tension in active shapes the concept of tension is introduced in the framework of active contours with prior shape information and it is used to improve image segmentation in particular two properties of this new quantity are shown 1 high values of the tension correspond to undesired equilibrium points of the cost function under minimization and 2 tension decreases if a curve is split into two or more parts based on these ideas a tree is generated whose nodes are different local minima of the cost function deeper nodes in the tree are expected to correspond to lower values of the cost function in this way the search for the global optimum is reduced to visiting and pruning a binary tree the proposed method has been applied to the problem of fish segmentation from low quality underwater images qualitative and quantitative comparison with existing algorithms based on the euler lagrange diffusion equations shows the superiority of the proposed approach in avoiding undesired local minima

a new benes network control algorithm a new benes network control algorithm is presented unlike the original looping algorithm the new algorithm is not recursive in this algorithm n x n benes network is viewed as a concatenation of two subnetworks sn1 and sn2 the first log n 1 stages of a benes network correspond to sn1 and the remaining log n stages correspond to sn2 sn1 is controlled by a full binary tree of set partitioning functions called a complete residue partition tree and sn2 is bit controlled the new control algorithm sets switches one stage at a time stage by stage

diffusion snakes introducing statistical shape knowledge into the mumford shah functional we present a modification of the mumford shah functional and its cartoon limit which facilitates the incorporation of a statistical prior on the shape of the segmenting contour by minimizing a single energy functional we obtain a segmentation process which maximizes both the grey value homogeneity in the separated regions and the similarity of the contour with respect to a set of training shapes we propose a closed form parameter free solution for incorporating invariance with respect to similarity transformations in the variational framework we show segmentation results on artificial and real world images with and without prior shape information in the cases of noise occlusion or strongly cluttered background the shape prior significantly improves segmentation finally we compare our results to those obtained by a level set implementation of geodesic active contours

birational automorphism groups and the movable cone theorem for calabi yau manifolds of wehler type via universal coxeter groups thanks to the theory of coxeter groups we produce the first family of calabi yau manifolds x of arbitrary dimension n for which rm bir x is infinite and the kawamata morrison movable cone conjecture is satisfied for this family the movable cone is explicitly described it s fractal nature is related to limit sets of kleinian groups and to the apollonian gasket then we produce explicit examples of biregular automorphisms with positive entropy on some calabi yau varieties

on a class of rearrangeable networks benes networks are nonblocking rearrangeable networks that can realize arbitrary permutations without conflict a class of 2 log sub b n stage networks which are equivalent to the benes networks is introduced networks in this class can be either symmetric or asymmetric in their structure regular or irregular in their interstage connections and even 2 log sub b n or 2 log sub b n 1 stages all networks in this class are nonblocking rearrangeable a switch labeling scheme is proposed to provide testing of the topological and functional equivalency for this class of networks this switch labeling scheme can also provide a novel matrix representation for network configuration this representation introduces a portability concept for the routing scheme on this class of networks with this representation a general routing scheme is also developed this routing scheme can realize arbitrary permutation for the whole class of 2 log sub b n stage networks

invariant properties of the shuffle exchange and a simplified cost effective version of the omega network let denote the set of permutations performable by a pass through the omega network an n stage shuffle exchange network and let denote an arbitrary permutation of n 2n elements in this paper we characterize the sets called left invariants and called right invariants this characterization provides a useful criterion for determining whether or not the composition of two permutations belongs to it also allows a number of known results to be generalized and their derivations simplified

active contours without edges we propose a new model for active contours to detect objects in a given image based on techniques of curve evolution mumford shah 1989 functional for segmentation and level sets our model can detect objects whose boundaries are not necessarily defined by the gradient we minimize an energy which can be seen as a particular case of the minimal partition problem in the level set formulation the problem becomes a mean curvature flow like evolving the active contour which will stop on the desired boundary however the stopping term does not depend on the gradient of the image as in the classical active contour models but is instead related to a particular segmentation of the image we give a numerical algorithm using finite differences finally we present various experimental results and in particular some examples for which the classical snakes methods based on the gradient are not applicable also the initial curve can be anywhere in the image and interior contours are automatically detected

