multiple paths extraction in images using a constrained expanded trellis single shortest path extraction algorithms have been used in a number of areas such as network flow and image analysis in image analysis shortest path techniques can be used for object boundary detection crack detection or stereo disparity estimation sometimes one needs to find multiple paths as opposed to a single path in a network or an image where the paths must satisfy certain constraints in this paper we propose a new algorithm to extract multiple paths simultaneously within an image using a constrained expanded trellis cet for feature extraction and object segmentation we also give a number of application examples for our multiple paths extraction algorithm

the lqg optimal regulation problem for systems with perfect measurements explicit solution properties and application to practical designs the continuous time stationary linear quadratic gaussian lqg optimal regulation problem is considered where the measurements are free of white noise components a simple direct solution in the s domain is derived for the optimal controller for general linear time variant right invertible or left invertible systems the explicit expressions that are found for the controller transference and for the regulator return ratio matrix can be used to obtain a practical suboptimal design in the s domain these expressions are applied to derive simple conditions for the precise recovery of the return ratio matrix of the lqg regulator

generalization of selberg s frac 3 16 theorem and affine sieve an analogue of the well known frac 3 16 lower bound for the first eigenvalue of the laplacian for a congruence hyperbolic surface is proven for a congruence tower associated with any non elementary subgroup l of sl 2 z the proof in the case that the hausdorff of the limit set of l is bigger than frac 1 2 is based on a general result which allows one to transfer such bounds from a combinatorial version to this archimedian setting in the case that delta is less than frac 1 2 we formulate and prove a somewhat weaker version of this phenomenon in terms of poles of the corresponding dynamical zeta function these spectral gaps are then applied to sieving problems on orbits of such groups

automatic finding of main roads in aerial images by using geometric stochastic models and estimation this paper presents an automated approach to finding main roads in aerial images the approach is to build geometric probabilistic models for road image generation we use gibbs distributions then given an image roads are found by map maximum a posteriori probability estimation the map estimation is handled by partitioning an image into windows realizing the estimation in each window through the use of dynamic programming and then starting with the windows containing high confidence estimates using dynamic programming again to obtain optimal global estimates of the roads present the approach is model based from the outset and is completely different than those appearing in the published literature it produces two boundaries for each road or four boundaries when a mid road barrier is present

high performance state feedback robust and output feedback stabilizing control a systematic design algorithm improves a fundamentally new design approach which can generally realize the robustness properties of the state feedback control for the first time by guaranteeing the resulting feedback system stability to the best of the authors knowledge this improved design also provides the first simple and systematic design procedure and design solution to the strong stabilization problem stabilize feedback system by a stable output feedback compensator finally high performance high robustness and low controller order can all be systematically achieved by this design

on the robustness of lq regulators it is shown that in spite of its large gain and phase margins the linear quadratic state feedback regulator may suffer from poor robustness where small changes in the parameters of the system may lead to fast unstable closed loop modes

author s reply to comments on the loop transfer recovery the author disagrees with the two comments made in the above paper by rachid ibid vol 40 no 2 1995 on the new loop transfer recovery ltr technique proposed by the author ibid vol ac 32 no 9 1987 1 the technique could lead to poor results and 2 the technique cannot be applied to nonminimum phase systems referring to the first comment it is pointed out that the new technique can yield exact solutions for all plants with more than inputs or with at least one stable transmission zero the author dismisses the second as incorrect

optimal l sub spl infin to l sub spl infin estimation for periodic systems in this paper we consider the problem of finding a filter that minimizes the worst case magnitude l sub spl infin of the estimation error in the case of linear periodically time varying systems subjected to unknown but magnitude bounded l sub spl infin inputs these inputs consist of process and observation noises and the optimization problem is considered over an infinite time horizon lifting techniques are utilized to transform the problem to a time invariant l sub 1 model matching problem subject to additional constraints taking advantage of the particular structure of the estimation problem it is shown how standard methods of l sub 1 optimization in particular the delay augmentation technique can be suitably modified to solve this nonstandard problem

