numerical methods for the estimation of multifractal singularity spectra on sampled data physical variables in scale invariant systems often show chaotic turbulent like behavior commonly associated to the existence of an underlying fractal or multifractal structure however the assessment of multifractality over experimental discretized data requires of appropriate methods and to establish criteria to measure the confidence degree on the estimates in this paper we have evaluated the quality of different techniques used for multifractal analysis we have tested four different techniques the moment m method the wavelet transform modulus maxima wtmm method the gradient modulus wavelet projection gmwp method and the gradient histogram gh method which are used to estimate the singularity spectra of multifractal signals the test consists in analyzing synthetic multifractal 1d signals with given multifractal spectrum we have compared the results studying the sensibility of each method to the length of the series size of the ensemble and type of spectrum our results show that gmwp method is the one attaining the best performance providing reliable estimates which can be improved when the statistics is increased all the other methods are affected by problems such as the linearization of the right tail of the spectrum and some of them are very demanding in data

nonlinear wavelet transforms for image coding via lifting we investigate central issues such as invertibility stability synchronization and frequency characteristics for nonlinear wavelet transforms built using the lifting framework the nonlinearity comes from adaptively choosing between a class of linear predictors within the lifting framework we also describe how earlier families of nonlinear filter banks can be extended through the use of prediction functions operating on a causal neighborhood of pixels preliminary compression results for model and real world images demonstrate the promise of our techniques

subpixel edge localization and the interpolation of still images in this paper we present a nonlinear interpolation scheme for still image resolution enhancement the algorithm is based on a source model emphasizing the visual integrity of detected edges and incorporates a novel edge fitting operator that has been developed for this application a small neighborhood about each pixel in the low resolution image is first mapped to a best fit continuous space step edge the bilevel approximation serves as a local template on which the higher resolution sampling grid can then be superimposed where disputed values in regions of local window overlap are averaged to smooth errors the result is an image of increased resolution with noticeably sharper edges and in all tried cases lower mean squared reconstruction error than that produced by linear techniques

dynamic programming alignment of sequences representing cyclic patterns string alignment by dynamic programming is generalized to include cyclic shift and corresponding optimal alignment cost for strings representing cyclic patterns a guided search algorithm uses bounds on alignment costs to find all optimal cyclic shifts the bounds are derived from submatrices of an initial dynamic programming matrix algorithmic complexity is analyzed for major stages in the search the applicability of the method is illustrated with satellite dna sequences and circularly permuted protein sequences

orthogonal and biorthogonal fir hexagonal filter banks with sixfold symmetry recently hexagonal image processing has attracted attention the hexagonal lattice has several advantages in comparison with the rectangular lattice the conventionally used lattice for image sampling and processing for example a hexagonal lattice needs less sampling points it has better consistent connectivity it has higher symmetry and its structure is plausible to human vision systems the multiresolution analysis method has been used for hexagonal image processing since the hexagonal lattice has high degree of symmetry it is desirable that the hexagonal filter banks designed for multiresolution hexagonal image processing also have high order of symmetry which is pertinent to the symmetry structure of the hexagonal lattice the orthogonal or prefect reconstruction pr hexagonal filter banks that are available in the literature have only threefold symmetry in this paper we investigate the construction of orthogonal and pr finite impulse response fir hexagonal filter banks with sixfold symmetry we obtain block structures of 7 size refinement seven channel two dimensional orthogonal and pr fir hexagonal filter banks with sixfold rotational symmetry radic7 refinement orthogonal and biorthogonal wavelets based on these block structures are constructed in this paper we also consider fir hexagonal filter banks with axial line symmetry and we present a block structure of fir hexagonal filter banks with pseudo sixfold axial symmetry

color image coding using morphological pyramid decomposition presents a new algorithm that utilizes mathematical morphology for pyramidal coding of color images the authors obtain lossy color image compression by using block truncation coding at the pyramid levels to attain reduced data rates the pyramid approach is attractive due to low computational complexity simple parallel implementation and the ability to produce acceptable color images at moderate data rates in many applications the progressive transmission capability of the algorithm is very useful the authors show experimental results for color images at data rates of 1 89 bits pixel

