multiregion image segmentation by parametric kernel graph cuts the purpose of this study is to investigate multiregion graph cut image partitioning via kernel mapping of the image data the image data is transformed implicitly by a kernel function so that the piecewise constant model of the graph cut formulation becomes applicable the objective function contains an original data term to evaluate the deviation of the transformed data within each segmentation region from the piecewise constant model and a smoothness boundary preserving regularization term the method affords an effective alternative to complex modeling of the original image data while taking advantage of the computational benefits of graph cuts using a common kernel function energy minimization typically consists of iterating image partitioning by graph cut iterations and evaluations of region parameters via fixed point computation a quantitative and comparative performance assessment is carried out over a large number of experiments using synthetic grey level data as well as natural images from the berkeley database the effectiveness of the method is also demonstrated through a set of experiments with real images of a variety of types such as medical synthetic aperture radar and motion maps

modularity maximization using completely positive programming abstract community detection is one of the most prominent problems of social network analysis in this paper a novel method for modularity maximization mm for community detection is presented which exploits the alternating direction augmented lagrangian adal method for maximizing a generalized form of newman s modularity function we first transform newman s modularity function into a quadratic program and then use completely positive programming cpp to map the quadratic program to a linear program which provides the globally optimal maximum modularity partition in order to solve the proposed cpp problem a closed form solution using the adal merged with a rank minimization approach is proposed the performance of the proposed method is evaluated on several real world data sets used for benchmarks community detection simulation results shows the proposed technique provides outstanding results in terms of modularity value for crisp partitions

stereo without epipolar lines a maximum flow formulation this paper describes a new algorithm for solving the stereo correspondence problem with a global 2 d optimization by transforming it into a maximum flow problem in a graph this transformation effectively removes explicit use of epipolar geometry thus allowing direct use of multiple cameras with arbitrary geometries the maximum flow solved both efficiently and globally yields a minimum cut that corresponds to a disparity surface for the whole image at once this global and efficient approach to stereo analysis allows the reconstruction to proceed in an arbitrary volume of space and provides a more accurate and coherent depth map than the traditional stereo algorithms in particular smoothness is applied uniformly instead of only along epipolar lines while the global optimality of the depth surface is guaranteed results show improved depth estimation as well as better handling of depth discontinuities while the worst case running time is o n 1 5 d 1 5 log nd the observed average running time is o n 1 2 d 1 3 for an image size of n pixels and depth resolution d

accurate and scalable surface representation and reconstruction from images we introduce a new surface representation method called patchwork to extend three dimensional surface reconstruction capabilities from multiple images a patchwork is the combination of several patches that are built one by one this design potentially allows for the reconstruction of an object with arbitrarily large dimensions while preserving a fine level of detail we formally demonstrate that this strategy leads to a spatial complexity independent of the dimensions of the reconstructed object and to a time complexity that is linear with respect to the object area the former property ensures that we never run out of storage and the latter means that reconstructing an object can be done in a reasonable amount of time in addition we show that the patchwork representation handles equivalently open and closed surfaces whereas most of the existing approaches are limited to a specific scenario an open or closed surface but not both the patchwork concept is orthogonal to the method chosen for surface optimization most of the existing optimization techniques can be cast into this framework to illustrate the possibilities offered by this approach we propose two applications that demonstrate how our method dramatically extends a recent accurate graph technique based on minimal cuts we first revisit the popular carving techniques this results in a well posed reconstruction problem that still enjoys the tractability of voxel space we also show how we can advantageously combine several image driven criteria to achieve a finely detailed geometry by surface propagation these two examples demonstrate the versatility and flexibility of patchwork reconstruction they underscore other properties inherited from patchwork representation although some min cut methods have difficulty in handling complex shapes e g with complex topologies they can naturally manipulate any geometry through the patchwork representation while preserving their intrinsic qualities the above properties of patchwork representation and reconstruction are demonstrated with real image sequences

graph partitioning using linear and semidefinite programming graph partition is used in the telecommunication industry to subdivide a transmission network into small clusters we consider both linear and semidefinite relaxations for the equipartition problem and present numerical results on real data from france telecom networks with up 900 nodes and also on randomly generated problems

