the image foresting transform theory algorithms and applications the image foresting transform ift is a graph based approach to the design of image processing operators based on connectivity it naturally leads to correct and efficient implementations and to a better understanding of how different operators relate to each other we give here a precise definition of the ift and a procedure to compute it a generalization of dijkstra s algorithm with a proof of correctness we also discuss implementation issues and illustrate the use of the ift in a few applications

new algorithms for unconstrained nonlinear optimal control problems a family of new first order algorithms for solving continuous time optimal control problems is presented the algorithms make use of the riccati matrix differential equation and are capable of solving the linear quadratic problem in one step the paper includes an analysis of the convergence of the proposed algorithms in the space of relaxed controls as well as the proof of the reduction of the cost functional at each iteration and numerical examples

fast joint estimation of silhouettes and dense 3d geometry from multiple images we propose a probabilistic formulation of joint silhouette extraction and 3d reconstruction given a series of calibrated 2d images instead of segmenting each image separately in order to construct a 3d surface consistent with the estimated silhouettes we compute the most probable 3d shape that gives rise to the observed color information the probabilistic framework based on bayesian inference enables robust 3d reconstruction by optimally taking into account the contribution of all views we solve the arising maximum a posteriori shape inference in a globally optimal manner by convex relaxation techniques in a spatially continuous representation for an interactively provided user input in the form of scribbles specifying foreground and background regions we build corresponding color distributions as multivariate gaussians and find a volume occupancy that best fits to this data in a variational sense compared to classical methods for silhouette based multiview reconstruction the proposed approach does not depend on initialization and enjoys significant resilience to violations of the model assumptions due to background clutter specular reflections and camera sensor perturbations in experiments on several real world data sets we show that exploiting a silhouette coherency criterion in a multiview setting allows for dramatic improvements of silhouette quality over independent 2d segmentations without any significant increase of computational efforts this results in more accurate visual hull estimation needed by a multitude of image based modeling approaches we made use of recent advances in parallel computing with a gpu implementation of the proposed method generating reconstructions on volume grids of more than 20 million voxels in up to 4 41 seconds

optimal surface segmentation in volumetric images a graph theoretic approach efficient segmentation of globally optimal surfaces representing object boundaries in volumetric data sets is important and challenging in many medical image analysis applications we have developed an optimal surface detection method capable of simultaneously detecting multiple interacting surfaces in which the optimality is controlled by the cost functions designed for individual surfaces and by several geometric constraints defining the surface smoothness and interrelations the method solves the surface segmentation problem by transforming it into computing a minimum s hbox t cut in a derived arc weighted directed graph the proposed algorithm has a low order polynomial time complexity and is computationally efficient it has been extensively validated on more than 300 computer synthetic volumetric images 72 ct scanned data sets of different sized plexiglas tubes and tens of medical images spanning various imaging modalities in all cases the approach yielded highly accurate results our approach can be readily extended to higher dimensional image segmentation

reduced order multiple tuned mass damper optimization a bounded real lemma for descriptor systems approach abstract this paper presents a novel technique for multiple tuned mass damper optimization based on the dissipativity inequalities for a class of descriptor systems under the assumptions of regularity asymptotic stability and index one property of the descriptor system representing the structure with tuned mass dampers optimization criterion is defined in terms of h norm of the system in doing so special structure of the system matrices is utilized to eliminate some of the optimization variables to overcome its high computational cost and make it applicable for optimization of large scale structures a novel reduced order optimization algorithm is proposed unlike the existing approaches the presented optimization framework does not impose restrictions regarding regularity and constantness of the mass matrix and consequently allows simultaneous optimization of mass damping and stiffness matrices numerical examples which clearly illustrate the applicability and effectiveness of the proposed optimization procedure as well as the comparison with other methods are presented

partitions of a simplex leading to accurate spectral finite volume reconstruction in this paper we present several systematic techniques based on the voronoi diagram and its variants to partition a one and two dimensional simplex the fekete points are used as input to generate the voronoi diagram as they concentrate near the edges and are almost optimal for polynomial interpolation in a simplex spectral finite volume reconstructions on the resultant partitions have small lebesgue constants when using the dubiner basis the reconstruction matrix is well conditioned moreover the total number of edges of the partitions the total work when being used in spectral volume methods is shown to be at most twice the minimum number of edges of all partitions for reconstructions of the same order accuracy these suggest that the obtained partitions are well suited for spectral volume methods and other numerical methods which rely on reconstructions from cell averages

