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

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

automatic ventricular cavity boundary detection from sequential ultrasound images using simulated annealing an automatic algorithm has been developed for high speed detection of cavity boundaries in sequential 2 d echocardiograms using an optimization algorithm called simulated annealing sa the algorithm has three stages 1 a predetermined window of size n m is decimated to size n m after low pass filtering 2 an iterative radial gradient algorithm is employed to determine the center of gravity cg of the cavity 3 64 radii which originate from the cg defined in stage 2 are bounded by the high probability region each bounded radius is defined as a link in a 1 d 64 member cyclic markov random field this algorithm is unique in that it compounds spatial and temporal information along with a physical model in its decision rule whereas most other algorithms base their decisions on spatial data alone this is the first implementation of a relaxation algorithm for edge detection in echocardiograms results attained using this algorithm on real data have been highly encouraging

multiple window parallel adaptive boundary finding in computer vision the problem considered in this paper is the estimation of highly variable object boundaries in noisy images boundaries may be those of a tank in an ir image a spinal canal in a cat scan a cloud in a visible light image etc or they may be internal to an object such as the boundary between a spherical surface and a cylindrical surface in a manufactured object the focus of the paper is on parallel multiple window boundary estimation algorithms here the image field is parti tioned into an array of rectangular windows and boundary finders are run simultaneously within the windows the boundary segments found within the windows are then seamed together to obtain meaningful global boundaries the entire procedure is treated within a maximum likelihood estimation framework that we have developed for boundary finding although our multiple window estimation approach can be used with a number of local boundary finding algorithms we concen trate on one which is based on dynamic programming and will produce the true maximum likelihood boundary some theoretical considera tions for boundary model design and boundary finding runtime are covered included is the use of a low computational cost f test for test ing whether a window contains a boundary and an analytical treatment which shows that use of coarse pixels with a chi square test or an f test improves the probability of correctly recognizing whether a boundary is present in a window

the integration of image segmentation maps using region and edge information we present an algorithm that integrates multiple region segmentation maps and edge maps it operates independently of image sources and specific region segmentation or edge detection techniques user specified weights and the arbitrary mixing of region edge maps are allowed the integration algorithm enables multiple edge detection region segmentation modules to work in parallel as front ends the solution procedure consists of three steps a maximum likelihood estimator provides initial solutions to the positions of edge pixels from various inputs an iterative procedure using only local information without edge tracing then minimizes the contour curvature finally regions are merged to guarantee that each region is large and compact the channel resolution width controls the spatial scope of the initial estimation and contour smoothing to facilitate multiscale processing experimental results are demonstrated using data from different types of sensors and processing techniques the results show an improvement over individual inputs and a strong resemblance to human generated segmentation

on the sandpile group of the square cycle cn2 abstract the sandpile group of a graph is a refinement of the number of spanning trees of the graph and is closely connected with the graph laplacian in this paper the structure of the sandpile group on the square cycle c n 2 is determined and it is shown that the smith normal form of the sandpile group is always the direct sum of two or three cyclic groups

on the sandpile group of the graph k3 cn abstract the sandpile group of a graph is a refinement of the number of spanning trees of the graph and is closely connected with the graph laplacian matrix in this paper the structure of the sandpile group on the graph k 3 c n is determined and it is shown that the smith normal form of the sandpile group of k 3 c n is always the direct sum of four or five cyclic groups our methods can be generated to the graphs k 4 c n and k 5 c n

attractable snakes based on the greedy algorithm for contour extraction abstract while most improved snakes were built under the original variational scheme this paper presents an attractable snake based on the greedy snake williams and shah cvgip image understanding 55 1 1992 14 26 by use of a direct feedback mechanism that is seamlessly consistent with the search strategy of the greedy algorithm the proposed approach is capable of inheriting the simplicity and efficiency of that algorithm and performing competitively with related snakes to avoid undesirable local minima an overall optimal edge detector is designed a suitable synthetic convergent criterion is proposed which enables snakes to converge normally or oscillatingly on target objects an adaptive interpolation scheme that encourages snakes to accurately sense the details of object shapes is also described this model is applied to extract contours from various images with encouraging results