anti modularity and anti community detecting in complex networks abstract many networks of interest in sciences and social research can be divided naturally into anti communities the problem of detecting and characterizing such anti community structure has attracted recent attention in this paper we first define the anti modularity as a quantitative measure of anti community partitioning on a network we also theoretically and empirically show the reliability of anti modularity as a measurement of the quality of an anti community partitioning a label propagation algorithm lpad for anti community detection is proposed experimental results on synthetic and real world networks show that our algorithm lpad can obtain higher quality anti community partitioning than other methods

a nonlinear programming algorithm for solving semidefinite programs via low rank factorization in this paper we present a nonlinear programming algorithm for solving semidefinite programs sdps in standard form the algorithm s distinguishing feature is a change of variables that replaces the symmetric positive semidefinite variable x of the sdp with a rectangular variable r according to the factorization x rr t the rank of the factorization i e the number of columns of r is chosen minimally so as to enhance computational speed while maintaining equivalence with the sdp fundamental results concerning the convergence of the algorithm are derived and encouraging computational results on some large scale test problems are also presented

on the rank of extreme matrices in semidefinite programs and the multiplicity of optimal eigenvalues we derive some basic results on the geometry of semidefinite programming sdp and eigenvalue optimization i e the minimization of the sum of the k largest eigenvalues of a smooth matrix valued function we provide upper bounds on the rank of extreme matrices in sdps and the first theoretically solid explanation of a phenomenon of intrinsic interest in eigenvalue optimization in the spectrum of an optimal matrix the kth and k 1 st largest eigenvalues tend to be equal and frequently have multiplicity greater than two this clustering is intuitively plausible and has been observed as early as 1975 when the matrix valued function is affine we prove that clustering must occur at extreme points of the set of optimal solutions if the number of variables is sufficiently large we also give a lower bound on the multiplicity of the critical eigenvalue these results generalize to the case of a general matrix valued function under appropriate conditions

a stability analysis of two dimensional nonlinear digital state space filters two different methods for a stability analysis of 2 d nonlinear discrete state space systems under zero input conditions are provided the first method reduces the task of testing a 2 d discrete nonlinear or shift varying system to a single 2 d linear stability test of a system matrix with nonnegative system matrix entries the second method is based on a number of norm tests for products of extreme matrices and can be considered the 2 d counterpart of the method for 1 d systems described by k t erickson and a n michel 1985 both of the introduced methods are based on the sector description of the nonlinearity and can be used to analyze digital filter stability under finite word length effects

community detection in complex networks using extremal optimization we propose a method to find the community structure in complex networks based on an extremal optimization of the value of modularity the method outperforms the optimal modularity found by the existing algorithms in the literature giving a better understanding of the community structure we present the results of the algorithm for computer simulated and real networks and compare them with other approaches the efficiency and accuracy of the method make it feasible to be used for the accurate identification of community structure in large complex networks

benchmark graphs for testing community detection algorithms community structure is one of the most important features of real networks and reveals the internal organization of the nodes many algorithms have been proposed but the crucial issue of testing i e the question of how good an algorithm is with respect to others is still open standard tests include the analysis of simple artificial graphs with a built in community structure that the algorithm has to recover however the special graphs adopted in actual tests have a structure that does not reflect the real properties of nodes and communities found in real networks here we introduce a class of benchmark graphs that account for the heterogeneity in the distributions of node degrees and of community sizes we use this benchmark to test two popular methods of community detection modularity optimization and potts model clustering the results show that the benchmark poses a much more severe test to algorithms than standard benchmarks revealing limits that may not be apparent at a first analysis

column generation algorithms for exact modularity maximization in networks finding modules or clusters in networks currently attracts much attention in several domains the most studied criterion for doing so due to newman and girvan phys rev e 69 026113 2004 is modularity maximization many heuristics have been proposed for maximizing modularity and yield rapidly near optimal solution or sometimes optimal ones but without a guarantee of optimality there are few exact algorithms prominent among which is a paper by xu et al eur phys j b 60 231 2007 modularity maximization can also be expressed as a clique partitioning problem and the row generation algorithm of grotschel and wakabayashi math program 45 59 1989 applied we propose to extend both of these algorithms using the powerful column generation methods for linear and non linear integer programming performance of the four resulting algorithms is compared on problems from the literature instances with up to 512 entities are solved exactly moreover the computing time of previously solved problems are reduced substantially