optimality approximation and complexity in set membership h sub spl infin identification investigates the set membership identification of time invariant discrete time exponentially stable possibly infinite dimensional linear systems from time or frequency domain data corrupted by deterministic noise the aim is to deliver not a single model but a set of models whose size in h sub spl infin norm measures the uncertainty in the identification the main focus of the note is on the optimality properties for finite data and on the tradeoff between optimality and complexity of approximated low order model sets a method is given for evaluating convergent and computationally efficient inner and outer approximations of the value set for a given frequency such approximations allow one to compute within any desired accuracy the identification error of any identified model and to evaluate an optimal model at any given number of frequencies by suitably approximating these values model sets with nominal models in rh sub spl infin are then derived whose order is selected by trading off between model set complexity and identification accuracy degradation this degradation is evaluated by computing the optimality level defined as the ratio between the reduced model identification error and the optimal one a numerical example demonstrates the effectiveness of the presented results

comparison of optimization algorithms the measured convergence rates of several algorithms belonging to the class of 1 gradient methods in function space are compared the steepest descent conjugate gradient and quasi newton algorithms and the effect of different types of linear search routine and initial guess parameters on their convergence rates are considered it is concluded that conjugate gradient methods do offer significant advantages even for non linear system models and bounded controls

a linear time algorithm for computing exact euclidean distance transforms of binary images in arbitrary dimensions a sequential algorithm is presented for computing the exact euclidean distance transform dt of a k dimensional binary image in time linear in the total number of voxels n the algorithm which is based on dimensionality reduction and partial voronoi diagram construction can be used for computing the dt for a wide class of distance functions including the l sub p and chamfer metrics at each dimension level the dt is computed by constructing the intersection of the voronoi diagram whose sites are the feature voxels with each row of the image this construction is performed efficiently by using the dt in the next lower dimension the correctness and linear time complexity are demonstrated analytically and verified experimentally the algorithm may be of practical value since it is relatively simple and easy to implement and it is relatively fast not only does it run in o n time but the time constant is small a simple modification of the algorithm computes the weighted euclidean dt which is useful for images with anisotropic voxel dimensions a parallel version of the algorithm runs in o n p time with p processors

space time tradeoffs for emptiness queries we develop the first nontrivial lower bounds on the complexity of online hyperplane and halfspace emptiness queries our lower bounds apply to a general class of geometric range query data structures called partition graphs informally a partition graph is a directed acyclic graph that describes a recursive decomposition of space we show that any partition graph that supports hyperplane emptiness queries implicitly defines a halfspace range query data structure in the fredman yao semigroup arithmetic model with the same asymptotic space and time bounds thus results of bronnimann chazelle and pach imply that any partition graph of size s that supports hyperplane emptiness queries in time t satisfies the inequality st d omega n log n d d 1 d 1 using different techniques we improve previous lower bounds for hopcroft s problem given a set of points and hyperplanes does any hyperplane contain a point in dimensions four and higher using this offline result we show that for online hyperplane emptiness queries omega n d mbox polylog n space is required to achieve polylogarithmic query time and omega n d 1 d mbox polylog n query time is required if only o n polylog n space is available these two lower bounds are optimal up to polylogarithmic factors for two dimensional queries we obtain an optimal continuous tradeoff st 2 omega n 2 between these two extremes finally using a lifting argument we show that the same lower bounds hold for both offline and online halfspace emptiness queries in mathbb r d d 3 2

geodesic matting a framework for fast interactive image and video segmentation and matting an interactive framework for soft segmentation and matting of natural images and videos is presented in this paper the proposed technique is based on the optimal linear time computation of weighted geodesic distances to user provided scribbles from which the whole data is automatically segmented the weights are based on spatial and or temporal gradients considering the statistics of the pixels scribbled by the user without explicit optical flow or any advanced and often computationally expensive feature detectors these could be naturally added to the proposed framework as well if desired in the form of weights in the geodesic distances an automatic localized refinement step follows this fast segmentation in order to further improve the results and accurately compute the corresponding matte function additional constraints into the distance definition permit to efficiently handle occlusions such as people or objects crossing each other in a video sequence the presentation of the framework is complemented with numerous and diverse examples including extraction of moving foreground from dynamic background in video natural and 3d medical images and comparisons with the recent literature

