robust stability and control of uncertain linear discrete time periodic systems with time delay this paper deals with the problems of robust stability analysis and robust control of linear discrete time periodic systems with a delayed state and subject to polytopic type parameter uncertainty in the state space matrices a robust stability criterion independent of the time delay length as well as a delay dependent criterion is proposed where the former applies to the case of a constant time delay and the latter allows for a time varying delay lying in a given interval the developed robust stability criteria are based on affinely uncertainty dependent lyapunov krasovskii functionals and are given in terms of linear matrix inequalities these stability conditions are then applied to solve the problems of robust stabilization and robust h control via static periodic state feedback numerical examples illustrate the potentials of the proposed robust stability and control methods

density evolution for deterministic generalized product codes on the binary erasure channel at high rates generalized product codes gpcs are extensions of product codes pcs where code symbols are protected by two component codes but not necessarily arranged in a rectangular array we consider a deterministic construction of gpcs as opposed to randomized code ensembles and analyze the asymptotic performance over the binary erasure channel under iterative decoding our code construction encompasses several classes of gpcs previously proposed in the literature such as irregular pcs blockwise braided codes and staircase codes it is assumed that the component codes can correct a fixed number of erasures and that the length of each component code tends to infinity we show that this setup is equivalent to studying the behavior of a peeling algorithm applied to a sparse inhomogeneous random graph using a convergence result for these graphs we derive the density evolution equations that characterize the asymptotic decoding performance as an application we discuss the design of irregular gpcs employing a mixture of component codes with different erasure correcting capabilities

a polynomial piecewise constant approximation method based on dual constraint relaxation for segmenting images with intensity inhomogeneity abstract in the past decade several local region based level set models have been proposed to segment images with intensity inhomogeneity in general these models are designed based on one assumption i e intensity inhomogeneity is slowly varying in image domain however this assumption is not valid for those images with serious intensity inhomogeneity which inevitably leads to poor segmentation performance of existing models in this paper we propose a novel level set method named as polynomial piecewise constant approximation ppca to well segment images with serious intensity inhomogeneity the basic idea of the ppca method is to transform the original image to piecewise constant image so as to make piecewise constant segmentation criterion become applicable specially we firstly define an initial objective function with some constraint conditions to transform the original image then in order to obtain desirable piecewise constant image and highlight the anti noise performance the ppca method is used to realize the dual constraint relaxation for objective function the dual constraint relaxation reflects in two parts on one hand the objective function based on local region is exploited to replace the pointwise approximation method on the other hand considering the variance of local intensity distribution and the reliability of polynomial approximation we utilize a gaussian pyramid convolution strategy to devise polynomial fitting the ppca method relaxes the constraint condition of objective function so that the piecewise constant image is easily approximated according to piecewise constant segmentation criterion we obtain the partial differential equation based on polynomial piecewise constant approximation finally we utilize level set method to construct the energy functional the visual and quantitative experimental results demonstrate that the proposed ppca method can yield better results than existing classical local models for segmenting images with serious intensity inhomogeneity

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

random subspace based ensemble sparse representation a new random subspace based joint sparse representation model is proposed the sparse representations in multiple subspaces are integrated into an ensemble sparse representation the spectral clustering algorithm with random subspace based ensemble sparse representation is shown the semi supervised classification method with random subspace based ensemble sparse representation is described in this paper a new random subspace based ensemble sparse representation rs esr algorithm is proposed where the random subspace is introduced into sparse representation model for high dimensional data the random subspace method can not only reduce dimension of data but also make full use of effective information of data it is not like traditional dimensionality reduction methods that may lose some information of original data additionally a joint sparse representation model is emloyed to obtain the sparse representation of a sample set in the low dimensional random subspace then the sparse representations in multiple random subspaces are integrated as an ensemble sparse representation moreover the obtained rs esr is applied in classical clustering and semi supervised classification the experimental results on different real world data sets show the superiority of rs esr over traditional methods