dense features for semi dense stereo correspondence we present a new feature based algorithm for stereo correspondence most of the previous feature based methods match sparse features like edge pixels producing only sparse disparity maps our algorithm detects and matches dense features between the left and right images of a stereo pair producing a semi dense disparity map our dense feature is defined with respect to both images of a stereo pair and it is computed during the stereo matching process not a preprocessing step in essence a dense feature is a connected set of pixels in the left image and a corresponding set of pixels in the right image such that the intensity edges on the boundary of these sets are stronger than their matching error which is the difference in intensities between corresponding boundary pixels our algorithm produces accurate semi dense disparity maps leaving featureless regions in the scene unmatched it is robust requires little parameter tuning can handle brightness differences between images nonlinear errors and is fast linear complexity

revealing network communities with a nonlinear programming method the detection of network communities has attracted significant research attention lately to discover such structures a mathematical measure known as modularity is often used for optimization unfortunately the optimization is np hard and approximated solutions have to be sought for large networks in this paper we propose a nonlinear programming method for optimization that is based on the augmented lagrangian technique we further identify the inherent connection between the proposed method and positive semi definite programming and its low rank reduction which helps to justify the performance of the method compared with previously published approaches the proposed method is empirically efficient and effective at detecting underlying network communities

exact optimization for markov random fields with convex priors we introduce a method to solve exactly a first order markov random field optimization problem in more generality than was previously possible the mrf has a prior term that is convex in terms of a linearly ordered label set the method maps the problem into a minimum cut problem for a directed graph for which a globally optimal solution can be found in polynomial time the convexity of the prior function in the energy is shown to be necessary and sufficient for the applicability of the method

robust parameter estimation in computer vision estimation techniques in computer vision applications must estimate accurate model parameters despite small scale noise in the data occasional large scale measurement errors outliers and measurements from multiple populations in the same data set increasingly robust estimation techniques some borrowed from the statistics literature and others described in the computer vision literature have been used in solving these parameter estimation problems ideally these techniques should effectively ignore the outliers and measurements from other populations treating them as outliers when estimating the parameters of a single population two frequently used techniques are least median of squares lms p j rousseeuw j amer statist assoc 79 1984 pp 871 880 and m estimators robust statistics the approach based on influence functions f r hampel et al john wiley 1986 robust statistics p j huber john wiley 1981 lms handles large fractions of outliers up to the theoretical limit of 50 for estimators invariant to affine changes to the data but has low statistical efficiency m estimators have higher statistical efficiency but tolerate much lower percentages of outliers unless properly initialized while robust estimators have been used in a variety of computer vision applications three are considered here in analysis of range images images containing depth or x y z measurements at each pixel instead of intensity measurements robust estimators have been used successfully to estimate surface model parameters in small image regions in stereo and motion analysis they have been used to estimate parameters of what is called the fundamental matrix which characterizes the relative imaging geometry of two cameras imaging the same scene recently robust estimators have been applied to estimating a quadratic image to image transformation model necessary to create a composite mosaic image from a series of images of the human retina in each case a straightforward application of standard robust estimators is insufficient and carefully developed extensions are used to solve the problem

matching 3 d models to 2 d images we consider the problem of analytically characterizing the set of all 2 d images that a group of 3 d features may produce and demonstrate that this is a useful thing to do our results apply for simple point features and point features with associated orientation vectors when we model projection as a 3 d to 2 d affine transformation we show how to represent the set of images that a group of 3 d points produces with two lines 1 d subspaces one in each of two orthogonal high dimensional spaces where a single image group corresponds to one point in each space the images of groups of oriented point features can be represented by a 2 d hyperbolic surface in a single high dimensional space the problem of matching an image to models is essentially reduced to the problem of matching a point to simple geometric structures moreover we show that these are the simplest and lowest dimensional representations possible for these cases we demonstrate the value of this way of approaching matching by applying our results to a variety of vision problems in particular we use this result to build a space efficient indexing system that performs 3 d to 2 d matching by table lookup this system is analytically built and accessed accounts for the effects of sensing error and is tested on real images we also derive new results concerning the existence of invariants and non accidental properties in this domain finally we show that oriented points present unexpected difficulties indexing requires fundamentally more space with oriented than with simple points we must use more images in a motion sequence to determine the affine structure of oriented points and the linear combinations result does not hold for oriented points

