an algorithm for global minimization of linearly constrained concave quadratic functions we present an algorithm for the global minimization of a quadratic function x y xtqx htx dty over a polytope x y rn k ax by b x 0 y 0 where x h rn y d rk b rm and where a and b are m n and m k matrices respectively and q is an n n symmetric positive definite matrix we first consider the case where k 0 and construct a tight parallelpiped r containing by using an arbitrary set of q conjugate directions and by solving 2n linear programs we show that the convex envelope of with respect to r is linear and obtain an explicit formula for it we then describe a branch and bound algorithm in which the linearity of the convex envelope allows efficient lower bounding for the subproblems for each subproblem we obtain the linear convex envelope of over a smaller parallelepiped r with facets parallel to those of r then we obtain a lower bound by minimizing this convex envelope over r if is the optimal objective value for each e 0 the algorithm generates a sequence of feasible points zj with nonincreasing function values j and a nondecreasing sequence j of lower bounds to moreover if e 0 there exist j0 such that j j e for all j j0 and if e 0 j j converges to 0 the results are then generalized to the case where k is nonzero and possibly much larger than n preliminary computational results are also presented

domain contraction in nonlinear programming minimizing a quadratic concave objective over a polyhedron using linear underestimating approximations and their dual solutions we develop new results for the nonconvex problem of minimizing a quadratic concave function under linear constraints for solving this problem which has such important management applications as economies of scale fixed charge and quadratic assignment problems some results provide and tighten bounds on the global minimum value while others identify the domains of the variables which may be excluded from further consideration this leads to successive reduction of domains containing a global solution called domain contraction and ideally to a solution with the objective value within some acceptable error level for most results specific problem instances are provided to establish their use in theory in practice experience with solving the problems presented here indicates that a combination of the proposed domain contraction via linear underestimation and its dual information with the branch and bound approach offers a computa

image estimation using doubly stochastic gaussian random field models the two dimensional 2 d doubly stochastic gaussian dsg model was introduced by one of the authors to provide a complete model for spatial filters which adapt to the local structure in an image signal here we present the optimal estimator and 2 d fixed lag smoother for this dsg model extending earlier work of ackerson and fu as the optimal estimator has an exponentially growing state space we investigate suboptimal estimators using both a tree and a decision directed method experimental results are presented

nonlinear restoration of noisy images the restoration of images degraded by an additive white noise is performed by nonlinearly filtering a noisy image the standard wiener approach to this problem is modified to take into account the edge information of the image various filters of increasing complexity are derived experimental results are shown and compared to the standard wiener filter results and other earlier attempts involving nonstationary filters

markov and recursive least squares methods for the estimation of data with discontinuities an algorithm is presented for smoothing data piecewise modeled by linear equations within regions of a one dimensional or two dimensional field from measurements corrupted by additive noise its main feature is the combination of markov random field mrf models with recursive least squares rls techniques in order to estimate the model parameters within the regions applications to one dimensional and two dimensional data are given with particular emphasis on the segmentation of images with piecewise constant intensity levels

the interacting multiple model algorithm for systems with markovian switching coefficients an important problem in filtering for linear systems with markovian switching coefficients dynamic multiple model systems is the management of hypotheses which is necessary to limit the computational requirements a novel approach to hypotheses merging is presented for this problem the novelty lies in the timing of hypotheses merging when applied to the problem of filtering for a linear system with markovian coefficients the method is an elegant way to derive the interacting multiple model imm algorithm evaluation of the imm algorithm shows that it performs well at a relatively low computational load these results imply a significant change in the state of the art of approximate bayesian filtering for systems with markovian coefficients