performance analysis of ldpc coded diversity combining on rayleigh fading channels with impulsive noise spatial diversity is an effective method to mitigate the effects of fading and when used in conjunction with low density parity check ldpc codes it can achieve excellent error correcting performance noise added at each branch of the diversity combiner is generally assumed to be additive white gaussian noise but there are many applications where the received signal is impaired by noise with a non gaussian distribution in this paper we derive the exact bit error probability of different linear combining techniques on rayleigh fading channels with impulsive noise which is modeled using symmetric alpha stable distributions the relationship for the signal to noise ratios of these linear combiners is derived and then different non linear detectors are presented a detector based on the bi parameter cauchy gaussian mixture model is used and shows near optimal performance with a significant reduction in complexity when compared with the optimal detector furthermore the threshold signal to noise ratio of ldpc codes for different combining techniques on these channels is derived using density evolution and an estimation of the waterfall performance of ldpc codes is derived that reduces the gap between simulated and asymptotic performance

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

efficient erasure correcting codes we introduce a simple erasure recovery algorithm for codes derived from cascades of sparse bipartite graphs and analyze the algorithm by analyzing a corresponding discrete time random process as a result we obtain a simple criterion involving the fractions of nodes of different degrees on both sides of the graph which is necessary and sufficient for the decoding process to finish successfully with high probability by carefully designing these graphs we can construct for any given rate r and any given real number spl epsiv a family of linear codes of rate r which can be encoded in time proportional to ln 1 spl epsiv times their block length n furthermore a codeword can be recovered with high probability from a portion of its entries of length 1 spl epsiv rn or more the recovery algorithm also runs in time proportional to n ln 1 spl epsiv our algorithms have been implemented and work well in practice various implementation issues are discussed

numerical conditioning problems and solutions for nonparametric i i d statistical active contours in this paper we propose an active contour model based on nonparametric independent and identically distributed i i d statistics of the image that can segment an image without any a priori information about the intensity distributions of the region of interest or the background this is not however the first active contour model proposed to solve the segmentation problem under these same assumptions in contrast to prior active contour models based on nonparametric i i d statistics we do not formulate our optimization criterion according to any distance measure between estimated probability densities inside and outside the active contour instead treating the segmentation problem as a pixel wise classification problem we formulate an active contour to minimize the unbiased pixel wise average misclassification probability amp this not only simplifies the problem by avoiding the need to arbitrarily select among many sensible distance measures to measure the difference between the probability densities estimated inside and outside the active contour but it also solves a numerical conditioning problem that arises with such prior active contour models as a result the amp model exhibits faster convergence with higher accuracy and robustness when compared to active contour models previously formulated to solve the same nonparametric i i d statistical segmentation problem via probability distances to discuss this improved numerical behavior more precisely we introduce the notion of x201c conditioning ratio x201d and demonstrate that the proposed amp active contour is numerically better conditioned i e exhibits a much smaller conditioning ratio than prior probability distance based active contours

improving level set method for fast auroral oval segmentation auroral oval segmentation from ultraviolet imager images is of significance in the field of spatial physics compared with various existing image segmentation methods level set is a promising auroral oval segmentation method with satisfactory precision however the traditional level set methods are time consuming which is not suitable for the processing of large aurora image database for this purpose an improving level set method is proposed for fast auroral oval segmentation the proposed algorithm combines four strategies to solve the four problems leading to the high time complexity the first two strategies including our shape knowledge based initial evolving curve and neighbor embedded level set formulation can not only accelerate the segmentation process but also improve the segmentation accuracy and then the latter two strategies including the universal lattice boltzmann method and sparse field method can further reduce the time cost with an unlimited time step and narrow band computation experimental results illustrate that the proposed algorithm achieves satisfactory performance for auroral oval segmentation within a very short processing time