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

a sharp weak type p p inequality p 2 for martingale transforms and other subordinate martingales if d n n o is a martingale difference sequence e n n 0 a sequence of numbers in 1 1 and n a positive integer then p max 0 m n m k 0 e k d k 1 p n k 0 d k p p here p denotes the best constant if 1 2 and that p p 1 2 is also the best constant in the analogous inequality for two martingales m and n indexed by 0 right continuous with limits from the left adapted to the same filtration and such that m m t n n t is nonnegative and nondecreasing in t in section 7 we prove a similar inequality for harmonic functions

degree maximal graphs are laplacian integral abstract an integer sequence d d 1 d 2 d n is graphic if there is a graph whose degree sequence is d a graph g is maximal if its degree sequence is majorized by no other graphic sequence the laplacian matrix of g is l g d g a g where d g is the diagonal matrix of vertex degrees and a g is the 0 1 adjacency matrix the article contains an explicit algorithmic construction of all maximal graphs from which it follows e g that apart from 0 the laplacian spectrum of a maximal graph is the conjugate of its degree sequence

algebraic aspects of abelian sandpile models the abelian sandpile models feature a finite abelian group g generated by the operators corresponding to particle addition at various sites we study the canonical decomposition of g as a product of cyclic groups g z d1 z d2 z d3 z dg where g is the least number of generators of g and di is a multiple of di 1 the structure of g is determined in terms of the toppling matrix delta we construct scalar functions linear in the height variables of the pile that are invariant under toppling at any site these invariants provide convenient coordinates to label the recurrent configurations of the sandpile for an l l square lattice we show that g l in this case we observe that the system has non trivial symmetries transcending the obvious symmetries of the square namely those coming from the action of the cyclotomic galois group gall of the 2 l 1 th roots of unity which operates on the set of eigenvalues of h these eigenvalues are algebraic integers the product of which is the order mod g mod with the help of gall we are able to group the eigenvalues into certain subsets the products of which are separately integers and thus obtain an explicit factorization of mod g mod we also use gall to define other simpler sets of toppling invariants

probe based automatic target recognition in infrared imagery a probe based approach combined with image modeling is used to recognize targets in spatially resolved single frame forward looking infrared flir imagery a probe is a simple mathematical function that operates locally on pixel values and produces an output that is directly usable by an algorithm an empirical probability density function of the probe values is obtained from a local region of the image and used to estimate the probability that a target of known shape is present target shape information is obtained from three dimensional 3 d computer aided design cad models knowledge of the probe values along with probe probability density functions and target shape information allows the likelihood ratio between a target hypothesis and background hypothesis to be written the generalized likelihood ratio test is then used to accept one of the target poses or to choose the background hypothesis we present an image model for infrared images the resulting recognition algorithm and experimental results on three sets of real and synthetic flir imagery

brownian strings segmenting images with stochastically deformable contours this paper describes an image segmentation technique in which an arbitrarily shaped contour was deformed stochastically until it fitted around an object of interest the evolution of the contour was controlled by a simulated annealing process which caused the contour to settle into the global minimum of an image derived energy function the nonparametric energy function was derived from the statistical properties of previously segmented images thereby incorporating prior experience since the method was based on a state space search for the contour with the best global properties it was stable in the presence of image errors which confound segmentation techniques based on local criteria such as connectivity unlike snakes and other active contour approaches the new method could handle arbitrarily irregular contours in which each interpixel crack represented an independent degree of freedom furthermore since the contour evolved toward the global minimum of the energy the method was more suitable for fully automatic applications than the snake algorithm which frequently has to be reinitialized when the contour becomes trapped in local energy minima high computational complexity was avoided by efficiently introducing a random local perturbation in a time independent of contour length providing control over the size of the perturbation and assuring that resulting shape changes were unbiased the method was illustrated by using it to find the brain surface in magnetic resonance head images and to track blood vessels in angiograms