scale based diffusive image filtering preserving boundary sharpness and fine structures image acquisition techniques often suffer from low signal to noise ratio snr and or contrast to noise ratio cnr although many acquisition techniques are available to minimize these post acquisition filtering is a major off line image processing technique commonly used to improve the snr and cnr a major drawback of filtering is that it often diffuses blurs important structures along with noise here the authors introduce two scale based filtering methods that use local structure size or object scale information to arrest smoothing around fine structures and across even low gradient boundaries the first of these methods uses a weighted average over a scale dependent neighborhood while the other employs scale dependent diffusion conductance to perform filtering both methods adaptively modify the degree of filtering at any image location depending on local object scale object scale allows the authors to accurately use a restricted homogeneity parameter for filtering in regions with fine details and in the vicinity of boundaries while a generous parameter in the interiors of homogeneous regions qualitative experiments based on both phantoms and patient magnetic resonance images show significant improvements using the scale based methods over the extant anisotropic diffusive filtering method in preserving fine details and sharpness of object boundaries quantitative analyses utilizing 25 phantom images generated under a range of conditions of blurring noise and background variation confirm the superiority of the new scale based approaches

technical note construction of difficult linearly constrained concave minimization problems given a polytope and an arbitrary subset of its vertices we show how to construct a differentiable concave function that assumes any arbitrary value within a specified e tolerance at each vertex of the subset with each vertex in the subset a strong local constrained minimum we also show how this construction method can be used to generate test problems for linearly constrained concave minimization algorithms

geodesic estimation for large deformation anatomical shape averaging and interpolation the goal of this research is to promote variational methods for anatomical averaging that operate within the space of the underlying image registration problem this approach is effective when using the large deformation viscous framework where linear averaging is not valid or in the elastic case the theory behind this novel atlas building algorithm is similar to the traditional pairwise registration problem but with single image forces replaced by average forces these group forces drive an average transport ordinary differential equation allowing one to estimate the geodesic that moves an image toward the mean shape configuration this model gives large deformation atlases that are optimal with respect to the shape manifold as defined by the data and the image registration assumptions we use the techniques in the large deformation context here but they also pertain to small deformation atlas construction furthermore a natural inherently inverse consistent image registration is gained for free as is a tool for constant arc length geodesic shape interpolation the geodesic atlas creation algorithm is quantitatively compared to the euclidean anatomical average to elucidate the need for optimized atlases the procedures generate improved average representations of highly variable anatomy from distinct populations

expectation maximization algorithms null spaces and map image restoration a computationally efficient easily implementable algorithm for map restoration of images degraded by blur and additive correlated gaussian noise using gibbs prior density functions is derived this algorithm is valid for a variety of complete data spaces the constraints upon the complete data space arising from the gaussian image formation model are analyzed and a motivation is provided for the choice of the complete data based upon the ease of computation of the resulting em algorithms the overlooked role of the null space of the blur operator in image restoration is introduced an examination of this role reveals an important drawback to the use of the simulated annealing algorithm in maximizing a specific class of functionals an alternative iterative method for computing the nullspace component of a vector is given the ability of a simple gibbs prior density function to enable partial recovery of the component of an image within the nullspace of the blur operator is demonstrated

dr tamas diffeomorphic registration for tensor accurate alignment of anatomical structures in this work we propose dr tamas diffeomorphic registration for tensor accurate alignment of anatomical structures a novel framework for intersubject registration of diffusion tensor imaging dti data sets this framework is optimized for brain data and its main goal is to achieve an accurate alignment of all brain structures including white matter wm gray matter gm and spaces containing cerebrospinal fluid csf currently most dti based spatial normalization algorithms emphasize alignment of anisotropic structures while some diffusion derived metrics such as diffusion anisotropy and tensor eigenvector orientation are highly informative for proper alignment of wm other tensor metrics such as the trace or mean diffusivity md are fundamental for a proper alignment of gm and csf boundaries moreover it is desirable to include information from structural mri data e g t1 weighted or t2 weighted images which are usually available together with the diffusion data the fundamental property of dr tamas is to achieve global anatomical accuracy by incorporating in its cost function the most informative metrics locally another important feature of dr tamas is a symmetric time varying velocity based transformation model which enables it to account for potentially large anatomical variability in healthy subjects and patients the performance of dr tamas is evaluated with several data sets and compared with other widely used diffeomorphic image registration techniques employing both full tensor information and or dti derived scalar maps our results show that the proposed method has excellent overall performance in the entire brain while being equivalent to the best existing methods in wm