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

lazy random walks for superpixel segmentation we present a novel image superpixel segmentation approach using the proposed lazy random walk lrw algorithm in this paper our method begins with initializing the seed positions and runs the lrw algorithm on the input image to obtain the probabilities of each pixel then the boundaries of initial superpixels are obtained according to the probabilities and the commute time the initial superpixels are iteratively optimized by the new energy function which is defined on the commute time and the texture measurement our lrw algorithm with self loops has the merits of segmenting the weak boundaries and complicated texture regions very well by the new global probability maps and the commute time strategy the performance of superpixel is improved by relocating the center positions of superpixels and dividing the large superpixels into small ones with the proposed optimization algorithm the experimental results have demonstrated that our method achieves better performance than previous superpixel approaches

anytime reliability of spatially coupled codes anytime transmission was previously shown to be necessary and sufficient for tracking and controlling an unstable plant over a noisy channel in this paper we propose an efficient channel coding scheme for anytime transmission we design this coding scheme based on spatially coupled codes and investigate its performance over binary erasure channels bec and binary input additive white gaussian noise biawgn channels through density evolution analysis we asymptotically show the desired anytime properties of the proposed code for the bec we derive the corresponding delay exponent and numerically predict the finite length performance of the proposed anytime code we also propose adaptive window decoding techniques to ensure low complexity anytime receivers

a scaling law to predict the finite length performance of spatially coupled ldpc codes spatially coupled low density parity check sc ldpc codes are known to have excellent asymptotic properties much less is known regarding their finite length performance we propose a scaling law to predict the error probability of finite length spatially coupled code ensembles when transmission takes place over the binary erasure channel we discuss how the parameters of the scaling law are connected to fundamental quantities appearing in the asymptotic analysis of these ensembles and we verify that the predictions of the scaling law fit well to the data derived from simulations over a wide range of parameters the ultimate goal of this line of research is to develop analytic tools for the design of sc ldpc codes under practical constraints

patch alignment manifold matting image matting is generally modeled as a space transform from the color space to the alpha space by estimating the alpha factor of the model the foreground of an image can be extracted however there is some dimensional information redundancy in the alpha space it usually leads to the misjudgments of some pixels near the boundary between the foreground and the background in this paper a manifold matting framework named patch alignment manifold matting is proposed for image matting in particular we first propose a part modeling of color space in the local image patch we then perform whole alignment optimization for approximating the alpha results using subspace reconstructing error furthermore we utilize nesterov s algorithm to solve the optimization problem finally we apply some manifold learning methods in the framework and obtain several image matting methods such as named isomap matting and its derived cascade isomap matting the experimental results reveal that the manifold matting framework and its two examples are effective when compared with several representative matting methods

generalized flooding and multicue pde based image segmentation image segmentation remains an important but hard to solve problem since it appears to be application dependent with usually no a priori information available regarding the image structure moreover the increasing demands of image analysis tasks in terms of segmentation results quality introduce the necessity of employing multiple cues for improving image segmentation results in this paper we attempt to incorporate cues such as intensity contrast region size and texture in the segmentation procedure and derive improved results compared to using individual cues separately we emphasize on the overall segmentation procedure and we propose efficient simplification operators and feature extraction schemes capable of quantifying important characteristics like geometrical complexity rate of change in local contrast variations and orientation that eventually favor the final segmentation result based on the well known morphological paradigm of watershed transform segmentation which exploits intensity contrast and region size criteria we investigate its partial differential equation pde formulation and we extend it in order to satisfy various flooding criteria thus making it applicable to a wider range of images going a step further we introduce a segmentation scheme that couples contrast criteria in flooding with texture information the modeling of the proposed scheme is done via pdes and the efficient incorporation of the available contrast and texture information is done by selecting an appropriate cartoon texture image decomposition scheme the proposed coupled segmentation scheme is driven by two separate image components artoon u for contrast information and texture component the performance of the proposed segmentation scheme is demonstrated through a complete set of experimental results and substantiated using quantitative and qualitative criteria