a surface reconstruction method using global graph cut optimization surface reconstruction from multiple calibrated images has been mainly approached using local methods either as a continuous optimization problem driven by level sets or by discrete volumetric methods such as space carving we propose a direct surface reconstruction approach which starts from a continuous geometric functional that is minimized up to a discretization by a global graph cut algorithm operating on a 3d embedded graph the method is related to the stereo disparity computation based on graph cut formulation but fundamentally different in two aspects first existing stereo disparity methods are only interested in obtaining layers of constant disparity while we focus on high resolution surface geometry second most of the existing graph cut algorithms only reach approximate solutions while we guarantee a global minimum the whole procedure is consistently incorporated into a voxel representation that handles both occlusions and discontinuities we demonstrate our algorithm on real sequences yielding remarkably detailed surface geometry up to 1 10th of a pixel

fast approximate energy minimization via graph cuts many tasks in computer vision involve assigning a label such as disparity to every pixel a common constraint is that the labels should vary smoothly almost everywhere while preserving sharp discontinuities that may exist e g at object boundaries these tasks are naturally stated in terms of energy minimization the authors consider a wide class of energies with various smoothness constraints global minimization of these energy functions is np hard even in the simplest discontinuity preserving case therefore our focus is on efficient approximation algorithms we present two algorithms based on graph cuts that efficiently find a local minimum with respect to two types of large moves namely expansion moves and swap moves these moves can simultaneously change the labels of arbitrarily large sets of pixels in contrast many standard algorithms including simulated annealing use small moves where only one pixel changes its label at a time our expansion algorithm finds a labeling within a known factor of the global minimum while our swap algorithm handles more general energy functions both of these algorithms allow important cases of discontinuity preserving energies we experimentally demonstrate the effectiveness of our approach for image restoration stereo and motion on real data with ground truth we achieve 98 percent accuracy

robust diagonal stabilization an lmi approach addresses the problem of robust diagonal stabilization for discrete time systems linear matrix inequality lmi conditions are derived for the search of a diagonal solution to the associated lyapunov equation this approach can be applied to guarantee stability of quantized systems and to find numerous illustrative applications e g for the design of robust digital filters

detection of community structures in networks via global optimization abstract we present an analysis of communality structure in networks based on the application of simulated annealing techniques in this case we use as cost function the already introduced modularity q 1 which is based on the relative number of links within a commune against the number of links that would correspond in case the links were distributed randomly we compare the results of our approach against other methodologies based on betweenness analysis and show that in all cases a better community structure can be attained

suppression of limit cycles in the first order two dimensional direct form digital filter with a controlled rounding arithmetic the first order two dimensional direct form digital filter with magnitude truncation is known to be free from limit cycles for a limited range of allowed filter coefficients in this correspondence the quantization technique of controlled rounding is used to extend the region of filter coefficients for which suppression of limit cycles can be proved with controlled rounding a signal is quantized in the direction of a control signal which is formed by an integer combination of preceding signal values the absence of limit cycles is proved with a properly chosen lyapunov function

a divide and link algorithm for hierarchical clustering in networks this paper introduces a hierarchical clustering algorithm in networks based upon a first divisive stage to break the graph and a second linking stage which is used to join nodes as a particular case this algorithm is applied to the specific problem of community detection in social networks where a betweenness measure is considered for the divisive criterion and a similarity measure associated to data is used for the linking criterion we show that this algorithm is very flexible as well as quite competitive from both a performance and a computational complexity point of view in relation with a set of state of the art algorithms furthermore the output given by the proposed algorithm allows to show in a dynamic and interpretable way the evolution of how the groups are split in the network

multilevel enhancement and detection of stereo disparity surfaces abstract the problem of stereo vision has been of increasing interest to the computer vision community over the past decade this paper presents a new computational framework for matching a pair of stereo images arising from viewing the same object from two different positions in contrast to previous work this approach formulates the matching problem as detection of a bright coherent disparity surface in a 3d image called the spatio disparity space sds image the sds images represents the goodness of each and every possible match a nonlinear filter is proposed for enhancing the disparity surface in the sds image and for suppressing the noise this filter is used to construct a hyperpyramid representation of the sds image then the disparity surface is detected using a coarse to fine control structure the proposed method is robust to photometric and geometric distortions in the stereo images and has a number of computational advantages it produces good results for complex scenes