robust simultaneous registration and segmentation with sparse error reconstruction we introduce a fast and efficient variational framework for simultaneous registration and segmentation srs applicable to a wide variety of image sequences we demonstrate that a dense correspondence map between consecutive frames can be reconstructed correctly even in the presence of partial occlusion shading and reflections the errors are efficiently handled by exploiting their sparse nature in addition the segmentation functional is reformulated using a dual rudin osher fatemi rof model for fast implementation moreover nonparametric shape prior terms that are suited for this dual rof model are proposed the efficacy of the proposed method is validated with extensive experiments on both indoor outdoor natural and biological image sequences demonstrating the higher accuracy and efficiency compared to various state of the art methods

the isometric log ratio transform for probabilistic multi label anatomical shape representation sources of uncertainty in the boundaries of structures in medical images have motivated the use of probabilistic labels in segmentation applications an important component in many medical image segmentation tasks is the use of a shape model often generated by applying statistical techniques to training data standard statistical techniques e g principal component analysis often assume data lies in an unconstrained vector space but probabilistic labels are constrained to the unit simplex if these statistical techniques are used directly on probabilistic labels relative uncertainty information can be sacrificed a standard method for facilitating analysis of probabilistic labels is to map them to a vector space using the logodds transform however the logodds transform is asymmetric in one of the labels which skews results in some applications the isometric log ratio ilr transform is a symmetrized version of the logodds transform and is so named as it is an isometry between the aitchison geometry the inherent geometry of the simplex and standard euclidean geometry we explore how to interpret the aitchison geometry when applied to probabilistic labels in medical image segmentation applications we demonstrate the differences when applying the logodds transform or the ilr transform to probabilistic labels prior to statistical analysis specifically we show that statistical analysis of ilr transformed data better captures the variability of anatomical shapes in cases where multiple different foreground regions share boundaries as opposed to foreground background boundaries

a fast level set method for propagating interfaces a method is introduced to decrease the computational labor of the standard level set method for propagating interfaces the fast approach uses only points close to the curve at every time step we describe this new algorithm and compare its efficiency and accuracy with the standard level set approach

parallel permutation and sorting algorithms and a new generalized connection network o k log n algorithms are obtained to permute and sort n data items on cube and perfect shuffle computers with n sup 1 1 k processing elements 1 k log n these algorithms lead directly to a generalized connection network construction having o k log n delay and o kn sup 1 1 k log n contact pairs this network has the advantage that the switches can be set in o k log n time by either a cube or perfect shuffle computer with n sup 1 1 k processing elements 23 references

geometric reid s recipe for dimer models crepant resolutions of three dimensional toric gorenstein singularities are derived equivalent to noncommutative algebras arising from consistent dimer models by choosing a special stability parameter and hence a distinguished crepant resolution y this derived equivalence generalises the fourier mukai transform relating the g hilbert scheme and the skew group algebra mathbb c x y z g for a finite abelian subgroup of mathrm sl 3 mathbb c we show that this equivalence sends the vertex simples to pure sheaves except for the zero vertex which is mapped to the dualising complex of the compact exceptional locus this generalises results of cautis logvinenko j reine angew math 636 193 236 2009 and cautis craw logvinenko j reine angew math arxiv 1205 3110 2014 to the dimer setting though our approach is different in each case we also describe some of these pure sheaves explicitly and compute the support of the remainder providing a dimer model analogue of results from logvinenko j algebra 324 2064 2087 2010

the kr benes network a control optimal rearrangeable permutation network the benes network has been used as a rearrangeable network for over 40 years yet the uniform n 2 log n 1 control complexity of the n spl times n benes is not optimal for many permutations in this paper we present a novel o log n depth rearrangeable network called kr benes that is permutation specific control optimal the kr benes routes every permutation with the minimal control complexity specific to that permutation and its worst case complexity for arbitrary permutations is bounded by the benes thus it replaces the benes when considering control complexity latency we design the kr benes by first constructing a restricted 2log k 2 depth rearrangeable network called k benes for routing k bounded permutations with control 2n log k 0 spl les k spl les n 4 we then show that the n spl times n benes network itself with one additional stage contains every kr benes network as a subgraph and use this property to construct the kr benes network with regard to the control optimality of the kr benes we show that any optimal network for rearrangeably routing k bounded permutations must have depth 2log k 2 and therefore the k benes and hence the kr benes is optimal