scaling exponent of list decoders with applications to polar codes motivated by the significant performance gains which polar codes experience under successive cancellation list decoding their scaling exponent is studied as a function of the list size in particular the error probability is fixed and the tradeoff between the block length and back off from capacity is analyzed a lower bound is provided on the error probability under rm map decoding with list size l for any binary input memoryless output symmetric channel and for any class of linear codes such that their minimum distance is unbounded as the block length grows large then it is shown that under rm map decoding although the introduction of a list can significantly improve the involved constants the scaling exponent itself i e the speed at which capacity is approached stays unaffected for any finite list size in particular this result applies to polar codes since their minimum distance tends to infinity as the block length increases a similar result is proved for genie aided successive cancellation decoding when transmission takes place over the binary erasure channel namely the scaling exponent remains constant for any fixed number of helps from the genie note that since genie aided successive cancellation decoding might be strictly worse than successive cancellation list decoding the problem of establishing the scaling exponent of the latter remains open

tree structure expectation propagation for ldpc decoding over the bec we present the tree structure expectation propagation tree ep algorithm to decode low density parity check ldpc codes over discrete memoryless channels dmcs expectation propagation generalizes belief propagation bp in two ways first it can be used with any exponential family distribution over the cliques in the graph second it can impose additional constraints on the marginal distributions we use this second property to impose pairwise marginal constraints over pairs of variables connected to a check node of the ldpc code s tanner graph thanks to these additional constraints the tree ep marginal estimates for each variable in the graph are more accurate than those provided by bp we also reformulate the tree ep algorithm for the binary erasure channel bec as a peeling type algorithm tep and we show that the algorithm has the same computational complexity as bp and it decodes a higher fraction of errors we describe the tep decoding process by a set of differential equations that represents the expected residual graph evolution as a function of the code parameters the solution of these equations is used to predict the tep decoder performance in both the asymptotic regime and the finite length regimes over the bec while the asymptotic threshold of the tep decoder is the same as the bp decoder for regular and optimized codes we propose a scaling law for finite length ldpc codes which accurately approximates the tep improved performance and facilitates its optimization

statistical mechanics of error exponents for error correcting codes error exponents characterize the exponential decay when increasing message length of the probability of error of many error correcting codes to tackle the long standing problem of computing them exactly we introduce a general thermodynamic formalism that we illustrate with maximum likelihood decoding of low density parity check codes on the binary erasure channel and the binary symmetric channel in this formalism we apply the cavity method for large deviations to derive expressions for both the average and typical error exponents which differ by the procedure used to select the codes from specified ensembles when decreasing the noise intensity we find that two phase transitions take place at two different levels a glass to ferromagnetic transition in the space of codewords and a paramagnetic to glass transition in the space of codes

multigrid geometric active contour models geometric active contour models are very popular partial differential equation based tools in image analysis and computer vision we present a new multigrid algorithm for the fast evolution of level set based geometric active contours and compare it with other established numerical schemes we overcome the main bottleneck associated with most numerical implementations of geometric active contours namely the need for very small time steps to avoid instability by employing a very stable fully 2 d implicit explicit time integration numerical scheme the proposed scheme is more accurate and has improved rotational invariance properties compared with alternative split schemes particularly when big time steps are utilized we then apply properly designed multigrid methods to efficiently solve the occurring sparse linear system the combined algorithm allows for the rapid evolution of the contour and convergence to its final configuration after very few iterations image segmentation experiments demonstrate the efficiency and accuracy of the method

b spline based globally optimal segmentation combining low level and high level information abstract image segmentation is an important step for large scale image analysis and object recognition variational based segmentation methods are widely studied due to their good performance but they still suffer from incapability to deal with images bearing weak contrast overlapped noise and cluttered texture to tackle this problem we propose a new statistical information analysis based multi scale and global optimization method for image segmentation this multi scale processing which is consistent with human s cognition mechanism enables us identify target at coarse scale the high level prior is obtained by the multiple gaussian kernel gray equalization and used as shape constraint in following fine scale an efficient energy functional is proposed with convexity and improved tv regularization in order to segment inhomogeneous target from noisy background a convex relaxation function is explicitly represented by cubic b spline basis for fast convergence and intrinsic smooth segmentation finally the energy functional is minimized by standard methods of split bregman gradient descent flow and the corresponding euler lagrange equation experimental results on synthetic and real world images validate the robustness and high accuracy boundaries detection for low contrast noisy and texture images