linear quadratic gaussian synthesis with reduced parameter sensitivity we present a method for improving the tolerance of a conventional lqg controller to parameter errors in the plant model the improvement is achieved by introducing additional terms reflecting the structure of the parameter errors into the lqr cost function and also the process and measurement noise models adjusting the sizes of these additional terms permits a trade off between robustness and nominal performance manipulation of some of the additional terms leads to high gain controllers while other terms lead to low gain controllers conditions are developed under which the high gain approach asymptotically recovers the robustness of the corresponding full state feedback design and the low gain approach makes the closed loop poles asymptotically insensitive to parameter errors

expanders and box spaces we consider box spaces of finitely generated residually finite groups g and try to distinguish them up to coarse equivalence we show that for n 2 the group sln z has a continuum of box spaces which are pairwise non coarsely equivalent expanders moreover varying the integer n 3 expanders given as box spaces of sln z are pairwise inequivalent similarly varying the prime p expanders given as box spaces of sl2 z p are pairwise inequivalent a strong form of non expansion for a box space is the existence of 0 1 such that the diameter of each component xn satisfies diam xn xn by bt15 the existence of such a box space implies that g virtually maps onto z we establish the converse for the lamplighter group z 2z z and for a semi direct product z 2 z such box spaces are explicitly constructed using specific congruence subgroups we finally introduce the full box space of g i e the coarse disjoint union of all finite quotients of g we prove that the full box space of a group mapping onto the free group f2 is not coarsely equivalent to the full box space of an s arithmetic group satisfying the congruence subgroup property

discretization of riemannian manifolds applied to the hodge laplacian for kappa geq 0 and r 0 0 let bbb m n kappa r 0 be the set of all connected compact n dimensional riemannian manifolds such that k g leq kappa and inj m g geq r 0 we study the relation between the k rm th positive eigenvalue of the hodge laplacian on differential forms and the k rm th positive eigenvalue of the combinatorial laplacian associated to an open cover acting on v c ech cochains we show that for a fixed sufficiently small varepsilon 0 there exist positive constants c 1 and c 2 depending only on n kappa and varepsilon such that for any m in bbb m n kappa r 0 and for any varepsilon discretization x of m we have c 1 lambda k p x leq lambda k p m leq c 2 lambda k p x for any k leq k k depends on x moreover we find a lower bound for the spectrum of the combinatorial laplacian and a lower bound for the spectrum of the hodge laplacian

an energy based three dimensional segmentation approach for the quantitative interpretation of electron tomograms electron tomography allows for the determination of the three dimensional structures of cells and tissues at resolutions significantly higher than that which is possible with optical microscopy electron tomograms contain in principle vast amounts of information on the locations and architectures of large numbers of subcellular assemblies and organelles the development of reliable quantitative approaches for the analysis of features in tomograms is an important problem and a challenging prospect due to the low signal to noise ratios that are inherent to biological electron microscopic images this is in part a consequence of the tremendous complexity of biological specimens we report on a new method for the automated segmentation of hiv particles and selected cellular compartments in electron tomograms recorded from fixed plastic embedded sections derived from hiv infected human macrophages individual features in the tomogram are segmented using a novel robust algorithm that finds their boundaries as global minimal surfaces in a metric space defined by image features the optimization is carried out in a transformed spherical domain with the center an interior point of the particle of interest providing a proper setting for the fast and accurate minimization of the segmentation energy this method provides tools for the semi automated detection and statistical evaluation of hiv particles at different stages of assembly in the cells and presents opportunities for correlation with biochemical markers of hiv infection the segmentation algorithm developed here forms the basis of the automated analysis of electron tomograms and will be especially useful given the rapid increases in the rate of data acquisition it could also enable studies of much larger data sets such as those which might be obtained from the tomographic analysis of hiv infected cells from studies of large populations