local optimization based segmentation of spatially recurring multi region objects with part configuration constraints incorporating prior knowledge into image segmentation algorithms has proven useful for obtaining more accurate and plausible results two important constraints containment and exclusion of regions have gained attention in recent years mainly due to their descriptive power in this paper we augment the level set framework with the ability to handle these two intuitive geometric relationships containment and exclusion along with a distance constraint between boundaries of multi region objects level set s important property of automatically handling topological changes of evolving contours surfaces enables us to segment spatially recurring objects e g multiple instances of multi region cells in a large microscopy image while satisfying the two aforementioned constraints in addition the level set approach gives us a very simple and natural way to compute the distance between contours surfaces and impose constraints on it the downside however is a local optimization framework in which the final segmentation solution depends on the initialization in fact here we sacrifice the optimizability local instead of global solution in exchange for lower space complexity less memory usage and faster runtime especially for large microscopic images as well as no grid artifacts nevertheless the result from validating our method on several biomedical applications showed the utility and advantages of this augmented level set framework even with rough initialization that is distant from the desired boundaries we also compared our framework with its counterpart methods in the discrete domain and reported the pros and cons of each of these methods in terms of metrication error and efficiency in memory usage and runtime

flops of g hilb and equivalences of derived categories by variation of git quotient for a finite subgroup g in sl 3 c bridgeland king and reid proved that the moduli space of g clusters is a crepant resolution of the quotient c 3 g this paper considers the moduli spaces m theta introduced by kronheimer and further studied by sardo infirri which coincide with g hilb for a particular choice of the git parameter theta for g abelian we prove that every projective crepant resolution of c 3 g is isomorphic to m theta for some parameter theta the key step is the description of git chambers in terms of the k theory of the moduli space via the appropriate fourier mukai transform we also uncover explicit equivalences between the derived categories of moduli m theta for parameters lying in adjacent git chambers

a level set model for image classification we present a supervised classification model based on a variational approach this model is devoted to find an optimal partition composed of homogeneous classes with regular interfaces the originality of the proposed approach concerns the definition of a partition by the use of level sets each set of regions and boundaries associated to a class is defined by a unique level set function we use as many level sets as different classes and all these level sets are moving together thanks to forces which interact in order to get an optimal partition we show how these forces can be defined through the minimization of a unique fonctional the coupled partial differential equations pde related to the minimization of the functional are considered through a dynamical scheme given an initial interface set zero level set the different terms of the pde s are governing the motion of interfaces such that at convergence we get an optimal partition as defined above each interface is guided by internal forces regularity of the interface and external ones data term no vacuum no regions overlapping several experiments were conducted on both synthetic and real images

multi reference shape priors for active contours in this paper we present a new way of constraining the evolution of an active contour with respect to a set of fixed reference shapes this approach is based on a description of shapes by the legendre moments computed from their characteristic function this provides a region based representation that can handle arbitrary shape topologies moreover exploiting the properties of moments it is possible to include intrinsic affine invariance in the descriptor which solves the issue of shape alignment without increasing the number of d o f of the initial problem and allows introducing geometric shape variabilities our new shape prior is based on a distance in terms of descriptors between the evolving curve and the reference shapes minimizing the corresponding shape energy leads to a geometric flow that does not rely on any particular representation of the contour and can be implemented with any contour evolution algorithm we introduce our prior into a two class segmentation functional showing its benefits on segmentation results in presence of severe occlusions and clutter examples illustrate the ability of the model to deal with large affine deformation and to take into account a set of reference shapes of different topologies

snakes active contour models a snake is an energy minimizing spline guided by external constraint forces and influenced by image forces that pull it toward features such as lines and edges snakes are active contour models they lock onto nearby edges localizing them accurately scale space continuation can be used to enlarge the capture region surrounding a feature snakes provide a unified account of a number of visual problems including detection of edges lines and subjective contours motion tracking and stereo matching we have used snakes successfully for interactive interpretation in which user imposed constraint forces guide the snake near features of interest