on the finite length scaling of q ary polar codes the polarization process of polar codes over a prime q ary alphabet is studied recently it has been shown that the blocklength of polar codes with prime alphabet size scales polynomially with respect to the inverse of the gap between code rate and channel capacity however except for the binary case the degree of the polynomial in the bound is extremely large in this paper a different approach to computing the degree of this polynomial for any prime alphabet size is shown this approach yields a lower degree polynomial for various values of the alphabet size that were examined it is also shown that even lower degree polynomial can be computed with an additional numerical effort

finite length analysis of low density parity check codes on the binary erasure channel in this paper we are concerned with the finite length analysis of low density parity check ldpc codes when used over the binary erasure channel bec the main result is an expression for the exact average bit and block erasure probability for a given regular ensemble of ldpc codes when decoded iteratively we also give expressions for upper bounds on the average bit and block erasure probability for regular ldpc ensembles and the standard random ensemble under maximum likelihood ml decoding finally we present what we consider to be the most important open problems in this area

waterfall performance analysis of finite length ldpc codes on symmetric channels an efficient method for analyzing the performance of finite length low density parity check ldpc codes in the waterfall region when transmission takes place on a memoryless binary input output symmetric channel is proposed this method is based on studying the variations of the channel quality around its expected value when observed during the transmission of a finite length codeword we model these variations with a single parameter this parameter is then viewed as a random variable and its probability distribution function is obtained assuming that a decoding failure is the result of an observed channel worse than the codeiquests decoding threshold the block error probability of finite length ldpc codes under different decoding algorithms is estimated using an extrinsic information transfer chart analysis the bit error probability is obtained from the block error probability different parameters can be used for modeling the channel variations in this work two of such parameters are studied through examples it is shown that this method can closely predict the performance of ldpc codes of a few thousand bits or longer in the waterfall region

unified scaling of polar codes error exponent scaling exponent moderate deviations and error floors consider the transmission of a polar code of block length n and rate r over a binary memoryless symmetric channel w and let p mathrm e be the block error probability under successive cancellation decoding in this paper we develop new bounds that characterize the relationship of the parameters r n p mathrm e and the quality of the channel w quantified by its capacity i w and its bhattacharyya parameter z w in previous work two main regimes were studied in the error exponent regime the channel w and the rate r are fixed and it was proved that the error probability p mathrm e scales roughly as 2 sqrt n in the scaling exponent approach the channel w and the error probability p mathrm e are fixed and it was proved that the gap to capacity i w r scales as n 1 mu here mu is called scaling exponent and this scaling exponent depends on the channel w a heuristic computation for the binary erasure channel bec gives mu 3 627 and it was shown that for any channel w 3 579 le mu le 5 702 our contributions are as follows first we provide the tighter upper bound mu le 4 714 valid for any w with the same technique we obtain the upper bound mu le 3 639 for the case of the bec this upper bound approaches very closely the heuristically derived value for the scaling exponent of the erasure channel second we develop a trade off between the gap to capacity i w r and the error probability p mathrm e as the functions of the block length n in other words we neither fix the gap to capacity error exponent regime nor the error probability scaling exponent regime but we do consider a moderate deviations regime in which we study how fast both quantities as the functions of the block length n simultaneously go to 0 third we prove that polar codes are not affected by error floors to do so we fix a polar code of block length n and rate r then we vary the channel w and study the impact of this variation on the error probability we show that the error probability p mathrm e scales as the bhattacharyya parameter z w raised to a power that scales roughly like sqrt n this agrees with the scaling in the error exponent regime

designing a good low rate sparse graph code this paper deals with the design of low rate sparse graph codes having a linear minimum distance d min in the blocklength n its main contributions are a a necessary condition on a general family of sparse graph codes with linear d min b a justification of having degree 1 bits in the low rate code structure c a new efficient ensemble of low rate sparse graph codes with bits of degree 1 designed so that the necessary condition a is satisfied