digital image restoration using spatial interaction models this paper is concerned with developing fast nonrecursive algorithms for the minimum mean squared error restoration of degraded images the degradation is assumed to be due to a space invariant periodic nonseparable known point spread function and additive white noise our basic approach is to represent the images by a class of spatial interaction models namely the simultaneous autoregressve models and the conditional markov models defined on toroidal lattices and develop minimum mean squared error restoration algorithms using these models the restoration algorithms are optimal if the parameters characterizing the interaction models are exactly known however in practice the parameters are estimated from the images by using spatial interaction models we develop restoration algorithms that do not require the availability of the original image or its prototype the specific structure of the underlying lattice enables the implementation of the filters using fast fourier transform fft computations several restoration examples are given

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

an integrated approach to 2d object recognition a multilevel markov random field mrf energy environment has been developed that simultaneously performs delineation representation and classification of two dimensional objects by using a global optimization technique this environment supports a multipolar shape representation which establishes a dynamic mrf structure this structure is initialized as a single center polar representation and uses minimum description length tests to determine whether to establish new polar centers the polar representations at these centers are compared with a database of such representations in order to identify pieces of objects and the results of these comparisons are used to compile evidence for global object identifications this method is potentially more robust than conventional multistaged approaches to object recognition because it incorporates all the information about the objects into a single adaptive decision process and its use of a multipolar representation allows it to handle partially occluded objects

deformable contour method a constrained optimization approach in this paper a class of deformable contour methods using a constrained optimization approach of minimizing a contour energy function satisfying an interior homogeneity constraint is proposed the class is defined by any positive potential function describing the contour interior characterization an evolutionary strategy is used to derive the algorithm a similarity threshold tv can be used to determine the interior size and shape of the contour sensitivity and significance of tv and a spreadness measure are also discussed and shown experiments on noisy images and the convergence to a minimum energy gap contour are included the developed method has been applied to a variety of medical images from ct abdominal section mri image slices of brain brain tumor a pig heart ultrasound image sequence to visual blood cell images as the results show the algorithm can be adapted to a broad range of medical images containing objects with vague complex and or irregular shape boundary inhomogeneous and noisy interior and contour with small gaps

region based strategies for active contour models the variational method has been introduced by kass et al 1987 in the field of object contour modeling as an alternative to the more traditional edge detection edge thinning edge sorting sequence since the method is based on a pre processing of the image to yield an edge map it shares the limitations of the edge detectors it uses in this paper we propose a modified variational scheme for contour modeling which uses no edge detection step but local computations instead only around contour neighborhoods as well as an anticipating strategy that enhances the modeling activity of deformable contour curves many of the concepts used were originally introduced to study the local structure of discontinuity in a theoretical and formal statement by leclerc zucker 1987 but never in a practical situation such as this one the first part of the paper introduces a region based energy criterion for active contours and gives an examination of its implications as compared to the gradient edge map energy of snakes then a simplified optimization scheme is presented accounting for internal and external energy in separate steps this leads to a complete treatment which is described in the last sections of the paper 4 and 5 the optimization technique used here is mostly heuristic and is thus presented without a formal proof but is believed to fill a gap between snakes and other useful image representations such as split and merge regions or mixed line labels image fields

on the sandpile group of 3 n twisted bracelets abstract the sandpile group of a graph is an abelian group that arises in several contexts and a refinement of the number of spanning trees of the graph it is a subtle isomorphism invariant of the graph and closely connected with the graph laplacian matrix in this paper the abstract structures of the sandpile groups on 3 n twisted bracelets are determined and it is shown that the sandpile groups of those twisted bracelets are always isomorphic the direct sum of two or three cyclic groups