incorporating shape prior into geodesic active contours for detecting partially occluded object a new method to incorporate shape prior knowledge into geodesic active contours for detecting partially occluded object is proposed in this paper the level set functions of the collected shapes are used as training data they are projected onto a low dimensional subspace using pca and their distribution is approximated by a gaussian function a shape prior model is constructed and is incorporated into the geodesic active contour formulation to constrain the contour evolution process to balance the strength between the image gradient force and the shape prior force a weighting factor is introduced to adaptively guide the evolving curve to move under both forces the curve converges with due consideration of both local shape variations and global shape consistency experimental results demonstrate that the proposed method makes object detection robust against partial occlusions

a multiphase level set framework for image segmentation using the mumford and shah model we propose a new multiphase level set framework for image segmentation using the mumford and shah model for piecewise constant and piecewise smooth optimal approximations the proposed method is also a generalization of an active contour model without edges based 2 phase segmentation developed by the authors earlier in t chan and l vese 1999 in scale space 99 m nilsen et al eds lncs vol 1682 pp 141 151 and t chan and l vese 2001 ieee ip 10 2 266 277 the multiphase level set formulation is new and of interest on its own by construction it automatically avoids the problems of vacuum and overlaps it needs only log n level set functions for n phases in the piecewise constant cases it can represent boundaries with complex topologies including triple junctionss in the piecewise smooth case only two level set functions formally suffice to represent any partition based on the four color theorem finally we validate the proposed models by numerical results for signal and image denoising and segmentation implemented using the osher and sethian level set method

notes on shuffle exchange type permutation sets properties of some shuffle exchange type permutation sets are studied from operational points of view the permutation sets studied are omega omega sup 1 psi l and u omega and omega sup 1 are respectively the omega and inverse omega permutation sets omega identical to omega intersection omega sup 1 and l and u are respectively the admissible lower and upper triangular permutation sets several intuitive operations are introduced based on these operations important known results relating to these sets are readdressed the recursive nature of the sets is also discussed

using prior shapes in geometric active contours in a variational framework in this paper we report an active contour algorithm that is capable of using prior shapes the energy functional of the contour is modified so that the energy depends on the image gradient as well as the prior shape the model provides the segmentation and the transformation that maps the segmented contour to the prior shape the active contour is able to find boundaries that are similar in shape to the prior even when the entire boundary is not visible in the image i e when the boundary has gaps a level set formulation of the active contour is presented the existence of the solution to the energy minimization is also established we also report experimental results of the use of this contour on 2d synthetic images ultrasound images and fmri images classical active contours cannot be used in many of these images

an efficient routing algorithm for realizing linear permutations on p sup t shuffle exchange networks the authors present an efficient routing algorithm for realizing any permutation in lin linear permutation class on single stage shuffle exchange networks with k k switching elements where k p is a prime number for any positive integer number n there are n k sup n processors connected by the network the proposed algorithm can realize lin in 2n 1 passes it can be implemented by using nn processors in o n time it can also be extended to the shuffle exchange networks with p sup t p sup t switching elements where t is a positive integer number in addition the routing of any arbitrary permutations on the networks with any integer k 2 is discussed further by using the techniques developed here the authors present an optimal o log n parallel algorithm for solving a set of linear equations with a nonsingular coefficient matrix when the arithmetic is over the finite field gf p sup t

robust similarity registration technique for volumetric shapes represented by characteristic functions this paper proposes a novel similarity registration technique for volumetric shapes implicitly represented by characteristic functions cfs here the calculation of rotation parameters is considered as a spherical cross correlation problem and the solution is therefore found using the standard phase correlation technique facilitated by principal components analysis pca thus fast fourier transform fft is employed to vastly improve efficiency and robustness geometric moments are then used for shape scale estimation which is independent from rotation and translation parameters it is numerically demonstrated that our registration method is able to handle shapes with various topologies and robust to noise and initial poses further validation of our method is performed by registering a lung database highlightswe propose a similarity registration method that registers volumetric shapes the method naturally handles shapes with topological differences the method is validated by registering a lung database the method can be applied to shape based image segmentation

artin group actions on derived categories of threefolds motivated by the enhanced gauge symmetry phenomenon of the physics literature and mirror symmetry this paper constructs an action of an artin group on the derived category of coherent sheaves of a smooth quasiprojective threefold containing a configuration of ruled surfaces described by a finite type dynkin diagram the action ex tends over deformations of the threefold via a compatible action of the corresponding re flection group on the base of its deformation space all finite type dynkin diagrams are realized