the coarse baum connes conjecture for spaces which admit a uniform embedding into hilbert space corollary 1 2 let be a finitely generated group if as a metric space with a word length metric admits a uniform embedding into hilbert space and its classifying space b has the homotopy type of a finite cw complex then the strong novikov conjecture holds for i e the index map from k b to k c r is injective corollary 1 2 follows from theorem 1 1 and the descent principle 23 by index theory the strong novikov conjecture implies the novikov conjecture on the homotopy invariance of higher signatures cf 8 for an excellent

globally minimal surfaces by continuous maximal flows in this paper we address the computation of globally minimal curves and surfaces for image segmentation and stereo reconstruction we present a solution simulating a continuous maximal flow by a novel system of partial differential equations existing methods are either grid biased graph based methods or suboptimal active contours and surfaces the solution simulates the flow of an ideal fluid with isotropic velocity constraints velocity constraints are defined by a metric derived from image data an auxiliary potential function is introduced to create a system of partial differential equations it is proven that the algorithm produces a globally maximal continuous flow at convergence and that the globally minimal surface may be obtained trivially from the auxiliary potential the bias of minimal surface methods toward small objects is also addressed an efficient implementation is given for the flow simulation the globally minimal surface algorithm is applied to segmentation in 2d and 3d as well as to stereo matching results in 2d agree with an existing minimal contour algorithm for planar images results in 3d segmentation and stereo matching demonstrate that the new algorithm is robust and free from grid bias

robustness bound for receding horizon finite memory control lyapunov krasovskii approach this article presents a robustness bound rb of receding horizon finite memory control rhfmc kwon w h and han s 2004 receding horizon finite memory controls of output feedback controls for state space systems ieee transactions on automatic control 49 1905 1915 for continuous time state space systems with norm bounded uncertainties the proposed rb is easily obtained by solving a convex problem in terms of a linear matrix inequality we show through a numerical example that the rhfmc can guarantee the robust stabilisation for a larger class of uncertain systems than linear quadratic gaussian controls when some poles of closed loop systems are close to an imaginary axis in the complex plane

coarse non amenability and covers with small eigenvalues given a closed riemannian manifold m and a virtual epimorphism pi 1 m twoheadrightarrow mathbb f 2 of the fundamental group onto a free group of rank 2 we construct a tower of finite sheeted regular covers left m n right n 0 infty of m such that 1 mn 0 as n this is the first example of such a tower which is not obtainable up to uniform quasi isometry or even up to uniform coarse equivalence by the previously known methods where 1 m is supposed to surject onto an amenable group

isoperimetric control of the spectrum of a compact hypersurface upper bounds for the eigenvalues of the laplace beltrami operator on a hypersurface bounding a domain in some ambient riemannian manifold are given in terms of the isoperimetric ratio of the domain these results are applied to the extrinsic geometry of isometric embeddings

circular shortest path in images abstract shortest path algorithms have been used in a number of applications such as crack detection road or linear feature extraction in images there are applications where the starting and ending positions of the shortest path need to be constrained in this paper we present several new algorithms for the extraction of a circular shortest path in an image such that the starting and ending positions coincide the new algorithms we developed include multiple search algorithm image patching algorithm multiple backtracking algorithm the combination of image patching and multiple back tracking algorithm and approximate algorithm the typical running time of our circular shortest path extraction algorithm on a 256 256 image is about 0 3 s on a rather slow 85 mhz sun sparc computer a variety of real images for crack detection in borehole data and object boundary extraction have been tested and good results have been obtained

the constrained lyapunov problem and its application to robust output feedback stabilization given a dynamical system whose description includes time varying uncertain parameters it is often desirable to design an output feedback controller leading to asymptotic stability of a given equilibrium point when designing such a controller one may consider static i e memoryless or dynamic compensation in this paper we show that solvability of various output feedback design problems is implied by existence of a solution to a certain constrained lyapunov problem clp the clp can be stated in purely algebraic terms once the clp is described we provide necessary and sufficient conditions for its solution to exist subsequently we consider application of the clp to a number of robust stabilization problems involving static output feedback and observer based feedback