modularity from fluctuations in random graphs and complex networks the mechanisms by which modularity emerges in complex networks are not well understood but recent reports have suggested that modularity may arise from evolutionary selection we show that finding the modularity of a network is analogous to finding the ground state energy of a spin system moreover we demonstrate that due to fluctuations stochastic network models give rise to modular networks specifically we show both numerically and analytically that random graphs and scale free networks have modularity we argue that this fact must be taken into consideration to define statistically significant modularity in complex networks

robustness of community structure in networks the discovery of community structure is a common challenge in the analysis of network data many methods have been proposed for finding community structure but few have been proposed for determining whether the structure found is statistically significant or whether conversely it could have arisen purely as a result of chance in this paper we show that the significance of community structure can be effectively quantified by measuring its robustness to small perturbations in network structure we propose a suitable method for perturbing networks and a measure of the resulting change in community structure and use them to assess the significance of community structure in a variety of networks both real and computer generated

stereo matching using belief propagation in this paper we formulate the stereo matching problem as a markov network and solve it using bayesian belief propagation the stereo markov network consists of three coupled markov random fields that model the following a smooth field for depth disparity a line process for depth discontinuity and a binary process for occlusion after eliminating the line process and the binary process by introducing two robust functions we apply the belief propagation algorithm to obtain the maximum a posteriori map estimation in the markov network other low level visual cues e g image segmentation can also be easily incorporated in our stereo model to obtain better stereo results experiments demonstrate that our methods are comparable to the state of the art stereo algorithms for many test cases

a pixel dissimilarity measure that is insensitive to image sampling because of image sampling traditional measures of pixel dissimilarity can assign a large value to two corresponding pixels in a stereo pair even in the absence of noise and other degrading effects we propose a measure of dissimilarity that is provably insensitive to sampling because it uses the linearly interpolated intensity functions surrounding the pixels experiments on real images show that our measure alleviates the problem of sampling with little additional computational overhead

stereo correspondence with occlusion handling in a symmetric patch based graph cuts model a novel patch based correspondence model is presented in this paper many segment based correspondence approaches have been proposed in recent years untextured pixels and boundaries of discontinuities are imposed with hard constraints by the discontinuity assumption that large disparity variation only happens at the boundaries of segments in the above approaches significant improvements on performance of untextured and discontinuity area have been reported but the performance near occlusion is not satisfactory because a segmented region in one image may be only partially visible in the other one to solve this problem we utilize the observation that the shared edge of a visible area and an occluded area corresponds to the discontinuity in the other image so the proposed model conducts color segmentation on both images first and then a segment in one image is further cut into smaller patches corresponding to the boundaries of segments in the other when it is assigned with a disparity different visibility of patches in one segment is allowed the uniqueness constraint in a segment level is used to compute the occlusions an energy minimization framework using graph cuts is proposed to find a global optimal configuration including both disparities and occlusions besides some measurements are taken to make our segment based algorithm suffer less from violation of the discontinuity assumption experimental results have shown superior performance of the proposed approach especially on occlusions untextured areas and near discontinuities

the development and comparison of robust methodsfor estimating the fundamental matrix this paper has two goals the first is to develop a variety of robust methods for the computation of the fundamental matrix the calibration free representation of camera motion the methods are drawn from the principal categories of robust estimators viz case deletion diagnostics m estimators and random sampling and the paper develops the theory required to apply them to non linear orthogonal regression problems although a considerable amount of interest has focussed on the application of robust estimation in computer vision the relative merits of the many individual methods are unknown leaving the potential practitioner to guess at their value the second goal is therefore to compare and judge the methods comparative tests are carried out using correspondences generated both synthetically in a statistically controlled fashion and from feature matching in real imagery in contrast with previously reported methods the goodness of fit to the synthetic observations is judged not in terms of the fit to the observations per se but in terms of fit to the ground truth a variety of error measures are examined the experiments allow a statistically satisfying and quasi optimal method to be synthesized which is shown to be stable with up to 50 percent outlier contamination and may still be used if there are more than 50 percent outliers performance bounds are established for the method and a variety of robust methods to estimate the standard deviation of the error and covariance matrix of the parameters are examined the results of the comparison have broad applicability to vision algorithms where the input data are corrupted not only by noise but also by gross outliers