groupwise registration of multimodal images by an efficient joint entropy minimization scheme groupwise registration is concerned with bringing a group of images into the best spatial alignment if images in the group are from different modalities then the intensity correspondences across the images can be modeled by the joint density function jdf of the cooccurring image intensities we propose a so called treecode registration method for groupwise alignment of multimodal images that uses a hierarchical intensity space subdivision scheme through which an efficient yet sufficiently accurate estimation of the high dimensional jdf based on the parzen kernel method is computed to simultaneously align a group of images a gradient based joint entropy minimization was employed that also uses the same hierarchical intensity space subdivision scheme if the hilbert kernel is used for the jdf estimation then the treecode method requires no data dependent bandwidth selection and is thus fully automatic the treecode method was compared with the ensemble clustering ec method on four different publicly available multimodal image data sets and on a synthetic monomodal image data set the obtained results indicate that the treecode method has similar and for two data sets even superior performances compared to the ec method in terms of registration error and success rate the obtained good registration performances can be mostly attributed to the sufficiently accurate estimation of the jdf which is computed through the hierarchical intensity space subdivision scheme that captures all the important features needed to detect the correct intensity correspondences across a multimodal group of images undergoing registration

inhomogeneous prior models for image reconstruction abstract over recent years the use of homogeneous gibbs prior models in image processing has become widely accepted there has been however much discussion over precisely which models are most appropriate for most applications the simplest gaussian model tends to oversmooth reconstructions so it has been rejected in favor of various edge preserving alternatives we claim that the problem is not with the gaussian family but rather with the assumption of homogeneity in this article we propose an inhomogeneous gaussian random field as a general prior model for many image processing applications the simplicity of the gaussian model allows rapid calculation and the flexibility of the spatially varying prior parameter allows varying degrees of spatial smoothing this approach is in the spirit of adaptive kernel density methods where only the choice of the variable window width is important the analysis of real single photon emission computed tomography data is used to illustrate the methods and simu

computing large deformation metric mappings via geodesic flows of diffeomorphisms this paper examine the euler lagrange equations for the solution of the large deformation diffeomorphic metric mapping problem studied in dupuis et al 1998 and trouve 1995 in which two images i 0 i 1 are given and connected via the diffeomorphic change of coordinates i 0 1 i 1 where 1 is the end point at t 1 of curve t t 0 1 satisfying t v t t t 0 1 with 0 id the variational problem takes the form mathop arg text m in limits upsilon dot phi t upsilon t left dot phi right left int 0 1 left upsilon t right 2 text d t left i 0 circ phi 1 1 i 1 right l 2 2 right where v t v is an appropriate sobolev norm on the velocity field v t and the second term enforces matching of the images with l 2 representing the squared error norm in this paper we derive the euler lagrange equations characterizing the minimizing vector fields v t t 0 1 assuming sufficient smoothness of the norm to guarantee existence of solutions in the space of diffeomorphisms we describe the implementation of the euler equations using semi lagrangian method of computing particle flows and show the solutions for various examples as well we compute the metric distance on several anatomical configurations as measured by 0 1 v t v dt on the geodesic shortest paths

hierarchical unbiased graph shrinkage hugs a novel groupwise registration for large data set normalizing all images in a large data set into a common space is a key step in many clinical and research studies e g for brain development maturation and aging recently groupwise registration has been developed for simultaneous alignment of all images without selecting a particular image as template thus potentially avoiding bias in the registration however most conventional groupwise registration methods do not explore the data distribution during the image registration thus their performance could be affected by large inter subject variations in the data set under registration to solve this potential issue we propose to use a graph to model the distribution of all image data sitting on the image manifold with each node representing an image and each edge representing the geodesic pathway between two nodes or images then the procedure of warping all images to their population center turns to the dynamic shrinking of the graph nodes along their graph edges until all graph nodes become close to each other thus the topology of image distribution on the image manifold is always preserved during the groupwise registration more importantly by modeling the distribution of all images via a graph we can potentially reduce registration error since every time each image is warped only according to its nearby images with similar structures in the graph we have evaluated our proposed groupwise registration method on both infant and adult data sets by also comparing with the conventional group mean based registration and the absorb methods all experimental results show that our proposed method can achieve better performance in terms of registration accuracy and robustness