shortest paths algorithms we conduct an extensive computational study of shortest paths algorithms including some very recent algorithms we also suggest new algorithms motivated by the experimental results and prove inter

nearly singular filtering for uniform and non uniform rank linear continuous systems abstract the problem of the minimum variance stationary estimation of linear time invariant continuous systems is considered in the case where the norm of tho measurement white noise intensity approaches zero solutions in closed form are obtained for the kalman gain and the corresponding minimum error covariance matrix of the filtered estimate in terms of the noise intensity norm and the system transfer function matrix both uniform and non uniform rank systems are considered and for the first time a solution is obtained for the case where the infinite zeros of the system tond to infinity with multiple rates

robust stability and performance via fixed order dynamic compensation two robust control design problems are considered the robust stabilization problem in volves deterministically modeled bounded butunknown time varying parameter variations while the robust performance problem includes in addition a quadratic performance criterion averaged over stochastic disturbances and maximized over the admissible parameter variations for both problems the design goal is a fixed order i e reduced or full order dynamic strictly proper feedback compensator a sufficient condition for solving the robust stabilization problem is given by means of a quadratic lyapunov function parameterized by the compensator gains for the robust performance problem the lyapunov function provides an upper bound for the closed loop performance this leads to consideration of the auxiliary minimization problem minimize the performance bound over the class of fixed order controllers subject to the lyapunovofunction constraint necessary conditions for optimality in the auxiliary problem thus serve as sufficient conditions for robust stability and performance in the original problem two particular bounds are considered for constructing the quadratic lyapunov function the first corresponds to a right shift multi plicative white noise model while the second was suggested by recent work of petersen and hollot the main result is an extended version ofthe optimal projection equations for fixed order dynamic compensation whose solutions are guaranteed to provide both robust stability and robust performance

what shape are dolphins building 3d morphable models from 2d images 3d morphable models are low dimensional parameterizations of 3d object classes which provide a powerful means of associating 3d geometry to 2d images however morphable models are currently generated from 3d scans so for general object classes such as animals they are economically and practically infeasible we show that given a small amount of user interaction little more than that required to build a conventional morphable model there is enough information in a collection of 2d pictures of certain object classes to generate a full 3d morphable model even in the absence of surface texture the key restriction is that the object class should not be strongly articulated and that a very rough rigid model should be provided as an initial estimate of the mean shape the model representation is a linear combination of subdivision surfaces which we fit to image silhouettes and any identifiable key points using a novel combined continuous discrete optimization strategy results are demonstrated on several natural object classes and show that models of rather high quality can be obtained from this limited information

on the recovery procedure for lqg systems abstract the loop transfer function recovery ltr procedure of doyle and stein 1979 ieee trans aut control ac 24 607 611 is re examined in the context of singular measurement lqg systems using existing closed form expressions for singular optimal estimation an alternative proof of the ltr is presented some of the structural properties of the ltr are obtained naturally using this approach it is shown that in the limit the control effort becomes infinite and therefore the critical tradeoff is between control effort and robustness

new prospects in line detection by dynamic programming the detection of lines in satellite images has drawn a lot of attention within the last 15 years problems of resolution noise and image understanding are involved and one of the best methods developed so far is the f algorithm of fischler which achieves robustness rightness and rapidity like other methods of dynamic programming it consists of defining a cost which depends on local information then a summation minimization process in the image is performed the authors present herein a mathematical formalization of the f algorithm which allows them to extend the cost both to cliques of more than two points to deal with the contrast and to neighborhoods of size larger than one to take into account the curvature thus all the needed information contrast grey level curvature is synthesized in a unique cost function defined on the digital original image this cost is used to detect roads and valleys in satellite images spot