efficient euclidean distance transform algorithm of binary images in arbitrary dimensions in this paper we propose an efficient algorithm i e pbedt for short to compute the exact euclidean distance transform edt of a binary image in arbitrary dimensions the pbedt is based on independent scan and implemented in a recursive way i e the edt of a d dimensional image is able to be computed from the edts of its d 1 dimensional sub images in each recursion all of the rows in the current dimensional direction are processed one by one the points in the current processing row and their closest feature points in d 1 dimensional sub images can be shown in a euclidean plane by using the geometric properties of the perpendicular bisector the closest feature points of d 1 dimensional sub images are easily verified so as to lead to the edt of a d dimensional image after eliminating the invalid points the time complexity of the pbedt algorithm is linear in the amount of both image points and dimensions with a small coefficient compared with the state of the art edt algorithms the pbedt algorithm is much faster and more stable in most cases

compensator design for stability enhancement with collocated controllers a continuum model rather than a finite element model is used the optimal compensator design is formulated as a stochastic regulator problem and is shown to be solvable by the general infinite dimensional theory developed by the author despite the lack of exponential stabilizability infinite dimensional steady state riccati equations characterizing the feedback control gain and the kalman filter gain operators can be solved explicitly the associated performance indexes including the mean square control effort are calculated in closed form as a first approximation the compensator transfer function can be realized as a bank of bandpass filters in parallel centered at the undamped mode frequencies numerical calculations for the gain and bandwidths for a typical configuration are presented the performance of the compensator is evaluated when in fact in the true model there is no actuator noise the theoretical problem involved is to show that the infinite dimensional stochastic process is asymptotically stationary it is possible to calculate the steady state covariance in closed form and thereby calculate performance indexes of interest explicitly facilitating the choice of optimal design parameters

multiscale skeletons by image foresting transform and its application to neuromorphometry abstract the image foresting transform ift reduces optimal image partition problems based on seed pixels to a shortest path forest problem in a graph whose solution can be obtained in linear time such a strategy has allowed a unified and efficient approach to the design of image processing operators such as edge tracking region growing watershed transforms distance transforms and connected filters this paper presents a fast and simple method based on the ift to compute multiscale skeletons and shape reconstructions without border shifting the method also generates one pixel wide connected skeletons and the skeleton by influence zones simultaneously for objects of arbitrary topologies the results of the work are illustrated with respect to skeleton quality execution time and its application to neuromorphometry

computation of optimal feedforward and feedback control by a modified reduced gradient method a computational scheme for solving problems of optimal open loop control policy and optimal state feedback control was introduced the problems were first converted into a nonlinear programming problem the conjugate reduced gradient method was then applied to find the minimum solution the sensitivity matrices of the state trajectories with respect to the coefficients of control variables could be recursively calculated so that the reduced gradients could be easily evaluated in this computational algorithm the h orthogonal property for linear optimal control problems was demonstrated such that the global minimum solution of such problems was thus achieved in finite iterations using this algorithm the computational strategy was easily and efficiently extended to determine the optimal state feedback gain matrices

polygon based contact resolution for superquadrics the representation of discrete objects in the discrete element modelling is a fundamental issue which has a direct impact on the efficiency of discrete element implementation and the dynamic behaviour of particulate systems disks and spheres are the most commonly used geometric shapes due to their geometric simplicity and computational efficiency but they are unable to provide resistance to rolling motion for this reason some non circular spherical objects such as polygons polyhedrons superquadrics or the clustering of disks spheres to form irregular shapes are introduced when superquadrics are used as discrete elements the bottleneck of contact resolution is associated with the searching for intersections of two non linear functions which is a very expensive operation and may sometimes fail in finding the solution in this work an efficient and robust algorithm is proposed for contact resolution of 2d superquadrics in which any superquadric is approximated with a convex polygon through adaptive sampling then by clipping two polygons an efficient linear algorithm is performed to search for intersections and overlap area of the polygons the contact forces and directions are determined by employing a newly established corner corner contact model it is important to highlight that the proposed methodology can also be extended to general non circular discrete object cases the performance of the algorithm is demonstrated via numerical examples copyright 2005 john wiley sons ltd

paper low order control design for lmi problems using alternating projection methods computational techniques based on alternating projections are proposed to solve control design problems described by linear matrix inequalities lmis in particular we concentrate on the stabilization and the suboptimal h output feedback control design problems these problems can be described by a pair of lmis and an additional coupling condition this coupling condition is convex for the full order control design problem but convexity is lost for the control problem of order strictly less than the plant order we formulate these problems as feasibility problems with matrix constraint sets of simple geometry and we utilize this geometry to obtain analytical expressions for the orthogonal projection operators onto these sets full order and low order controllers are designed using alternating projection methods for the full order controller case global convergence of the alternating projection methods to a feasible solution is guaranteed however for the low order control case only local convergence is guaranteed an example is provided to illustrate the use of these methods for the full order and the low order controller design