a general discrete contour model in two three and four dimensions for topology adaptive multichannel segmentation we present a discrete contour model for the segmentation of image data with any dimension of image domain and value range the model consists of a representation using simplex meshes and a mechanical formulation of influences that drive an iterative segmentation the object s representation as well as the influences are valid for any dimension of the image domain the image influences introduced here can combine information from independent channels of higher dimensional value ranges additionally the topology of the model automatically adapts to objects contained in images noncontextual tests have validated the ability of the model to reproducibly delineate synthetic objects in particular images with a signal to noise ratio of snr spl les 0 5 are delineated within two pixels of their ground truth contour contextual validations have shown the applicability of the model for medical image analysis in image domains of two three and four dimensions in single as well as multichannel value ranges

a class of constrained clustering algorithms for object boundary extraction boundary extraction is a key task in many image analysis operations this paper describes a class of constrained clustering algorithms for object boundary extraction that includes several well known algorithms proposed in different fields deformable models constrained clustering data ordering and traveling salesman problems the algorithms belonging to this class are obtained by the minimization of a cost function with two terms a quadratic regularization term and an image dependent term defined by a set of weighting functions the minimization of the cost function is achieved by lowpass filtering the previous model shape and by attracting the model units toward the centroids of their attraction regions to define a new algorithm belonging to this class the user has to specify a regularization matrix and a set of weighting functions that control the attraction of the model units toward the data the usefulness of this approach is twofold it provides a unified framework for many existing algorithms in pattern recognition and deformable models and allows the design of new recursive schemes

on the sandpile group of the cone of a graph abstract in this article we study the sandpile group of the cone of a graph after introducing the concept of uniform homomorphism of graphs we prove that every surjective uniform homomorphism of graphs induces an injective homomorphism between their sandpile groups also we establish a relationship between the sandpile group of the cone of the cartesian product of graphs and the sandpile group of the cone of their factors as an application of these results we obtain an explicit description of a set of generators of the sandpile group of the cone of the hypercube

on the foundations of relaxation labeling processes a large class of problems can be formulated in terms of the assignment of labels to objects frequently processes are needed which reduce ambiguity and noise and select the best label among several possible choices relaxation labeling processes are just such a class of algorithms they are based on the parallel use of local constraints between labels this paper develops a theory to characterize the goal of relaxation labeling the theory is founded on a definition of con sistency in labelings extending the notion of constraint satisfaction in certain restricted circumstances an explicit functional exists that can be maximized to guide the search for consistent labelings this functional is used to derive a new relaxation labeling operator when the restrictions are not satisfied the theory relies on variational cal culus it is shown that the problem of finding consistent labelings is equivalent to solving a variational inequality a procedure nearly identical to the relaxation operator derived under restricted circum stances serves in the more general setting further a local convergence result is established for this operator the standard relaxation labeling formulas are shown to approximate our new operator which leads us to conjecture that successful applications of the standard methods are explainable by the theory developed here observations about con vergence and generalizations to higher order compatibility relations are described

markov random field texture models we consider a texture to be a stochastic possibly periodic two dimensional image field a texture model is a mathematical procedure capable of producing and describing a textured image we explore the use of markov random fields as texture models the binomial model where each point in the texture has a binomial distribution with parameter controlled by its neighbors and number of tries equal to the number of gray levels was taken to be the basic model for the analysis a method of generating samples from the binomial model is given followed by a theoretical and practical analysis of the method s convergence examples show how the parameters of the markov random field control the strength and direction of the clustering in the image the power of the binomial model to produce blurry sharp line like and blob like textures is demonstrated natural texture samples were digitized and their parameters were estimated under the markov random field model a hypothesis test was used for an objective assessment of goodness of fit under the markov random field model overall microtextures fit the model well the estimated parameters of the natural textures were used as input to the generation procedure the synthetic microtextures closely resembled their real counterparts while the regular and inhomogeneous textures did not

an image analysis problem in electron microscopy abstract this article considers the problem of identifying the irregular boundary of a magnetic domain in a thin multilayer film using data in the form of an electron micrograph two approaches are illustrated both of which are based on the concept of two smooth intensity surfaces one corresponding to the domain and one corresponding to the background so that the objective is to determine the boundary between the parts of the image where the two surfaces are present in the first a hierarchical bayesian approach priors are assumed for the set of domain background states and for the two intensity surfaces and restoration is carried out using a version of besag s icm procedure it is shown that it is important to initialize the method efficiently the second approach uses a template like model for the boundary and also relies on a bayesian approach the results from the second approach can be used as an end in themselves or as a way of initializing the more flexible first approach several illustrati