ends of locally symmetric spaces with maximal bottom spectrum let x be a symmetric space of non compact type and gnx a locally sym metric space then the bottom spectrum l1 gnx satisfies the inequality l1 gnx e l1 x we show that if equality l1 gnx l1 x holds then gnx has either one end which is necessarily of infinite volume or two ends one of infinite volume and another of finite vol ume in the latter case gnx is isometric to r 1 n endowed with a multi warped metric where n is compact

circular shortest paths by branch and bound shortest path algorithms are used for a large variety of optimisation problems in network and transportation analysis they are also used in image analysis for object segmentation disparity estimation path finding and crack detection sometimes the topology of the problem demands that the path be circular such circular path constraints occur in polar object segmentation disparity estimation for panoramic stereo images and in shortest paths around a cylinder in this paper we present a new efficient algorithm for circular shortest path determination on a u by v trellis in o u 1 6 v average time we impose a binary search tree on the set of path endpoints and use a best first branch and bound search technique to efficiently obtain the global minimum circular path the typical running time of our circular shortest path algorithm on a 256 times 256 image is in the order of 0 1 seconds on a 1ghz dell p3 workstation under the linux operating system applications to crack detection and object segmentation are presented

on the robustness of meop design versus asymptotic lqg synthesis an analysis is presented of generalized lqg linear quadratic gaussian type algorithms with regard to robustness characteristics comparisons are made of the maximum entropy optimal projection meop methodology versus the linear quadratic gaussian with loop transfer recovery lqg ltr technique and the parametric robust linear quadratic gaussian synthesis procedure the performance of a reduced order direct controller design is compared with the full order designs on a example representative of typical flexible structure dynamics

the first eigenvalue in a tower of coverings soit m une variete de riemann compacte et soit m i une famille d espaces de recouvrement riemanniens finis de m soit 1 m i la premiere valeur propre du laplacien sur m i on cherche l existence d une suite de i ou 1 m i est borne inferieurement

on the stability robustness of the continuous time lqg optimal control the robustness properties of the lqg optimal controller that is obtained by the asymptotic recovery method are discussed it is shown that in spite of the good recovered stability margins the resulting closed loop design is inherently unrobust in the sense that small parameter variations in the plant and or small realization errors in the controller may lead to an instantaneous instability of the design

robust static and dynamic output feedback stabilization deterministic and stochastic perspectives three parallel gaps in robust feedback control theory are examined sufficiency versus necessity deterministic versus stochastic uncertainty modeling and stability versus performance deterministic and stochastic output feedback control problems are considered with both static and dynamic controllers the static and dynamic robust stabilization problems involve deterministically modeled bounded but unknown measurable time varying parameter variations while the static and dynamic stochastic optimal control problems feature state control and measurement dependent white noise general sufficiency conditions for the deterministic problems are obtained using lyapunov s direct method while necessary conditions for the stochastic problems are derived as a consequence of minimizing a quadratic performance criterion the sufficiency tests are then applied to the necessary conditions to determine when solutions of the stochastic optimization problems also solve the deterministic robust stability problems as an additional application of the deterministic result the modified riccati equation approach of petersen and hollot is generalized in the static case and extended to dynamic compensation

modeling of parameter variations and asymptotic lqg synthesis conventional approaches in modern robustness and sensitivity theory are not adequate for the problems associated with parameter variation since the structure of parameter variations cannot be modeled properly or included in the synthesis procedure a new modeling technique is proposed to handle a class of structured plant uncertainties in a direct way the key is to treat deterministic parameter variations as an internal feedback loop so that the structure of parameter variations is embedded in its model an asymptotic lqg design synthesis based on this modeling method is also presented an important relationship between the structure of plant uncertainties and the lqg weighting matrices is obtained this relationship clearly specifies the kind of parameter variations allowable for the lqg ltr method