oriented image foresting transform segmentation by seed competition seed based methods for region based image segmentation are known to provide satisfactory results for several applications being usually easy to extend to multidimensional images however while boundary based methods like live wire can easily incorporate a preferred boundary orientation region based methods are usually conceived for undirected graphs and do not resolve well between boundaries with opposite orientations this motivated researchers to investigate extensions for some region based frameworks seeking to better solve oriented transitions in this same spirit we discuss how to incorporate this orientation information in a region based approach called ift segmentation by seed competition by exploring digraphs we give direct proof for the optimality of the proposed extensions in terms of energy functions associated with the cuts to stress these theoretical results we also present an experimental evaluation that shows the obtained gains in accuracy for some 2d and 3d data sets of medical images

damping parameter design optimization in structural systems using an explicit h norm bound abstract this paper examines the damping parameter design optimization problem for structural systems with collocated measurements and inputs so that h norm bound constraints are satisfied we utilize a particular solution of the bounded real lemma that provides an explicit upper bound on the h norm of a collocated structural system using this upper bound result the damping design is formulated as a linear matrix inequality lmi optimization problem with respect to the damping coefficients of the structural system the formulation is particularly useful for large scale structural systems where existing methods are computationally prohibitive numerical examples demonstrate the benefits and computational advantages of the proposed damping parameter design method

a scale based connected coherence tree algorithm for image segmentation this paper presents a connected coherence tree algorithm ccta for image segmentation with no prior knowledge it aims to find regions of semantic coherence based on the proposed epsiv neighbor coherence segmentation criterion more specifically with an adaptive spatial scale and an appropriate intensity difference scale ccta often achieves several sets of coherent neighboring pixels which maximize the probability of being a single image content including kinds of complex backgrounds in practice each set of coherent neighboring pixels corresponds to a coherence class cc the fact that each cc just contains a single equivalence class ec ensures the separability of an arbitrary image theoretically in addition the resultant ccs are represented by tree based data structures named connected coherence tree cct s in this sense ccta is a graph based image analysis algorithm which expresses three advantages 1 its fundamental idea epsiv neighbor coherence segmentation criterion is easy to interpret and comprehend 2 it is efficient due to a linear computational complexity in the number of image pixels 3 both subjective comparisons and objective evaluation have shown that it is effective for the tasks of semantic object segmentation and figure ground separation in a wide variety of images those images either contain tiny long and thin objects or are severely degraded by noise uneven lighting occlusion poor illumination and shadow

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

riverbed a novel user steered image segmentation method based on optimum boundary tracking this paper presents an optimum user steered boundary tracking approach for image segmentation which simulates the behavior of water flowing through a riverbed the riverbed approach was devised using the image foresting transform with a never exploited connectivity function we analyze its properties in the derived image graphs and discuss its theoretical relation with other popular methods such as live wire and graph cuts several experiments show that riverbed can significantly reduce the number of user interactions anchor points as compared to live wire for objects with complex shapes this paper also includes a discussion about how to combine different methods in order to take advantage of their complementary strengths

hybrid approaches for interactive image segmentation using the live markers paradigm interactive image segmentation methods normally rely on cues about the foreground imposed by the user as region constraints markers brush strokes or boundary constraints anchor points these paradigms often have complementary strengths and weaknesses which can be addressed to improve the interactive experience by reducing the user s effort we propose a novel hybrid paradigm based on a new form of interaction called live markers where optimum boundary tracking segments are turned into internal and external markers for region based delineation to effectively extract the object we present four techniques within this paradigm 1 livemarkers 2 rivercut 3 livecut and 4 rivermarkers the homonym livemarkers couples boundary tracking via live wire on the fly lwof with optimum seed competition by the image foresting transform ift sc the ift sc can cope with complex object silhouettes but presents a leaking problem on weaker parts of the boundary that is solved by the effective live markers produced by lwof conversely in rivercut the long boundary segments computed by riverbed around complex shapes provide markers for graph cuts by the min cut max flow algorithm gcmf to complete segmentation on poorly defined sections of the object s border livecut and rivermarkers further demonstrate that live markers can improve segmentation even when the combined approaches are not complementary e g gcmfs shrinking bias is also dramatically prevented when using it with lwof more over since delineation is always region based our methodology subsumes both paradigms representing a new way of extending boundary tracking to the 3d image domain while speeding up the addition of markers close to the object s boundary a necessary but time consuming task when done manually we justify our claims through an extensive experimental evaluation on natural and medical images data sets using recently proposed robot users for boundary tracking methods