a new family of nonredundant transforms using hybrid wavelets and directional filter banks we propose a new family of nonredundant geometrical image transforms that are based on wavelets and directional filter banks we convert the wavelet basis functions in the finest scales to a flexible and rich set of directional basis elements by employing directional filter banks where we form a nonredundant transform family which exhibits both directional and nondirectional basis functions we demonstrate the potential of the proposed transforms using nonlinear approximation in addition we employ the proposed family in two key image processing applications image coding and denoising and show its efficiency for these applications

representing images using points on image surfaces this paper presents a new approach to represent an image by verge points which are defined as high curvature points on the image surface this representation offers a compact and reversible way to preserve the essence of the original image various applications such as compression edge detection image enhancement and image editing can be achieved based on this representation in this paper the whole procedure for verge point representation is presented based on these verge points image reconstruction can be easily achieved via iterative linear interpolation these extracted verge points with compatible properties are further linked into verge curves to offer more compact representation progressive representation is also developed based on a multiscale extraction scheme some potential applications are then presented to demonstrate the versatility of this representation

ranging through gabor logons a consistent hierarchical approach in this work the correspondence problem in stereo vision is handled by matching two sets of dense feature vectors inspired by biological evidence these feature vectors are generated by a correlation between a bank of gabor sensors and the intensity image the sensors consist of two dimensional gabor filters at various scales spatial frequencies and orientations which bear close resemblance to the receptive field profiles of simple v1 cells in visual cortex a hierarchical stochastic relaxation method is then used to obtain the dense stereo disparities unlike traditional hierarchical methods for stereo feature based hierarchical processing yields consistent disparities to avoid false matchings due to static occlusion a dual matching based on the imaging geometry is used

image enhancement based on a nonlinear multiscale method an image enhancement method that reduces speckle noise and preserves edges is introduced the method is based on a new nonlinear multiscale reconstruction scheme that is obtained by successively combining each coarser scale image with the corresponding modified interscale image simulation results are included to demonstrate the performance of the proposed method

curvature of n dimensional space curves in grey value images local curvature represents an important shape parameter of space curves which are well described by differential geometry we have developed an estimator for local curvature of space curves embedded in n dimensional n d grey value images there is neither a segmentation of the curve needed nor a parametric model assumed our estimator works on the orientation field of the space curve this orientation field and a description of local structure is obtained by the gradient structure tensor the orientation field has discontinuities walking around a closed contour yields two such discontinuities in orientation this field is mapped via the knutsson 1985 mapping to a continuous representation from a n d vector to a symmetric n sup 2 d tensor field the curvature of a space curve a coordinate invariant property is computed in this tensor field representation an extensive evaluation shows that our curvature estimation is unbiased even in the presence of noise independent of the scale of the object and furthermore the relative error stays small

detail enhanced exposure fusion in a typical processing chain of image enhancement an exposure fusion scheme can be used to synthesize a more detailed low dynamic range ldr image directly from a set of differently exposed ldr images without generation of an intermediate high dynamic range image in this brief we introduce a new quadratic optimization based method to extract fine details from a vector field the new method extracts fine details from a set of differently exposed ldr images simultaneously the extracted fine details are then added to an intermediate ldr image which is fused by simply using an existing exposure fusion scheme with this the proposed scheme can enhance fine details to produce sharper images

algebraic description of curve structure the authors propose a compact and concise method of describing curves in terms of the quasi topological features and the structure of each singular point the quasi topological features are the convexity loop and connectivity the quasi topological structure is analyzed in a hierarchical way and algebraic structure is presented explicitly for each representation level the lower level representations are integrated into the higher level one in a systematic way when a curve has singular points branch points the curve is decomposed into components where each is a simple arc or a simple closed curve by decomposing each singular point the description scheme is applied to character recognition