the cone conjecture for calabi yau pairs in dimension 2 a central idea of minimal model theory as formulated by mori is to study algebraic varieties using convex geometry the cone of curves of a projective variety is defined as the convex cone spanned by the numerical equivalence classes of algebraic curves the dual cone is the cone of nef line bundles for fano varieties varieties with ample anticanonical bundle these cones are rational polyhedral by the cone theorem 21 theorem 3 7 for more general varieties these cones are not well understood they can have infinitely many isolated extremal rays or they can be round both phenomena occur among calabi yau varieties such as k3 surfaces 22 which can be considered the next simplest varieties after fano varieties the morrison kawamata cone conjecture would give a clear picture of the nef cone for calabi yau varieties 29 30 19 the conjecture says that the action of the automorphism group of the variety on the nef cone has a rational polyhedral fundamental domain the conjecture includes an analogous statement about the movable cone see section 2 for details thus for calabi yau varieties the failure of the nef cone to be rational polyhedral is always explained by an infinite discrete group of automorphisms of the variety it is not clear where these automorphisms should come from nonetheless the conjecture has been proved for calabi yau surfaces by sterk looijenga and namikawa 41 33 19 the heart of the proof being the torelli theorem for k3 surfaces of piatetski shapiro and shafarevich 3 theorem 11 1 kawamata proved the cone conjecture for all 3 dimensional calabi yau fiber spaces over a positive dimensional base 19 the conjecture is wide open for calabiyau 3 folds despite significant results by oguiso and peternell 38 szendroi 43 uehara 46 and wilson 48 the conjecture was generalized from calabi yau varieties to klt calabi yau pairs x in 45 here is a divisor on x and calabi yau means that kx rather than kx is numerically trivial in this paper we prove the cone conjecture for all klt calabi yau pairs of dimension 2 theorem 4 1 using the geometry of groups acting on convex cones and reduction to the case of k3 surfaces this is enough to show that the conjecture is reasonable in the greater generality of pairs more concretely the theorem gives control over the nef cone and the automorphism group for a large class of rational surfaces including the fano surfaces as well as many others in particular we get a good description of when the cox ring or total coordinate ring is finitely generated in this class of surfaces corollary 5 1 thanks to caucher birkar igor dolgachev brian harbourne artie prendergastsmith chenyang xu and the referees for their comments

the universality of a class of modified single stage shuffle exchange networks a class of modified single state shuffle exchange s e networks with reconfigurable connections is described the capability of these modified networks to simulate every arbitrary permutation and other multistage s e networks is studied in particular the upper bounds on simulating six multistage s e networks are given it is also shown that c l wu and t y feng s 1981 modified single stage s e network is optimal in terms of its universality and cost for the networks with one reconfigurable connection however some of the modified networks with two reconfigurable connections have better capability although they are slightly more expensive than wu and feng s network also proposed is a link folding scheme that can be used to reduce the connection complexity of implementing the connection selection mechanism

dream 2 s deformable regions driven by an eulerian accurate minimization method for image and video segmentation this paper deals with image and video segmentation using active contours we propose a general form for the energy functional related to region based active contours we compute the associated evolution equation using shape derivation tools and accounting for the evolving region based terms then we apply this general framework to compute the evolution equation from functionals that include various statistical measures of homogeneity for the region to be segmented experimental results show that the determinant of the covariance matrix appears to be a very relevant tool for segmentation of homogeneous color regions as an example it has been successfully applied to face segmentation in real video sequences

the weil petersson geometry of the moduli space of su n 3 calabi yau manifolds i the weil petersson metric is defined on the moduli space of calabi yau manifolds the curvature of this weil petersson metrics is computed and its potential is explicitely defined it is proved that the moduli space of calabi yau manifolds is unobstructed see tian

the tangent bundle of a calabi yau manifold deformations and restriction to rational curves the tangent bundle x of a calabi yau threefoldx is the only known example of a stable bundle with non trivial restriction to any rational curve onx by deforming the direct sum of x and the trivial line bundle one can try to obtain new examples we use algebro geometric techniques to derive results in this direction the relation to the finiteness of rational curves on calabi yau threefolds is discussed