a graph based approach for multiscale shape analysis abstract this paper presents two shape descriptors multiscale fractal dimension and contour saliences using a graph based approach the image foresting transform it introduces a robust approach to locate contour saliences from the relation between contour and skeleton the contour salience descriptor consists of a vector with salience location and value along the contour and a matching algorithm we compare both descriptors with fractal dimension fourier descriptors moment invariants curvature scale space and beam angle statistics regarding to their invariance to object characteristics that belong to a same class compact ability and to their ability to separate objects of distinct classes separability

convex analysis of output feedback control problems robust stability and performance this paper addresses the problem of optimal h sub 2 control by output feedback necessary and sufficient conditions on the existence of a linear stabilizing output feedback gain are provided in terms of the intersection of a convex set and a set defined by a nonlinear real valued function the results can be easily extended to deal with linear uncertain systems where uncertainties are supposed to belong to convex bounded domains providing an h sub 2 guaranteed cost output feedback control thanks to the properties of the above mentioned function we show that under certain conditions convex programming tools can be used for numerical purposes examples illustrate the theoretical results

the hamiltonian properties of supergrid graphs in this paper we first introduce a novel class of graphs namely supergrid supergrid graphs include grid graphs and triangular grid graphs as their subgraphs the hamiltonian cycle and path problems for grid graphs and triangular grid graphs were known to be np complete however they are unknown for supergrid graphs the hamiltonian cycle path problem on supergrid graphs can be applied to control the stitching traces of computerized sewing machines in this paper we will prove that the hamiltonian cycle problem for supergrid graphs is np complete it is easily derived from the hamiltonian cycle result that the hamiltonian path problem on supergrid graphs is also np complete we then show that two subclasses of supergrid graphs including rectangular parallelism and alphabet always contain hamiltonian cycles

watershed cuts thinnings shortest path forests and topological watersheds we recently introduced watershed cuts a notion of watershed in edge weighted graphs in this paper our main contribution is a thinning paradigm from which we derive three algorithmic watershed cut strategies the first one is well suited to parallel implementations the second one leads to a flexible linear time sequential implementation whereas the third one links the watershed cuts and the popular flooding algorithms we state that watershed cuts preserve a notion of contrast called connection value on which several morphological region merging methods are implicitly based we also establish the links and differences between watershed cuts minimum spanning forests shortest path forests and topological watersheds finally we present illustrations of the proposed framework to the segmentation of artwork surfaces and diffusion tensor images

icp registration using invariant features investigates the use of euclidean invariant features in a generalization of iterative closest point icp registration of range images pointwise correspondences are chosen as the closest point with respect to a weighted linear combination of positional and feature distances it is shown that under ideal noise free conditions correspondences formed using this distance function are correct more often than correspondences formed using the positional distance alone in addition monotonic convergence to at least a local minimum is shown to hold for this method when noise is present a method that automatically sets the optimal relative contribution of features and positions is described this method trades off the error in feature values due to noise against the error in positions due to misalignment experimental results suggest that using invariant features decreases the probability of being trapped in a local minimum and may be an effective solution for difficult range image registration problems where the scene is very small compared to the model

power watershed a unifying graph based optimization framework in this work we extend a common framework for graph based image segmentation that includes the graph cuts random walker and shortest path optimization algorithms viewing an image as a weighted graph these algorithms can be expressed by means of a common energy function with differing choices of a parameter q acting as an exponent on the differences between neighboring nodes introducing a new parameter p that fixes a power for the edge weights allows us to also include the optimal spanning forest algorithm for watershed in this same framework we then propose a new family of segmentation algorithms that fixes p to produce an optimal spanning forest but varies the power q beyond the usual watershed algorithm which we term the power watershed in particular when q 2 the power watershed leads to a multilabel scale and contrast invariant unique global optimum obtained in practice in quasi linear time placing the watershed algorithm in this energy minimization framework also opens new possibilities for using unary terms in traditional watershed segmentation and using watershed to optimize more general models of use in applications beyond image segmentation

structure of a simple scheduling polyhedron in a one machine nonpreemptive scheduling problem the feasible schedules may be defined by the vector of the corresponding job completion times for given positive processing times the associated simple scheduling polyhedronp is the convex hull of these feasible completion time vectors the main result of this paper is a complete description of the minimal linear system definingp we also give a complete combinatorial description of the face lattice ofp and a simple o n logn separation algorithm this algorithm has potential usefulness in cutting plane type algorithms for more difficult scheduling problems