fast geodesic active contours we use an unconditionally stable numerical scheme to implement a fast version of the geodesic active contour model the proposed scheme is useful for object segmentation in images like tracking moving objects in a sequence of images the method is based on the weickert romeney viergever additive operator splitting aos scheme it is applied at small regions motivated by the adalsteinsson sethian level set narrow band approach and uses sethian s 1996 fast marching method for re initialization experimental results demonstrate the power of the new method for tracking in color movies

an efficient mrf embedded level set method for image segmentation this paper presents a fast and robust level set method for image segmentation to enhance the robustness against noise we embed a markov random field mrf energy function to the conventional level set energy function this mrf energy function builds the correlation of a pixel with its neighbors and encourages them to fall into the same region to obtain a fast implementation of the mrf embedded level set model we explore algebraic multigrid amg and sparse field method sfm to increase the time step and decrease the computation domain respectively both amg and sfm can be conducted in a parallel fashion which facilitates the processing of our method for big image databases by comparing the proposed fast and robust level set method with the standard level set method and its popular variants on noisy synthetic images synthetic aperture radar sar images medical images and natural images we comprehensively demonstrate the new method is robust against various kinds of noises in particular the new level set method can segment an image of size 500 500 within 3 s on matlab r2010b installed in a computer with 3 30 ghz cpu and 4 gb memory

snakes shapes and gradient vector flow snakes or active contours are used extensively in computer vision and image processing applications particularly to locate object boundaries problems associated with initialization and poor convergence to boundary concavities however have limited their utility this paper presents a new external force for active contours largely solving both problems this external force which we call gradient vector flow gvf is computed as a diffusion of the gradient vectors of a gray level or binary edge map derived from the image it differs fundamentally from traditional snake external forces in that it cannot be written as the negative gradient of a potential function and the corresponding snake is formulated directly from a force balance condition rather than a variational formulation using several two dimensional 2 d examples and one three dimensional 3 d example we show that gvf has a large capture range and is able to move snakes into boundary concavities

local region descriptors for active contours evolution edge based and region based active contours are frequently used in image segmentation while edges characterize small neighborhoods of pixels region descriptors characterize entire image regions that may have overlapping probability densities in this paper we propose to characterize image regions locally by defining local region descriptors lrds these are essentially feature statistics from pixels located within windows centered on the evolving contour and they may reduce the overlap between distributions lrds are used to define general form energies based on level sets in general a particular energy is associated with an active contour by means of the logarithm of the probability density of features conditioned on the region in order to reduce the number of local minima of such energies we introduce two novel functions for constructing the energy functional which are both based on the assumption that local densities are approximately gaussian the first uses a similarity measure between features of pixels that involves confidence intervals the second employs a local markov random field mrf model by minimizing the associated energies we obtain active contours that can segment objects that have largely overlapping global probability densities our experiments show that the proposed method can accurately segment natural large images in very short time when using a fast level set implementation

finite length scaling for iteratively decoded ldpc ensembles we investigate the behavior of iteratively decoded low density parity check ldpc codes over the binary erasure channel in the so called ldquowaterfall region rdquo we show that the performance curves in this region follow a simple scaling law we conjecture that essentially the same scaling behavior applies in a much more general setting and we provide some empirical evidence to support this conjecture the scaling law together with the error floor expressions developed previously can be used for a fast finite length optimization

boundary detection using double opponency and spatial sparseness constraint brightness and color are two basic visual features integrated by the human visual system hvs to gain a better understanding of color natural scenes aiming to combine these two cues to maximize the reliability of boundary detection in natural scenes we propose a new framework based on the color opponent mechanisms of a certain type of color sensitive double opponent do cells in the primary visual cortex v1 of hvs this type of do cells has oriented receptive field with both chromatically and spatially opponent structure the proposed framework is a feedforward hierarchical model which has direct counterpart to the color opponent mechanisms involved in from the retina to v1 in addition we employ the spatial sparseness constraint ssc of neural responses to further suppress the unwanted edges of texture elements experimental results show that the do cells we modeled can flexibly capture both the structured chromatic and achromatic boundaries of salient objects in complex scenes when the cone inputs to do cells are unbalanced meanwhile the ssc operator further improves the performance by suppressing redundant texture edges with competitive contour detection accuracy the proposed model has the additional advantage of quite simple implementation with low computational cost