spectral log demons diffeomorphic image registration with very large deformations this paper presents a new framework for capturing large and complex deformations in image registration and atlas construction this challenging and recurrent problem in computer vision and medical imaging currently relies on iterative and local approaches which are prone to local minima and therefore limit present methods to relatively small deformations our general framework introduces to this effect a new direct feature matching technique that finds global correspondences between images via simple nearest neighbor searches more specifically very large image deformations are captured in spectral forces which are derived from an improved graph spectral representation we illustrate the benefits of our framework through a new enhanced version of the popular log demons algorithm named the spectral log demons as well as through a groupwise extension named the groupwise spectral log demons which is relevant for atlas construction the evaluations of these extended versions demonstrate substantial improvements in accuracy and robustness to large deformations over the conventional demons approaches

stochastic relaxation gibbs distributions and the bayesian restoration of images we make an analogy between images and statistical mechanics systems pixel gray levels and the presence and orientation of edges are viewed as states of atoms or molecules in a lattice like physical system the assignment of an energy function in the physical system determines its gibbs distribution because of the gibbs distribution markov random field mrf equivalence this assignment also determines an mrf image model the energy function is a more convenient and natural mechanism for embodying picture attributes than are the local characteristics of the mrf for a range of degradation mechanisms including blurring nonlinear deformations and multiplicative or additive noise the posterior distribution is an mrf with a structure akin to the image model by the analogy the posterior distribution defines another imaginary physical system gradual temperature reduction in the physical system isolates low energy states annealing or what is the same thing the most probable states under the gibbs distribution the analogous operation under the posterior distribution yields the maximum a posteriori map estimate of the image given the degraded observations the result is a highly parallel relaxation algorithm for map estimation we establish convergence properties of the algorithm and we experiment with some simple pictures for which good restorations are obtained at low signal to noise ratios

removal of compression artifacts using projections onto convex sets and line process modeling we present a new image recovery algorithm to remove in addition to blocking ringing artifacts from compressed images and video this new algorithm is based on the theory of projections onto convex sets pocs a new family of directional smoothness constraint sets is defined based on line processes modeling of the image edge structure the definition of these smoothness sets also takes into account the fact that the visibility of compression artifacts in an image is spatially varying to overcome the numerical difficulty in computing the projections onto these sets a divide and conquer dac strategy is introduced according to this strategy new smoothness sets are derived such that their projections are easier to compute the effectiveness of the proposed algorithm is demonstrated through numerical experiments using motion picture expert group based mpeg based coders decoders codecs

global minimization of a linearly constrained concave function by partition of feasible domain the problem of minimizing a concave function subject to linear inequality constraints may have many local solutions therefore finding the global constrained minimum is a computationally difficult problem a computational method is described which finds the global minimum of a smooth concave function over a polyhedron in rn the feasible domain is partitioned into a rectangular domain which can be excluded from further consideration and r 2n subdomains at least one of which contains the global minimum a known algorithm can be applied sequentially or in parallel to each of these r subdomains to compute the global minimum a method is also presented appendix b for the construction of nontrivial test problems for which the global minimum point is known given an arbitrary polyhedron and a selected vertex it is shown how to determine a concave quadratic function generally with many local minima with its global minimum at the selected vertex