directed connected operators asymmetric hierarchies for image filtering and segmentation connected operators provide well established solutions for digital image processing typically in conjunction with hierarchical schemes in graph based frameworks such operators basically rely on symmetric adjacency relations between pixels in this article we introduce a notion of directed connected operators for hierarchical image processing by also considering non symmetric adjacency relations the induced image representation models are no longer partition hierarchies i e trees but directed acyclic graphs that generalize standard morphological tree structures such as component trees binary partition trees or hierarchical watersheds we describe how to efficiently build and handle these richer data structures and we illustrate the versatility of the proposed framework in image filtering and image 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

all controllers for the general h control problem lmi existence conditions and state space formulas this paper presents all controllers for the general h control problem with no assumptions on the plant matrices necessary and sufficient conditions for the existence of an h controller of any order are given in terms of three linear matrix inequalities lmis our existence conditions are equivalent to scherer s results but with a more elementary derivation furthermore we provide the set of all h controllers explicitly parametrized in the state space using the positive definite solutions to the lmis even under standard assumptions full rank etc our controller parametrization has an advantage over the q parametrization the freedom q a real rational stable transfer matrix with the h norm bounded above by a specified number is replaced by a constant matrix l of fixed dimension with a norm bound and the solutions x y to the lmis the inequality formulation converts the existence conditions to a convex feasibility problem and also the free matrix l and the pair x y define a finite dimensional design space as opposed to the infinite dimensional space associated with the q parametrization

voronoi diagram and medial axis algorithm for planar domains with curved boundaries i theoretical foundations in this first installment of a two part paper the underlying theory for an algorithm that computes the voronoi diagram and medial axis of a planar domain bounded by free form polynomial or rational curve segments is presented an incremental approach to computing the voronoi diagram is used wherein a single boundary segment is added to an existing boundary segment set at each step the introduction of each new segment entails modifying the voronoi regions of the existing boundary segments and constructing the voronoi region of the new segment we accomplish this by i computing the bisector of the new segment with each of the current boundary segments ii updating the voronoi regions of the current boundary segments by partitioning them with these bisectors and iii constructing the voronoi region of the new segment as a union of regions obtained from the partitioning in ii when all boundary segments are included and their voronoi regions have been constructed the voronoi diagram of the boundary is obtained as the union of the voronoi polygons for each boundary segment to construct the medial axis of a planar domain we first compute the voronoi diagram of its boundary the medial axis is then obtained from the voronoi diagram by i removing certain edges of the voronoi diagram that do not belong to the medial axis and ii adding certain edges that do belong to the medial axis but are absent from the voronoi diagram unambiguous characterizations for edges in both these categories are given details of algorithms based on this theory are deferred to the second installment of this two part paper

surface bounded growth modeling applied to human mandibles from a set of longitudinal three dimensional scans of the same anatomical structure the authors have accurately modeled the temporal shape and size changes using a linear shape model on a total of 31 computed tomography scans of the mandible from six patients 14 851 semilandmarks are found automatically using shape features and a new algorithm called geometry constrained diffusion the semilandmarks are mapped into procrustes space principal component analysis extracts a one dimensional subspace which is used to construct a linear growth model the worst case mean modeling error in a cross validation study is 3 7 mm

morphological grayscale reconstruction in image analysis applications and efficient algorithms two different formal definitions of gray scale reconstruction are presented the use of gray scale reconstruction in various image processing applications discussed to illustrate the usefulness of this transformation for image filtering and segmentation tasks the standard parallel and sequential approaches to reconstruction are reviewed it is shown that their common drawback is their inefficiency on conventional computers to improve this situation an algorithm that is based on the notion of regional maxima and makes use of breadth first image scannings implemented using a queue of pixels is introduced its combination with the sequential technique results in a hybrid gray scale reconstruction algorithm which is an order of magnitude faster than any previously known algorithm

computational geometry an introduction from the reviews this book offers a coherent treatment at the graduate textbook level of the field that has come to be known in the last decade or so as computational geometry the book is well organized and lucidly written a timely contribution by two founders of the field it clearly demonstrates that computational geometry in the plane is now a fairly well understood branch of computer science and mathematics it also points the way to the solution of the more challenging problems in dimensions higher than two

a graph based framework for sub pixel image segmentation many image segmentation methods utilize graph structures for representing images where the flexibility and generality of the abstract structure is beneficial by using a fuzzy object representation i e allowing partial belongingness of elements to image objects the unavoidable loss of information when representing continuous structures by finite sets is significantly reduced enabling feature estimates with sub pixel precision this work presents a framework for object representation based on fuzzy segmented graphs interpreting the edges as one dimensional paths between the vertices of a graph we extend the notion of a graph cut to that of a located cut i e a cut with sub edge precision we describe a method for computing a located cut from a fuzzy segmentation of graph vertices further the notion of vertex coverage segmentation is proposed as a graph theoretic equivalent to pixel coverage segmentations and a method for computing such a segmentation from a located cut is given utilizing the proposed framework we demonstrate improved precision of area measurements of synthetic two dimensional objects we emphasize that although the experiments presented here are performed on two dimensional images the proposed framework is defined for general graphs and thus applicable to images of any dimension

