more accurate results than current state of the art endocardium tracking methods in two test sequences from healthy subjects using three test sequences containing different types of cardiopathies we show that our method correlates well with interuser statistics produced by four cardiologists

segmenting skin lesions with partial differential equations based image processing algorithms a partial differential equations pde based system for detecting the boundary of skin lesions in digital clinical skin images is presented the image is first preprocessed via contrast enhancement and anisotropic diffusion if the lesion is covered by hairs a pde based continuous morphological filter that removes them is used as an additional preprocessing step following these steps the skin lesion is segmented either by the geodesic active contours model or the geodesic edge tracing approach these techniques are based on computing again via pdes a geodesic curve in a space defined by the image content examples showing the performance of the algorithm are given

the geometric approach for linear periodic discrete time systems abstract recently the disturbance localization problem and the problems of designing disturbance decoupled observers and of giving a geometric characterization of invariant zeros were solved for linear periodic discrete time systems through an extension of the geometric approach based on the notions of controlled invariant and conditionally invariant subspaces to periodic ones here the existing periodic geometric theory is supplemented with the notions of outer reachable subspace and controllability subspace and with some further results on the previously introduced notions of inner reachable controllable subspace and outer controllable subspace in addition it is shown that any such periodic geometric theory can be restated in an equivalent time invariant form which is just the same theory written for a suitable time invariant system having an extended state space

on the stabilization of a class of bilinear systems abstract in this paper the problem of the stabilization of a class of continuous time bilinear systems containing the class of the homogeneous ones is studied and simple stabiliza bility conditions are derived expressed in terms of the stability or stabilizability of some linear or homogeneous bilinear subsystems of the given system on this basis it is shown that this problem can be decomposed into subproblems and reduced to the stabilization of homogeneous subsystems of the system obtained through successive decompositions of it a sufficient condition for the stabilization of a homogeneous bilinear system is also given

energy estimates for wave equations with time dependent propagation speeds in the gevrey class abstract the total energy of the wave equation is conserved with respect to time if the propagation speed is a constant but this is not true in general for time dependent propagation speeds indeed it is considered in hirosawa 2007 3 that the following properties of the propagation speed are crucial for the estimates of the total energy oscillating speed difference from the mean and the smoothness in c m category the main purpose of this paper is to derive a benefit of a further smoothness of the propagation speed in the gevrey class for the energy estimates

curvature and the evolution of fronts the evolution of a front propagating along its normal vector field with speedf dependent on curvaturek is considered the change in total variation of the propagating front is shown to depend only ondf dk only wherek changes sign analysis of the casef k 1 ek where e is a constant shows that curvature plays a role similar to that of viscosity in burgers equation for e 0 and non convex initial data the curvature blows up corners develop and an entropy condition can be formulated to provide an explicit construction for a weak solution beyond the singularity we then numerically show that the solution as e goes to zero converges to the constructed weak solution numerical methods based on finite difference schemes for marker particles along the front are shown to be unstable in regions where the curvature builds as a remedy we show that front tracking based on volume of fluid techniques can be used together with the entropy condition to provide transition from the classical to weak solution

a lifting based approach to observer based fault detection of linear periodic systems in this note an approach based on lifting is introduced for the observer based fault detection fd of linear discrete time periodic systems the main contribution of this note is to give an analytic expression to transform the linear time invariant lti observer based residual generator designed based on the lifted lti reformulation of the periodic system into a periodic observer based residual generator to reduce detection delay the result enables a systematic transfer of the existing observer based fd methods for discrete lti systems to discrete time periodic systems

left ventricular volume estimation for real time three dimensional echocardiography the application of level set techniques to echocardiographic data is presented this method allows semiautomatic segmentation of heart chambers which regularizes the shapes and improves edge fidelity especially in the presence of gaps as is common in ultrasound data the task of the study was to reconstruct left ventricular shape and to evaluate left ventricular volume data were acquired with a real time three dimensional 3 d echocardiographic system the method was applied directly in the three dimensional domain and was based on a geometric driven scheme the numerical scheme for solving the proposed partial differential equation is borrowed from numerical methods for conservation law results refer to in vitro and human in vivo acquired 3 d time echocardiographic data quantitative validation was performed on in vitro balloon phantoms clinical application of this segmentation technique is reported for 20 patient cases providing measures of left ventricular volumes and ejection fraction

global minimum for active contour models a minimal path approach a new boundary detection approach for shape modeling is presented it detects the global minimum of an active contour model s energy between two end points initialization is made easier and the curve is not trapped at a local minimum by spurious edges we modify the snake energy by including the internal regularization term in the external potential term our method is based on finding a path of minimal length in a riemannian metric we then make use of a new efficient numerical method to find this shortest path it is shown that the proposed energy though based only on a potential integrated along the curve imposes a regularization effect like snakes we explore the relation between the maximum curvature along the resulting contour and the potential generated from the image the method is capable to close contours given only one point on the objects boundary by using a topology based saddle search routine we show examples of our method applied to real aerial and medical images

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

a variational approach for the segmentation of the left ventricle in cardiac image analysis in this paper we propose a level set method to segment mr cardiac images our approach is based on a coupled propagation of two cardiac contours and integrates visual information with anatomical constraints the visual information is expressed through a gradient vector flow based boundary component and a region term that aims at best separating the cardiac contours regions according to their global intensity properties in order to deal with misleading visual support an anatomical constraint is considered that couples the propagation of the cardiac contours according to their relative distance the resulting motion equations are implemented using a level set approach and a fast and stable numerical approximation scheme the additive operator splitting encouraging experimental results are provided using real data

deadbeat control and tracking of discrete time systems a new approach for forcing the state of a linear discrete time system to zero in a minimum number of steps is discussed the problem is formulated as the solution to a steady state optimal control problem with no cost on the control this problem in turn is set up as the solution to an associated eigenvalue problem no special assumption on the open loop system matrix and or the ratio of the number of states to controls is required stable numerical techniques are presented for solving for the feedback gain robust deadbeat tracking is also discussed