a parallel algorithm for constrained concave quadratic global minimization the global minimization of large scale concave quadratic problems over a bounded polyhedral set using a parallel branch and bound approach is considered the objective function consists of both a concave part nonlinear variables and a strictly linear part which are coupled by the linear constraints these large scale problems are characterized by having the number of linear variables much greater than the number of nonlinear variables a linear underestimating function to the concave part of the objective is easily constructed and minimized over the feasible domain to get both upper and lower bounds on the global minimum function value at each minor iteration of the algorithm the feasible domain is divided into subregions and linear underestimating problems over each subregion are solved in parallel branch and bound techniques can then be used to eliminate parts of the feasible domain from consideration and improve the upper and lower bounds it is shown that the algorithm guarantees that a solution is obtained to within any specified tolerance in a finite number of steps computational results are presented for problems with 25 and 50 nonlinear variables and up to 400 linear variables these results were obtained on a four processor cray2 using both sequential and parallel implementations of the algorithm the average parallel solution time was approximately 15 seconds for problems with 400 linear variables and a relative tolerance of 0 001 for a relative tolerance of 0 1 the average computation time appears to increase only linearly with the number of linear variables

exhaustive nondegenerate conical processes for concave minimization on convex polytopes an exhaustive and nondegenerate cone splitting process is defined and an algorithm stated for minimizing a quasi concave function on a bounded convex polytope described by a system of linear inequalities the algorithm crucially splits upon vertices and it is shown that this class of algorithms converges finitely to an optimal solution

the geometric median on riemannian manifolds with application to robust atlas estimation one of the primary goals of computational anatomy is the statistical analysis of anatomical variability in large populations of images the study of anatomical shape is inherently related to the construction of transformations of the underlying coordinate space which map one anatomy to another it is now well established that representing the geometry of shapes or images in euclidian spaces undermines our ability to represent natural variability in populations in our previous work we have extended classical statistical analysis techniques such as averaging principal components analysis and regression to riemannian manifolds which are more appropriate representations for describing anatomical variability in this paper we extend the notion of robust estimation a well established and powerful tool in traditional statistical analysis of euclidian data to manifold valued representations of anatomical variability in particular we extend the geometric median a classic robust estimator of centrality for data in euclidean spaces we formulate the geometric median of data on a riemannian manifold as the minimizer of the sum of geodesic distances to the data points we prove existence and uniqueness of the geometric median on manifolds with non positive sectional curvature and give sufficient conditions for uniqueness on positively curved manifolds generalizing the weiszfeld procedure for finding the geometric median of euclidean data we present an algorithm for computing the geometric median on an arbitrary manifold we show that this algorithm converges to the unique solution when it exists in this paper we exemplify the robustness of the estimation technique by applying the procedure to various manifolds commonly used in the analysis of medical images using this approach we also present a robust brain atlas estimation technique based on the geometric median in the space of deformable images

a segmentation based regularization term for image deconvolution this paper proposes a new and original inhomogeneous restoration deconvolution model under the bayesian framework for observed images degraded by space invariant blur and additive gaussian noise in this model regularization is achieved during the iterative restoration process with a segmentation based a priori term this adaptive edge preserving regularization term applies a local smoothness constraint to pre estimated constant valued regions of the target image these constant valued regions the segmentation map of the target image are obtained from a preliminary wiener deconvolution estimate in order to estimate reliable segmentation maps we have also adopted a bayesian markovian framework in which the regularized segmentations are estimated in the maximum a posteriori map sense with the joint use of local potts prior and appropriate gaussian conditional luminance distributions in order to make these segmentations unsupervised these likelihood distributions are estimated in the maximum likelihood sense to compute the map estimate associated to the restoration we use a simple steepest descent procedure resulting in an efficient iterative process converging to a globally optimal restoration the experiments reported in this paper demonstrate that the discussed method performs competitively and sometimes better than the best existing state of the art methods in benchmark tests

compound gauss markov random fields for image estimation algorithms for obtaining approximations to statistically optimal estimates for images modeled as compound gauss markov random fields are discussed the authors consider both the maximum a posteriori probability map estimate and the minimum mean squared error mmse estimate for image estimation and image restoration compound image models consist of several submodels having different characteristics along with an underlying structure model which govern transitions between these image submodels two different compound random field models are employed the doubly stochastic gaussian dsg random field and a compound gauss markov cgm random field the authors present map estimators for dsg and cgm random fields using simulated annealing a fast converging algorithm called deterministic relaxation which however converges to only a locally optimal map estimate is also presented as an alternative for reducing computational loading on sequential machines for comparison purposes the authors include results on the fixed lag smoothing mmse estimator for the dsg field and its suboptimal m algorithm approximation