geometric classification of triangulations and their enumeration in a convex polygon abstract triangulation of polygons is a classical problem in computational geometry for an arbitrary polygon the triangulation may depend on its shape in this paper we describe a new geometric classification of triangulations of a convex polygon and then derive expressions for counting the number of nonisomorphic triangulations in each class

reduction of bivariate polynomials from convex dense to dense with application to factorizations in this article we present a new algorithm for reducing the usual sparse bivariate factorization problems to the dense case this reduction simply consists in computing an invertible monomial transformation that produces a polynomial with a dense size of the same order of magnitude as the size of the integral convex hull of the support of the input polynomial this approach turns out to be very efficient in practice as demonstrated with our implementation

image segmentation by iterated region merging with localized graph cuts this paper presents an iterated region merging based graph cuts algorithm which is a novel extension of the standard graph cuts algorithm graph cuts addresses segmentation in an optimization framework and finds a globally optimal solution to a wide class of energy functions however the extraction of objects in a complex background often requires a lot of user interaction the proposed algorithm starts from the user labeled sub graph and works iteratively to label the surrounding un segmented regions in each iteration only the local neighboring regions to the labeled regions are involved in the optimization so that much interference from the far unknown regions can be significantly reduced meanwhile the data models of the object and background are updated iteratively based on high confident labeled regions the sub graph requires less user guidance for segmentation and thus better results can be obtained under the same amount of user interaction experiments on benchmark datasets validated that our method yields much better segmentation results than the standard graph cuts and the grabcut methods in either qualitative or quantitative evaluation

natural image segmentation based on tree equipartition bayesian flooding and region merging we propose a general purpose image segmentation framework which involves feature extraction and classification in feature space followed by flooding and merging in spatial domain region growing is based on the computed local measurements and distances from the distribution of features describing the different classes using the properties of the label dependent distances spatial coherence is ensured since the image features are described globally the distribution of the features for the different classes are obtained by block wise unsupervised clustering based on the construction of the minimum spanning tree of the blocks grid using the mallows distance and the equipartition of the resulting tree the final clustering is obtained by using the k centroids algorithm with high probability and under topological constraints connected components of the maximum likelihood classification map are used to compute a map of initially labelled pixels an efficient flooding algorithm is introduced namely priority multi class flooding algorithm pmcfa that assign pixels to labels using bayesian dissimilarity criteria a new region merging method which incorporates boundary information is introduced for obtaining the final segmentation map therefore the merging stage is based on region features and edge localization segmentation results on the berkeley benchmark data set demonstrate the effectiveness of the proposed methods

an efficient uniform cost algorithm applied to distance transforms the uniform cost algorithm is a special case of the a algorithm for finding the shortest paths in graphs in the uniform cost algorithm nodes are expanded in order of increasing cost an efficient version of this algorithm is developed for integer cost values nodes are sorted by storing them at predefined places bucket sort keeping the overhead low the algorithm is applied to general distance transformation a constrained distance transform is an operation which calculates at each pixel of an image the distance to the nearest pixel of a reference set distance being defined as minimum path length the uniform cost algorithm in the constrained case proves to be the best solution for distance transformation it is fast the processing time is independent of the complexity of the image and memory requirements are moderate

model reduction for state space symmetric systems in this paper the model reduction problem for state space symmetric systems is investigated first it is shown that several model reduction methods such as balanced truncation balanced truncation which preserves the dc gain optimal and suboptimal hankel norm approximations inherit the state space symmetric property furthermore for single input and single output siso state space symmetric systems we prove that the h norm of its transfer functions can be calculated via two simple formulas moreover the siso state space symmetric systems are equivalent to systems with zeros interlacing the poles zip under mild conditions