a shape based approach to the segmentation of medical imagery using level sets we propose a shape based approach to curve evolution for the segmentation of medical images containing known object types in particular motivated by the work of leventon grimson and faugeras 2000 we derive a parametric model for an implicit representation of the segmenting curve by applying principal component analysis to a collection of signed distance representations of the training data the parameters of this representation are then manipulated to minimize an objective function for segmentation the resulting algorithm is able to handle multidimensional data can deal with topological changes of the curve is robust to noise and initial contour placements and is computationally efficient at the same time it avoids the need for point correspondences during the training phase of the algorithm we demonstrate this technique by applying it to two medical applications two dimensional segmentation of cardiac magnetic resonance imaging mri and three dimensional segmentation of prostate mri

a self routing benes network and parallel permutation algorithms a benes permutation network capable of setting its own switches dynamically is presented the total switch setting and delay time for the n input utput self routing network is o log n it is shown that the network is capable of performing a rich class of permutations the self routing scheme leads to efficient o log n parallel algorithms to perform the same class of permutations on cube connected and perfect shuffle computers

self routing technique in perfect shuffle networks using control tags the self routing technique using control tags on multiple pass perfect shuffle networks is generalized in particular they show that bit permute complement permutations can be realized and unscrambled in 2n 1 passes or less where n log sub 2 n n being the number of terminals on either side they also show that most of the frequently used permutations are in the intersection of omega realizing and inverse omega realizing sets and can be realized and unscrambled in n passes

deformation theory of singular symplectic n folds by a symplectic manifold or a symplectic n fold we mean a compact kaehler manifold of even dimension n with a non degenerate holomorphic 2form i e is a nowhere vanishing n form this notion is generalized to a variety with singularities we call x a projective symplectic variety if x is a normal projective variety with rational gorenstein singularities and if the regular locus u of x admits a non degenerate holomorphic 2 form a symplectic variety will play an important role together with a singular calabi yau variety in the generalized bogomolov decomposition conjecture now that essentially a few examples of symplectic manifolds are discovered it seems an important task to seek new symplectic manifolds by deforming symplectic varieties in this paper we shall study a projective symplectic variety from a view point of deformation theory if x has a resolution x x such that x is a symplectic manifold we say that x has a symplectic resolution our first results are concerned with a birational contraction map of a symplectic manifold

optimal approximations by piecewise smooth functions and associated variational problems abstract this reprint will introduce and study the most basic properties of three new variational problems which are suggested by applications to computer vision in computer vision a fundamental problem is to appropriately decompose the domain r of a function g x y of two variables this problem starts by describing the physical situation which produces images assume that a three dimensional world is observed by an eye or camera from some point p and that g1 rho represents the intensity of the light in this world approaching the point sub 1 from a direction rho if one has a lens at p focusing this light on a retina or a film in both cases a plane domain r in which we may introduce coordinates x y then let g x y be the strength of the light signal striking r at a point with coordinates x y g x y is essentially the same as sub 1 rho possibly after a simple transformation given by the geometry of the imaging syste the function g x y defined on the plane domain r will be called an image what sort of function is g the light reflected off the surfaces si of various solid objects o sub i visible from p will strike the domain r in various open subsets r sub i when one object o1 is partially in front of another object o2 as seen from p but some of object o2 appears as the background to the sides of o1 then the open sets r1 and r2 will have a common boundary the edge of object o1 in the image defined on r and one usually expects the image g x y to be discontinuous along this boundary jhd

constraining the kahler moduli in the heterotic standard model phenomenological implications of the volume of the calabi yau threefolds on the hidden and observable m theory boundaries together with slope stability of their corresponding vector bundles constrain the set of kahler moduli which give rise to realistic compactifications of the strongly coupled heterotic string when vector bundles are constructed using extensions we provide simple rules to determine lower and upper bounds to the region of the kahler moduli space where such compactifications can exist we show how small these regions can be working out in full detail the case of the recently proposed heterotic standard model more explicitly we exhibit kahler classes in these regions for which the visible vector bundle is stable on the other hand there is no polarization for which the hidden bundle is stable