computational anatomy shape growth and atrophy comparison via diffeomorphisms computational anatomy ca is the mathematical study of anatomy i in i i alpha o g an orbit under groups of diffeomorphisms i e smooth invertible mappings g in g of anatomical exemplars i alpha in i the observable images are the output of medical imaging devices there are three components that ca examines i constructions of the anatomical submanifolds ii comparison of the anatomical manifolds via estimation of the underlying diffeomorphisms g in g defining the shape or geometry of the anatomical manifolds and iii generation of probability laws of anatomical variation p on the images i for inference and disease testing within anatomical models this paper reviews recent advances in these three areas applied to shape growth and atrophy

image reconstruction and restoration overview of common estimation structures and problems developments in the theory of image reconstruction and restoration over the past 20 or 30 years are outlined particular attention is paid to common estimation structures and to practical problems not properly solved yet the problem of image reconstruction and restoration is first formulated some of the current regularization approaches used to solve the problem are then described the concepts of a priori information and compound criterion are introduced a bayesian interpretation of the regularization techniques is given which clarifies the role of the tuning parameters and indicates how they could be estimated the practical aspects of computing the solution first when the hyperparameters are known and second when they must be estimated are then considered conclusions are drawn and points that still need to be investigated are outlined

simulated annealing in compound gaussian random fields image processing recently a stochastic relaxation technique called simulated annealing has been developed to search for a globally optimal solution in image estimation and restoration problems the convergence of simulated annealing has been proved only for random fields with a compact range space because of this images were modeled as random fields with bounded discrete or continuous values however in most image processing problems it is more natural to model the image as a random field with values in a noncompact space e g conditional gaussian models the proof of convergence of the stochastic relaxation method is extended to a class of compound gauss markov random fields simulation results are provided to show the power of these methods

methods for global concave minimization a bibliographic survey the global concave minimization problem is to find the constrained global minimum of a concave function since such a function may have many local minima finding the global minimum is a computationally difficult problem in this bibliographic survey which includes most of the recent papers on constrained global concave minimization we have attempted to briefly summarize the main ideas in each paper these recent papers include those concerned with large scale global concave minimization and bilinear programming

an algorithm for indefinite integer quadratic programming abstract we present an algorithm for finding the global minimum of an indefinite quadratic function over the integers contained in a compact convex set to find this minimum the algorithm first transforms the problem into an equivalent problem with a separable objective function it then uses a branch and bound search on the values of the constraints rather than the variables of the transformed problem

3 d kalman filter for image motion estimation this paper presents a new three dimensional 3 d markov model for motion vector fields the three dimensions consist of the two space dimensions plus a scale dimension we use a compound signal model to handle motion discontinuity in this 3 d markov random field mrf for motion estimation we use an extended kalman filter as a pel recursive estimator since a single observation can be sensitive to local image characteristics especially when the model is not accurate we employ windowed multiple observations at each pixel to increase accuracy these multiple observations employ different weighting values for each observation since the uncertainty in each observation is different finally we compare this 3 d model with earlier proposed one dimensional 1 d coarse to fine scale and two dimensional 2d spatial compound models in terms of motion estimation performance on a synthetic and a real image sequence

metric optimization for surface analysis in the laplace beltrami embedding space in this paper we present a novel approach for the intrinsic mapping of anatomical surfaces and its application in brain mapping research using the laplace beltrami eigen system we represent each surface with an isometry invariant embedding in a high dimensional space the key idea in our system is that we realize surface deformation in the embedding space via the iterative optimization of a conformal metric without explicitly perturbing the surface or its embedding by minimizing a distance measure in the embedding space with metric optimization our method generates a conformal map directly between surfaces with highly uniform metric distortion and the ability of aligning salient geometric features besides pairwise surface maps we also extend the metric optimization approach for group wise atlas construction and multi atlas cortical label fusion in experimental results we demonstrate the robustness and generality of our method by applying it to map both cortical and hippocampal surfaces in population studies for cortical labeling our method achieves excellent performance in a cross validation experiment with 40 manually labeled surfaces and successfully models localized brain development in a pediatric study of 80 subjects for hippocampal mapping our method produces much more significant results than two popular tools on a multiple sclerosis study of 109 subjects