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 fuzzy approach to visibility maps creation over digital terrains the construction of inter visibility models for a terrain is an important tool for environmental and animal studies efficient crisp algorithms are known to address this problem directly on a raster digital elevation map dem of the study area randomness plays an important role several factors like vegetation height of the observer presence of unmapped human artifacts etc cannot be modeled in advance into a traditional dem model we propose the use of fuzzy terrain models to incorporate uncertainty and unpredictable variability of the landscape accordingly we propose a suitable definition of visibility to obtain intervisibility models an algorithm that uses approximation of fuzzy numbers with a discrete family of intervals is proposed the proposed model produces sound results and can be extended to model complex situations like triangulating a radio source using two directional receivers all of these situations are difficult to manage with a precise stochastic model and are a frequent occurrence in animal behavior studies under field conditions the proposed techniques have been implemented inside a user friendly software package that may easily exchange data with the most common giss we report also some experimental results obtained using over artificial terrain under controlled noise and under sampling conditions

combination of piecewise geodesic paths for interactive segmentation minimum cost paths have been extensively studied theoretical tools for interactive image segmentation the existing geodesically linked active contour glac model which basically consists of a set of vertices connected by paths of minimal cost blends the benefits of minimal paths and region based active contours this results in a closed piecewise smooth curve over which an edge or region energy functional can be formulated as an important shortcoming the glac in its initial formulation does not guarantee the curve to be simple consistent with respect to the purpose of segmentation in this paper we draw our inspiration from the glac and other boundary based interactive segmentation algorithms in the sense that we aim to extract a contour given a set of user provided points by connecting these points using paths the key idea is to select a combination among a set of possible paths such that the resulting structure represents a relevant closed curve instead of considering minimal paths only we switch to a more general formulation which we refer to as admissible paths these basically correspond to the roads travelling along the bottom of distinct valleys between given endpoints we introduce a novel term to favor the simplicity of the generated contour as well as a local search method to choose the best combination among possible paths

watershed cuts minimum spanning forests and the drop of water principle we study the watersheds in edge weighted graphs we define the watershed cuts following the intuitive idea of drops of water flowing on a topographic surface we first establish the consistency of these watersheds they can be equivalently defined by their catchment basinsrdquo through a steepest descent property or by the dividing linesrdquo separating these catchment basins through the drop of water principle then we prove through an equivalence theorem their optimality in terms of minimum spanning forests afterward we introduce a linear time algorithm to compute them to the best of our knowledge similar properties are not verified in other frameworks and the proposed algorithm is the most efficient existing algorithm both in theory and in practice finally the defined concepts are illustrated in image segmentation leading to the conclusion that the proposed approach improves on the tested images the quality of watershed based segmentations

a local convergence proof for the minvar algorithm for computing continuous piecewise linear approximations the class of continuous piecewise linear pl functions represents a useful family of approximants because invertibility can be readily imposed and if a pl function is invertible then it can be inverted in closed form many applications arising for example in control systems and robotics involve the simultaneous construction of a forward and inverse system model from data most approximation techniques require that separate forward and inverse models be trained whereas an invertible continuous pl affords simultaneously the forward and inverse system model in a single representation the minvar algorithm computes a continuous pl approximation to data local convergence of minvar is proven for the case when the data generating function is itself a pl function and available directly rather than through data

state space solutions to standard h sub 2 and h sub infinity control problems simple state space formulas are derived for all controllers solving the following standard h sub infinity problem for a given number gamma 0 find all controllers such that the h sub infinity norm of the closed loop transfer function is strictly less than gamma it is known that a controller exists if and only if the unique stabilizing solutions to two algebraic riccati equations are positive definite and the spectral radius of their product is less than gamma sup 2 under these conditions a parameterization of all controllers solving the problem is given as a linear fractional transformation lft on a contractive stable free parameter the state dimension of the coefficient matrix for the lft constructed using the two riccati solutions equals that of the plant and has a separation structure reminiscent of classical lqg i e h sub 2 theory this paper is intended to be of tutorial value so a standard h sub 2 solution is developed in parallel

a second order algorithm for continuous time nonlinear optimal control problems a second order algorithm is presented for the solution of continuous time nonlinear optimal control problems the algorithm is an adaptation of the trust region modifications of newton s method and solves at each iteration a linear quadratic control problem with an additional constraint under some assumptions the proposed algorithm is shown to possess a global convergence property a numerical example is presented to illustrate the method

stabilization and h control of symmetric systems an explicit solution abstract in this paper we address the h control analysis the output feedback stabilization and the output feedback h control synthesis problems for state space symmetric systems using a particular solution of the bounded real lemma for an open loop symmetric system we obtain an explicit expression to compute the h norm of the system for the output feedback stabilization problem we obtain an explicit parametrization of all asymptotically stabilizing control gains of state space symmetric systems for the h control synthesis problem we derive an explicit expression for the optimally achievable closed loop h norm and the optimal control gains extension to robust and positive real control of such systems are also examined these results are obtained from the linear matrix inequality formulations of the stabilization and the h control synthesis problems using simple matrix algebraic tools