a variational model for object segmentation using boundary information and shape prior driven by the mumford shah functional in this paper we propose a new variational model to segment an object belonging to a given shape space using the active contour method a geometric shape prior and the mumford shah functional the core of our model is an energy functional composed by three complementary terms the first one is based on a shape model which constrains the active contour to get a shape of interest the second term detects object boundaries from image gradients and the third term drives globally the shape prior and the active contour towards a homogeneous intensity region the segmentation of the object of interest is given by the minimum of our energy functional this minimum is computed with the calculus of variations and the gradient descent method that provide a system of evolution equations solved with the well known level set method we also prove the existence of this minimum in the space of functions with bounded variation applications of the proposed model are presented on synthetic and medical images

nonparametric joint shape and feature priors for image segmentation in many image segmentation problems involving limited and low quality data employing statistical prior information about the shapes of the objects to be segmented can significantly improve the segmentation result however defining probability densities in the space of shapes is an open and challenging problem especially if the object to be segmented comes from a shape density involving multiple modes classes existing techniques in the literature estimate the underlying shape distribution by extending parzen density estimator to the space of shapes in these methods the evolving curve may converge to a shape from a wrong mode of the posterior density when the observed intensities provide very little information about the object boundaries in such scenarios employing both shape and class dependent discriminative feature priors can aid the segmentation process such features may involve e g intensity based textural or geometric information about the objects to be segmented in this paper we propose a segmentation algorithm that uses nonparametric joint shape and feature priors constructed by parzen density estimation we incorporate the learned joint shape and feature prior distribution into a maximum a posteriori estimation framework for segmentation the resulting optimization problem is solved using active contours we present experimental results on a variety of synthetic and real data sets from several fields involving multimodal shape densities experimental results demonstrate the potential of the proposed method

the universality of the shuffle exchange network this paper has focused on the realization of every arbitrary permutation with the shuffle exchange network permutation properties of shuffle exchange networks are studied and are used to demonstrate several universal networks it is concluded that 3 log2 n 1 passes through a single stage regular shuffle exchange network are sufficient to realize every arbitrary permutation where n is network size a routing algorithm is also developed to calculate control settings of the shuffle exchange switches for the permutation realization three optimal universal networks namely expanded direct connection shuffle exchange network multiple pass omega network and modified shuffle exchange network are then exploited for better interconnection purposes in addition this work specifies the inherent relationship between the shuffle exchange network and the benes binary network so that designers can have a broad prospect

an easily controlled network for frequently used permutations a network which is a concatenation of 2 networks 2 along with a simple control algorithm is proposed this network is capable of performing all network realizable permutations and the bit permute complement bpc class of permutations 5 in 0 log n time the control algorithm is actually a multiple pass control algorithm on the network which is more general than pease s lu decomposition method 6 and lenfant s decomposition method 4

on 2 4 complete intersection threefolds that contain an enriques surface we study nodal complete intersection threefolds of type 2 4 in mathbb p 5 which contain an enriques surface in its fano embedding we completely determine calabi yau birational models of a generic such threefold these models have hodge numbers h 11 2 h 12 32 we also describe calabi yau varieties with hodge numbers h 11 h 12 equal to 2 26 23 5 and 31 1 the last two pairs of hodge numbers are to the best of our knowledge new

sectional curvatures of kahler moduli if x is a compact kahler manifold of dimension n we let open image in new window denote the cone of kahler classes and open image in new window the level set given by classes d with d n 1 this space is naturally a riemannian manifold and is isometric to the manifold open image in new window of kahler forms with n some fixed volume form equipped with the hodge metric as studied previously by huybrechts we study these spaces further in particular their geodesics and sectional curvatures conjecturally at least for calabi yau manifolds and probably rather more generally these sectional curvatures should be bounded between open image in new window and zero we find simple formulae for the sectional curvatures and prove both the bounds hold for various classes of varieties developing along the way a mirror to the weil petersson theory of complex moduli in the case of threefolds with h1 1 3 we produce an explicit formula for this curvature in terms of the invariants of the cubic form this enables us to check the bounds by computer for a wide range of examples finally we explore the implications of the non positivity of these curvatures

frames a simple characterization of permutations realized by frequently used networks rearrangeable multistage networks such as the benes network realize any permutation yet their routing algorithms are not cost effective on the other hand there exist inexpensive routing algorithms for nonrearrangeable networks but no simple technique exists to characterize all the permutations realized on these networks this paper introduces the concept of frame and shows how it can be used to characterize all the permutations realized on various multistage interconnection networks they include subnetworks of baseline benes and cascaded baseline and shuffle exchange networks