kalman filtering in two dimensions further results the two dimensional reduced update kalman filter was recently introduced the corresponding scalar filtering equations were derived for the case of estimating a gaussian signal in white gaussian noise and were shown to constitute a general nonsymmetric half plane recursive filter this paper extends the method to the deconvolution problem of image restoration this paper also provides a more thorough treatment of the uniquely two dimensional boundary condition problems numerical and subjective examples are presented

global optimization of mixed integer nonlinear programs a theoretical and computational study this work addresses the development of an efficient solution strategy for obtaining global optima of continuous integer and mixed integer nonlinear programs towards this end we develop novel relaxation schemes range reduction tests and branching strategies which we incorporate into the prototypical branch and bound algorithm in the theoretical algorithmic part of the paper we begin by developing novel strategies for constructing linear relaxations of mixed integer nonlinear programs and prove that these relaxations enjoy quadratic convergence properties we then use lagrangian linear programming duality to develop a unifying theory of domain reduction strategies as a consequence of which we derive many range reduction strategies currently used in nonlinear programming and integer linear programming this theory leads to new range reduction schemes including a learning heuristic that improves initial branching decisions by relaying data across siblings in a branch and bound tree finally we incorporate these relaxation and reduction strategies in a branch and bound algorithm that incorporates branching strategies that guarantee finiteness for certain classes of continuous global optimization problems in the computational part of the paper we describe our implementation discussing wherever appropriate the use of suitable data structures and associated algorithms we present computational experience with benchmark separable concave quadratic programs fractional 0 1 programs and mixed integer nonlinear programs from applications in synthesis of chemical processes engineering design just in time manufacturing and molecular design

global minimization of large scale constrained concave quadratic problems by separable programming the global minimization of a large scale linearly constrained concave quadratic problem is considered the concave quadratic part of the objective function is given in terms of the nonlinear variablesx r n while the linear part is in terms ofy r k for large scale problems we may havek much larger thann the original problem is reduced to an equivalent separable problem by solving a multiple cost row linear program with 2n cost rows the solution of one additional linear program gives an incumbent vertex which is a candidate for the global minimum and also gives a bound on the relative error in the function value of this incumbent ana priori bound on this relative error is obtained which is shown to be 0 25 in important cases if the incumbent is not a satisfactory approximation to the global minimum a guaranteede approximate solution is obtained by solving a single liner zero one mixed integer programming problem this integer problem is formulated by a simple piecewise linear underestimation of the separable problem

concave minimization via collapsing polytopes we present a procedure for globally minimizing a concave function over a bounded polytope by successively minimizing the function over polytopes containing the feasible region and collapsing to the feasible region the initial containing polytope is a simplex and at the kth iteration the procedure chooses the most promising vertex of the current containing polytope to refine the approximation the method generates a tree whose ultimate terminal nodes coincide with the vertices of the feasible region and accounts for the vertices of the containing polytopes

sharpmean groupwise registration guided by sharp mean image and tree based registration groupwise registration has become more and more popular due to its attractiveness for unbiased analysis of population data one of the most popular approaches for groupwise registration is to iteratively calculate the group mean image and then register all subject images towards the latest estimated group mean image however its performance might be undermined by the fuzzy mean image estimated in the very beginning of groupwise registration procedure because all subject images are far from being well aligned at that moment in this paper we first point out the significance of always keeping the group mean image sharp and clear throughout the entire groupwise registration procedure which is intuitively important but has not been explored in the literature yet to achieve this we resort to developing the robust mean image estimator by the adaptive weighting strategy where the weights are adaptive across not only the individual subject images but also all spatial locations in the image domain on the other hand we notice that some subjects might have large anatomical variations from the group mean image which challenges most of the state of the art registration algorithms to ensure good registration results in each iteration we explore the manifold of subject images and build a minimal spanning tree mst with the group mean image as the root of the mst therefore each subject image is only registered to its parent node often with similar shapes and its overall transformation to the group mean image space is obtained by concatenating all deformations along the paths connecting itself to the root of the mst the group mean image as a result all the subjects will be well aligned to the group mean image adaptively our method has been evaluated in both real and simulated datasets in all experiments our method outperforms the conventional algorithm which generally produces a fuzzy group mean image throughout the entire groupwise registration