deformable shape detection and description via model based region grouping a method for deformable shape detection and recognition is described deformable shape templates are used to partition the image into a globally consistent interpretation determined in part by the minimum description length principle statistical shape models enforce the prior probabilities on global parametric deformations for each object class once trained the system autonomously segments deformed shapes from the background while not merging them with adjacent objects or shadows the formulation can be used to group image regions obtained via any region segmentation algorithm e g texture color or motion the recovered shape models can be used directly in object recognition experiments with color imagery are reported

the critical group of km cn abstract in this paper we will show that the structure of the critical group of the graph k m p n is z tz z mtz m 2 where t 1 m 2 4 m x 1 n x 2 n where x 1 and x 2 are the two roots of the quadratic x 2 m 2 x 1 0

on deformable models for visual pattern recognition this paper reviews model based methods for non rigid shape recognition these methods model match and classify non rigid shapes which are generally problematic for conventational algorithms using rigid models issues including model representation optimization criteria formulation model matching and classification are examined in detail with the objective to provide interested researchers a roadmap for exploring the field this paper emphasizes on 2d deformable models their potential applications and future research directions particularly on deformable pattern classification are discussed

unimodular equivalence of graphs abstract let g be a simple graph with n vertices and m edges denote by q the vertex edge incidence matrix corresponding to some orientation of the edges of g define l g qqt and k g qtq then l g is the so called laplacian matrix and k g its edge version viewed as integer matrices the smith normal form of l g is complicated but the smith normal form of k g for connected graphs is always i n 2 n 0 m n 1 an edge version of the matrix tree theorem is used in the proof there is an application to digraph flows with constant resultants over abelian groups finally if l g and l h are congruent then g and h have the same chromatic polynomial

a sharp and strict l p inequality for stochastic integrals on donne une nouvelle preuve d une inegalite lp pointue pour des integrales stochastiques qui permet de montrer que l inegalite stricte est maintenue dans tous les cas non triviaux

sharp martingale inequalities and applications to riesz transforms on manifolds lie groups and gauss space abstract we prove new sharp l p logarithmic and weak type inequalities for martingales under the assumption of differential subordination the l p estimates are feynman kac type versions of burkholder s celebrated martingale transform inequalities from the martingale l p inequalities we obtain that riesz transforms on manifolds of nonnegative bakry emery ricci curvature have exactly the same l p bounds as those known for riesz transforms in the flat case of r d from the martingale logarithmic and weak type inequalities we obtain similar inequalities for riesz transforms on compact lie groups and spheres combining the estimates for spheres with poincare s limiting argument we deduce the corresponding results for riesz transforms associated with the ornstein uhlenbeck semigroup thus providing some extensions of p a meyer s l p inequalities

the critical group of a threshold graph the critical group of a connected graph is a finite abelian group whose order is the number of spanning trees in the graph the structure of this group is a subtle isomorphism invariant that has received much attention recently partly due to its relation to the graph laplacian and chip firing games however the group structure has been determined for relatively few classes of graphs based on computer evidence we conjecture the exact group structure for a well studied class of graphs having integer spectra the threshold graphs and prove this conjecture for the subclass which we call generic threshold graphs

on the critical group of the n cube abstract reiner proposed two conjectures about the structure of the critical group of the n cube q n in this paper we confirm them furthermore we describe its p primary structure for all odd primes p the results are generalized to cartesian product of complete graphs k n 1 k n k by jacobson niedermaier and reiner