divide and conquer algorithms on the hypercube abstract we show how to implement divide and conquer algorithms without undue overhead on a wide class of networks we give an optimal generic divide and conquer implementation on hypercubes for the class of divide and conquer algorithms for which the total size of the subproblems on any level of the recursion does not exceed the parent problem size for this implementation appropriately sized subcubes have to be allocated to the subproblems generated by the dividesteps we take care that these allocation steps do not cause any unbalanced distribution of work and that asymptotically they do not increase the running time variants of our generic algorithm also work for the butterfly network and by a general simulation for the class of hypercubic networks including the shuffle exchange and the cube connected cycles network our results can also be applied to optimally solve various types of routing problems

a variational level set approach to multiphase motion a coupled level set method for the motion of multiple junctions of e g solid liquid and grain boundaries which follows the gradient flow for an energy functional consisting of surface tension proportional to length and bulk energies proportional to area is developed the approach combines the level set method of s osher and j a sethian with a theoretical variational formulation of the motion by f reitich and h m soner the resulting method uses as many level set functions as there are regions and the energy functional is evaluated entirely in terms of level set functions the gradient projection method leads to a coupled system of perturbed by curvature terms hamilton jacobi equations the coupling is enforced using a single lagrange multiplier associated with a constraint which essentially prevents a regions from overlapping and b the development of a vacuum the numerical implementation is relatively simple and the results agree with and go beyond the theory as given in 12 other applications of this methodology including the decomposition of a domain into subregions with minimal interface length are discussed finally some new techniques and results in level set methodology are presented

parallel matrix and graph algorithms matrix multiplication algorithms for cube connected and perfect shuffle computers are presented it is shown that in both these models two n times n matrices can be multiplied in o n m log m time when n 2 m 1 leqq m leqq n processing elements pes are available when only m 2 1 leqq m leqq n pes are available two n times n matrices can be multiplied in o n 2 m m n m 2 61 time it is shown that many graph problems can be solved efficiently using the matrix multiplication algorithms

contour completion without region segmentation contour completion plays an important role in visual perception where the goal is to group fragmented low level edge elements into perceptually coherent and salient contours most existing methods for contour completion have focused on pixelwise detection accuracy in contrast fewer methods have addressed the global contour closure effect despite psychological evidences for its importance this paper proposes a purely contour based higher order crf model to achieve contour closure through local connectedness approximation this leads to a simplified problem structure where our higher order inference problem can be transformed into an integer linear program and be solved efficiently compared with the methods based on the same bottom up edge detector our method achieves a superior contour grouping ability measured by rand index a comparable precision recall performance and more visually pleasing results our results suggest that contour closure can be effectively achieved in contour domain in contrast to a popular view that segmentation is essential for this purpose

optic disc segmentation based on variational model with multiple energies accurate and reliable optic disc od segmentation is important for retinal image analysis and retinal disease screening this paper presents a novel method to automatically segment od in fundus images based on variational model with multiple energies firstly a sparse coding based technique is designed to localize the od center based on which an initial boundary curve is then estimated by a circular hough transform next od segmentation is regarded as an energy minimization problem and a variational model integrating three energy terms is proposed to evolve the curve to the od boundary in the proposed model the first term named phase based boundary energy is designed to attract the evolution curve to the od boundary even the one with low contrast the second term named pca based shape energy constraints the evolution curve to a common od shape which can suppress the negative effect of bright interferences e g the bright lesions and myelinated nerve fibers in od segmentation the last one is the region energy which drives the evolution curve to the boundary of the homogeneous regions and hence improve the robustness of the model to the noises boundary and the initial position of evolution curve the proposed od segmentation method is evaluated on three public available databases i e the messidor onhsd and drions databases and the experimental results demonstrate that the proposed method outperforms the state of the art techniques highlightsa sparse coding based method is designed to localize the optic disc od in fundus image variational model integrating three energy terms is proposed to segment od boundary phase based edge stop function is designed in the boundary energy the proposed method is evaluated and analyzed on three public databases and outperforms the state of the art approaches