polar codes speed of polarization and polynomial gap to capacity we prove that for all binary input symmetric memoryless channels polar codes enable reliable communication at rates within an additive gap e 0 to the shannon capacity with a block length construction complexity and decoding complexity all bounded by a polynomial in 1 e polar coding gives the first known explicit construction with rigorous proofs of all these properties previous constructions were not known to achieve capacity with less than exp 1 e decoding complexity except for erasure channels we establish the capacity achieving property of polar codes via a direct analysis of the underlying martingale of conditional entropies without relying on the martingale convergence theorem this step gives rough polarization noise levels e for the good channels which can then be adequately amplified by tracking the decay of the channel bhattacharyya parameters our effective bounds imply that polar codes can have block length and encoding decoding complexity bounded by a polynomial in 1 e the generator matrix of such polar codes can be constructed in polynomial time by algorithmically computing an adequate approximation of the polarization process

the recognition of the point symbols in the scanned topographic maps it is difficult to separate the point symbols from the scanned topographic maps accurately which brings challenges for the recognition of the point symbols in this paper based on the framework of generalized hough transform ght we propose a new algorithm which is named shear line segment ght sls ght to recognize the point symbols directly in the scanned topographic maps sls ght combines the line segment ght ls ght and the shear transformation on the one hand ls ght is proposed to represent the features of the point symbols more completely its r table has double level indices the first one is the color information of the point symbols and the other is the slope of the line segment connected a pair of the skeleton points on the other hand the shear transformation is introduced to increase the directional features of the point symbols it can make up for the directional limitation of ls ght indirectly in this way the point symbols are detected in a series of the sheared maps by ls ght and the final optimal coordinates of the setpoints are gotten from a series of the recognition results sls ght detects the point symbols directly in the scanned topographic maps totally different from the traditional pattern of extraction before recognition moreover several experiments demonstrate that the proposed method allows improved recognition in complex scenes than the existing methods

multigrid anisotropic diffusion a multigrid anisotropic diffusion algorithm for image processing is presented the multigrid implementation provides an efficient hierarchical relaxation method that facilitates the application of anisotropic diffusion to time critical processes through a multigrid v cycle the anisotropic diffusion equations are successively transferred to coarser grids and used in a coarse to fine error correction scheme when a coarse grid with a trivial solution is reached the coarse grid estimates of the residual error can be propagated to the original grid and used to refine the solution the main benefits of the multigrid approach are rapid intraregion smoothing and reduction of artifacts due to the elimination of low frequency error the theory of multigrid anisotropic diffusion is developed then the intergrid transfer functions relaxation techniques diffusion coefficients and boundary conditions are discussed the analysis includes the examination of the storage requirements the computational cost and the solution quality finally experimental results are reported that demonstrate the effectiveness of the multigrid approach

the threshold probability of a code we define and estimate the threshold probability spl theta of a linear code using a theorem of margulis 1974 originally conceived for the study of the probability of disconnecting a graph we then apply this concept to the study of the erasure and z channels for which we propose linear coding schemes that admit simple decoding we show that spl theta is particularly relevant to the erasure channel since linear codes achieve a vanishing error probability as long as p spl lesspl theta where p is the probability of erasure in effect spl theta can be thought of as a capacity notion designed for codes rather than for channels binomial codes haven the highest possible spl theta and achieve capacity as for the z channel a subcapacity is derived with respect to the linear coding scheme for a transition probability in the range log 3 2 1 we show how to achieve this subcapacity as a by product we obtain improved constructions and existential results for intersecting codes linear sperner families which are used in our coding schemes