registration and interactive planar segmentation for stereo images of polyhedral scenes we introduce a two step iterative segmentation and registration method to find coplanar surfaces among stereo images of a polyhedral environment the novelties of this paper are i to propose a user defined initialization easing the image matching and segmentation ii to incorporate color appearance and planar projection information into a bayesian segmentation scheme and iii to add consistency to the projective transformations related to the polyhedral structure of the scenes the method utilizes an assisted bayesian color segmentation scheme the initial user assisted segmentation is used to define search regions for planar homography image registration the two reliable methods cooperate to obtain probabilities for coplanar regions with similar color information that are used to get a new segmentation by means of quadratic markov measure fields qmmf we search for the best regions by iterating both steps registration and segmentation

non rigid image registration of brain magnetic resonance images using graph cuts we present a graph cuts based method for non rigid medical image registration on brain magnetic resonance images in this paper the non rigid medical image registration problem is reformulated as a discrete labeling problem based on a voxel to voxel intensity similarity measure each voxel in the source image is assigned a displacement label which represents a displacement vector indicating which position in the floating image it is spatially corresponding to in the proposed method a smoothness constraint based on the first derivative is used to penalize sharp changes in the adjacent displacement labels across voxels the image registration problem is therefore modeled by two energy terms based on intensity similarity and smoothness of the displacement field these energy terms are submodular and can be optimized by using the graph cuts method via email protected expansions which is a powerful combinatorial optimization tool and capable of yielding either a global minimum or a local minimum in a strong sense using the realistic brain phantoms obtained from the simulated brain database we compare the registration results of the proposed method with two state of the art medical image registration approaches free form deformation based method and demons method in addition the registration results are also compared with that of the linear programming based image registration method it is found that the proposed method is more robust against different challenging non rigid registration cases with consistently higher registration accuracy than those three methods and gives realistic recovered deformation fields

surfaces with occlusions from layered stereo we propose a new binocular stereo algorithm that estimates scene structure as a collection of smooth surface patches the disparities within each patch are modeled by a continuous valued spline while the extent of each patch is represented via a pixelwise partitioning of the images disparities and extents are alternately estimated in an iterative energy minimization framework experimental results demonstrate that for scenes consisting of smooth surfaces the proposed algorithm significantly improves upon the state of the art

predicting protein complexes in protein interaction networks using a core attachment algorithm based on graph communicability studying protein complexes is very important in biological processes because it helps reveal the structure functionality relationships in a protein complex much attention has been paid to accurately predicting the protein complexes from the increasing amount of protein protein interaction ppi data almost all of the current algorithms that concern the detection of protein complexes focus on discovering dense subgraphs based on the observation that dense subgraphs in a biological network may correspond to protein complexes however such an assumption would throw away further topological information about complexes in this paper introducing the core attachment concept a novel core attachment algorithm is developed by detecting the cores and attachments respectively to detect the cores of protein complexes a virtual network is constructed using the eigenvalues and eigenvectors of the network involved where each maximal clique corresponds to a protein complex core with this notion the problem of detecting protein complex cores is transformed into the classic all cliques problem the attachments are then merged into their cores to yield biologically meaningful complexes a comprehensive comparison between mcl dpclus coach decaff and our algorithm has been made by comparing the predicted protein complexes with the benchmarked complexes experimental results indicate that our algorithm outperforms the mcl dpclus and decaff and has comparative performance with the coach algorithm in terms of the accuracy of prediction moreover the detected complexes with core attachment structures match well with the benchmark data demonstrating that our algorithm can provide more insightful perspectives robustness analysis further shows that the algorithm is very robust

maximizing modularity intensity for community partition and evolution most previous studies of community partition have often focused on the network topology the topology and link weights are in fact closely associated with each other for community formation in complex networks this paper proposes a function modularity intensity a variation of modularity density d value for evaluating the cohesiveness of a community which considers links between vertices as well as link weights the results showed that maximizing the modularity intensity not only can resolve the resolution limits problem but also achieve better performance for community partition to further evaluate the function and clarify the weight topology correlation with communities we give a simple model to simulate the topology and link weights development for community evolution and use the modularity intensity to capture communities of networks in each step of this process in this model a network is treated as a fuzzy relation and two operations of the fuzzy relation are used to make the link weights stronger and weaker respectively with the growth of the network in each evolutionary step by simulation experiments we found that in the model the modularity intensity catches communities of networks that undergo a gradual transition from faintness to clearness our model also reproduces the finding of granovetter that strong links are confined mainly in tight communities and the links between communities are predominantly weak from the results above we believe that the modularity intensity gives a more comprehensive evaluation for communities and by studying the weight topology correlation this model provides a new view for community evolution