a bayesian approach to dynamic contours through stochastic sampling and simulated annealing in many applications of image analysis simply connected objects are to be located in noisy images during the last 5 6 years active contour models have become popular for finding the contours of such objects connected to these models are iterative algorithms for finding the minimizing energy curves making the curves behave dynamically through the iterations these approaches do however have several disadvantages the numerical algorithms that are in use constrain the models that can be used furthermore in many cases only local minima can be achieved in this paper the author discusses a method for curve detection based on a fully bayesian approach a model for image contours which allows the number of nodes on the contours to vary is introduced iterative algorithms based on stochastic sampling is constructed which make it possible to simulate samples from the posterior distribution making estimates and uncertainty measures of specific quantities available further simulated annealing schemes making the curve move dynamically towards the global minimum energy configuration are presented in theory no restrictions on the models are made in practice however computational aspects must be taken into consideration when choosing the models much more general models than the one used for active contours may however be applied the approach is applied to ultrasound images of the left ventricle and to magnetic resonance images of the human brain and show promising results

precise segmentation of multimodal images we propose new techniques for unsupervised segmentation of multimodal grayscale images such that each region of interest relates to a single dominant mode of the empirical marginal probability distribution of grey levels we follow the most conventional approaches in that initial images and desired maps of regions are described by a joint markov gibbs random field mgrf model of independent image signals and interdependent region labels however our focus is on more accurate model identification to better specify region borders each empirical distribution of image signals is precisely approximated by a linear combination of gaussians lcg with positive and negative components we modify an expectation maximization em algorithm to deal with the lcgs and also propose a novel em based sequential technique to get a close initial lcg approximation with which the modified em algorithm should start the proposed technique identifies individual lcg models in a mixed empirical distribution including the number of positive and negative gaussians initial segmentation based on the lcg models is then iteratively refined by using the mgrf with analytically estimated potentials the convergence of the overall segmentation algorithm at each stage is discussed experiments show that the developed techniques segment different types of complex multimodal medical images more accurately than other known algorithms

variable neighborhood search for extremal graphs 16 some conjectures related to the largest eigenvalue of a graph abstract we consider four conjectures related to the largest eigenvalue of the adjacency matrix of a graph i e to the index of the graph three of them have been formulated after some experiments with the programming system autographix designed for finding extremal graphs with respect to given properties by the use of variable neighborhood search the conjectures are related to the maximal value of the irregularity and spectral spread in n vertex graphs to a nordhaus gaddum type upper bound for the index and to the maximal value of the index for graphs with given numbers of vertices and edges none of the conjectures has been resolved so far we present partial results and provide some indications that the conjectures are very hard

differential subordination and strong differential subordination for continuous time martingales and related sharp inequalities let x and y be two continuous time martingales if quadratic variation of x minus that of y is a nondecreasing and nonnegative function of time we say that y is differentially subordinate to x and prove that y p p 1 x p for 1 p where p p v q and q is the conjugate of p this inequality contains burkholder s l p inequality for stochastic integrals which implies that the above inequality is sharp we also extend his concept of strong differential subordination and several other of his inequalities and sharpen an inequality of banuelos

constructably laplacian integral graphs a graph is laplacian integral if the spectrum of its laplacian matrix consists entirely of integers we consider the class of constructably laplacian integral graphs those graphs that be constructed from an empty graph by adding a sequence of edges in such a way that each time a new edge is added the resulting graph is laplacian integral we characterize the constructably laplacian integral graphs in terms of certain forbidden vertex induced subgraphs and consider the number of nonisomorphic laplacian integral graphs that can be constructed by adding a suitable edge to a constructably laplacian integral graph we also discuss the eigenvalues of constructably laplacian integral graphs and identify families of isospectral nonisomorphic graphs within the class

compact object recognition using energy function based optimization describes a method of recognizing objects whose contours can be represented in smoothly varying polar coordinate form both low and high level information about the object contour smoothness and edge sharpness at the low level and contour shape at the high level are incorporated into a single energy function that defines a 1d cyclic markov random field 1dcmrf this 1dcmrf is based on a polar coordinate object representation whose center can be initialized at any location within the object the recognition process is based on energy function minimization which is implemented by simulated annealing