cross indexing of binary sift codes for large scale image search in recent years there has been growing interest in mapping visual features into compact binary codes for applications on large scale image collections encoding high dimensional data as compact binary codes reduces the memory cost for storage besides it benefits the computational efficiency since the computation of similarity can be efficiently measured by hamming distance in this paper we propose a novel flexible scale invariant feature transform sift binarization fsb algorithm for large scale image search the fsb algorithm explores the magnitude patterns of sift descriptor it is unsupervised and the generated binary codes are demonstrated to be dispreserving besides we propose a new searching strategy to find target features based on the cross indexing in the binary sift space and original sift space we evaluate our approach on two publicly released data sets the experiments on large scale partial duplicate image retrieval system demonstrate the effectiveness and efficiency of the proposed algorithm

parameter free modelling of 2d shapes with ellipses our goal is to represent a given 2d shape with an automatically determined number of ellipses so that the total area covered by the ellipses is equal to the area of the original shape without any assumption or prior knowledge about the object structure to solve this interesting theoretical problem first we employ the skeleton of the 2d shape which provides important information on the parameters of the ellipses that could approximate the original shape for a given number of such ellipses the hard expectation maximisation em algorithm is employed to maximise the shape coverage under the equal area constraint different models i e solutions involving different numbers of ellipses are evaluated based on the akaike information criterion aic this considers a novel entropy based shape complexity measure that balances the model complexity and the model approximation error in order to minimise the aic criterion two variants are proposed and evaluated a the augmentative method that gradually increases the number of considered ellipses starting from a single one and b the decremental method that decreases the number of ellipses starting from a large automatically defined set the obtained quantitative results on more than 4000 2d shapes included in standard as well as in custom datasets quantify the performance of the proposed methods and illustrate that their solutions agree with human intuition highlights2d shape representation with an automatically determined number of ellipses we propose a novel definition of shape complexity that exploits the shape skeleton good balance between model complexity and shape coverage experiments on more than 4000 2d shapes show the effectiveness of the proposed methods the solutions proposed by aefa and defa seem to agree with human intuition

brownian motion with a parabolic drift and airy functions let w t t be two sided brownian motion originating from zero and let v a be defined by v a sup t w t t a 2 is maximal then v a a is a markovian jump process running through the locations of maxima of two sided brownian motion with respect to the parabolas fa t t a 2 we give an analytic expression for the infinitesimal generators of the processes a in terms of airy functions in theorem 4 1 this makes it possible to develop asymptotics for the global behavior of a large class of isotonic estimators i e estimators derived under order restrictions an example of this is given in groeneboom 1985 where the asymptotic distribution of the standardized l1 distance between a decreasing density and the grenander maximum likelihood estimator of this density is determined on our way to theorem 4 1 we derive some other results for example we give an analytic expression for the joint density of the maximum and the location of the maximum of the process w t ct2 t where c is an aribrary positive constant we also determine the laplace transform of the integral over a brownian excursion these last results also have recently been derived by several other authors using a variety of methods

sar image segmentation based on level set approach and cal g _a 0 model this paper proposes an image segmentation method for synthetic aperture radar sar exploring statistical properties of sar data to characterize image regions we consider cal g a 0 distribution parameters for sar image segmentation combined to the level set framework the cal g a 0 distribution belongs to a class of cal g distributions that have been successfully used to model different regions in amplitude sar images for data modeling purpose such statistical data model is fundamental to deriving the energy functional to perform region mapping which is input into our level set propagation numerical scheme that splits sar images into homogeneous heterogeneous and extremely heterogeneous regions moreover we introduce an assessment procedure based on stochastic distance and the cal g a 0 model to quantify the robustness and accuracy of our approach our results demonstrate the accuracy of the algorithms regarding experiments on synthetic and real sar data

efficient multilevel eigensolvers with applications to data analysis tasks multigrid solvers proved very efficient for solving massive systems of equations in various fields these solvers are based on iterative relaxation schemes together with the approximation of the smooth error function on a coarser level grid we present two efficient multilevel eigensolvers for solving massive eigenvalue problems that emerge in data analysis tasks the first solver a version of classical algebraic multigrid amg is applied to eigenproblems arising in clustering image segmentation and dimensionality reduction demonstrating an order of magnitude speedup compared to the popular lanczos algorithm the second solver is based on a new much more accurate interpolation scheme it enables calculating a large number of eigenvectors very inexpensively