bayesian template estimation in computational anatomy abstract templates play a fundamental role in computational anatomy in this paper we present a bayesian model for template estimation it is assumed that observed images i 1 i 2 i n are generated by shooting the template j through gaussian distributed random initial momenta 1 2 n the template is j modeled as a deformation from a given hypertemplate j 0 with initial momentum which has a gaussian prior we apply a mode approximation of the em maem procedure where the conditional expectation is replaced by a dirac measure at the mode this leads us to an image matching problem with a jacobian weight term and we solve it by deriving the weighted euler lagrange equation the results of template estimation for hippocampus and cardiac data are presented

a conical algorithm for globally minimizing a concave function over a closed convex set in this paper we are concerned with the problem of finding the global minimum of a concave function over a closed convex possibly unbounded set in rn the intrinsic difficulty of this problem is due to the fact that a local minimum of the objective function may fail to be a global one which makes the conventional methods of local optimization almost useless

quasiconvex relaxations based on interval arithmetic abstract interval analysis provides a tool for i forward error analysis ii estimating and controlling rounding and approximation errors automatically and iii proving existence and uniqueness of solutions in this context the terms self validating methods inclusion methods orverification methods are in use in this paper we present a new self validating method for solving global constrained optimization problems this method is based on the construction of quasiconvex lower bound and quasiconcave upper bound functions of a given function the latter defined by an arithmetical expression no further assumptions about the nonlinearities of the given function are necessary these lower and upper bound functions are rigorous by using the tools of interval arithmetic in its easiest form they are constructed by taking appropriate linear and or quadratical estimators which yield quasiconvex quasiconcave bound functions we show how these bound functions can be used to define rigorous quasiconvex relaxations for constrained global optimization problems and nonlinear systems these relaxations can be incorporated in a branch and bound framework yielding a self validating method

intermediate templates guided groupwise registration of diffusion tensor images registration of a population of diffusion tensor images dtis is one of the key steps in medical image analysis and it plays an important role in the statistical analysis of white matter related neurological diseases however pairwise registration with respect to a pre selected template may not give precise results if the selected template deviates significantly from the distribution of images to cater for more accurate and consistent registration a novel framework is proposed for groupwise registration with the guidance from one or more intermediate templates determined from the population of images specifically we first use a euclidean distance defined as a combinative measure based on the fa map and adc map for gauging the similarity of each pair of dtis a fully connected graph is then built with each node denoting an image and each edge denoting the distance between a pair of images the root template image is determined automatically as the image with the overall shortest path length to all other images on the minimum spanning tree mst of the graph finally a sequence of registration steps is applied to progressively warping each image towards the root template image with the help of intermediate templates distributed along its path to the root node on the mst extensive experimental results using diffusion tensor images of real subjects indicate that registration accuracy and fiber tract alignment are significantly improved compared with the direct registration from each image to the root template image

statistical am fm models extended kalman filter demodulation cramer rao bounds and speech analysis a stochastic dynamical system model for describing time signals that are jointly amplitude am and frequency fm modulated is presented the signal is assumed to be bandpass perhaps originating from a filter bank applied to a broadband signal and includes the constraint that the magnitude of the complex baseband signal is positive motivated by speech processing and the desire for narrowband modulating signals time is divided into frames and the modulating signals are smoothly interpolated across each frame the model allows a detailed characterization of the bandwidth of the modulating signals and the statistical character of the measurement noise an adaptive estimation algorithm based on extended kalman filtering ideas for extracting the modulating signals from the measured signal is described and demonstrated on both voiced and unvoiced speech signals the cramer rao bound on the performance of any estimator is computed