an algorithm for a class of continuous linear programs this paper discusses a class of continuous linear programs posed in a function space called separated continuous linear programs sclp a dual linear program and a corresponding discrete approximation are introduced followed by a discussion of their properties the discrete approximation gives rise to an improvement step which is constructed from any given feasible nonoptimal solution for sclp a strong duality result follows from this there are a variety of possible implementations of an algorithm for solving sclp problems using this improvement step finally some computational results are given from one possible implementation

a potential based approach for shape matching and recognition this paper presents a novel potential based approach for recognizing the shape of a two dimensional 2d region by identifying the best match from a selected group of shape templates the proposed model assumes that the border of every 2d region is uniformly charged an initially small shape template placed inside a shape sample will experience the repulsive force and torque arising from the potential field a better match in the shape between the template and the sample can be obtained if the template translates and reorients itself to reduce the potential while growing in size the shape template with the largest final size corresponds to the best match and represents the shape of the given sample the potential and the associated repulsive force and torque between the polygonal contours are analytically tractable hence resulting in high computational efficiency of the matching process the proposed approach is intrinsically invariant under translation rotation and size changes of the shape sample moreover not only can the matching be carried out directly for shape contours at different viewscales but the contours can also be unconnected provided that the template is confined within the shape sample throughout the matching process

classification with nonmetric distances image retrieval and class representation a key problem in appearance based vision is understanding how to use a set of labeled images to classify new images systems that model human performance or that use robust image matching methods often use nonmetric similarity judgments but when the triangle inequality is not obeyed most pattern recognition techniques are not applicable exemplar based nearest neighbor methods can be applied to a wide class of nonmetric similarity functions the key issue however is to find methods for choosing good representatives of a class that accurately characterize it we show that existing condensing techniques are ill suited to deal with nonmetric dataspaces we develop techniques for solving this problem emphasizing two points first we show that the distance between images is not a good measure of how well one image can represent another in nonmetric spaces instead we use the vector correlation between the distances from each image to other previously seen images second we show that in nonmetric spaces boundary points are less significant for capturing the structure of a class than in euclidean spaces we suggest that atypical points may be more important in describing classes we demonstrate the importance of these ideas to learning that generalizes from experience by improving performance we also suggest ways of applying parametric techniques to supervised learning problems that involve a specific nonmetric distance functions showing how to generalize the idea of linear discriminant functions in a way that may be more useful in nonmetric spaces

on the equivalence of soft wavelet shrinkage total variation diffusion total variation regularization and sides soft wavelet shrinkage total variation tv diffusion tv regularization and a dynamical system called sides are four useful techniques for discontinuity preserving denoising of signals and images in this paper we investigate under which circumstances these methods are equivalent in the one dimensional case first we prove that haar wavelet shrinkage on a single scale is equivalent to a single step of space discrete tv diffusion or regularization of two pixel pairs in the translationally invariant case we show that applying cycle spinning to haar wavelet shrinkage on a single scale can be regarded as an absolutely stable explicit discretization of tv diffusion we prove that space discrete tv diffusion and tv regularization are identical and that they are also equivalent to the sides system when a specific force function is chosen afterwards we show that wavelet shrinkage on multiple scales can be regarded as a single step diffusion filtering or regularization of the laplacian pyramid of the signal we analyze possibilities to avoid gibbs like artifacts for multiscale haar wavelet shrinkage by scaling the thresholds finally we present experiments where hybrid methods are designed that combine the advantages of wavelets and pde variational approaches these methods are based on iterated shift invariant wavelet shrinkage at multiple scales with scaled thresholds

wavelet transforms associated with finite cyclic groups multiresolution analysis via decomposition on wavelet bases has emerged as an important tool in the analysis of signals and images when these objects are viewed as sequences of complex or real numbers an important class of multiresolution decompositions are the laplacian pyramid schemes in which the resolution is successively halved by recursively low pass filtering the signal under analysis and decimating it by a factor of two in general the principal framework within which multiresolution techniques have been studied and applied is the same as that used in the discrete time fourier analysis of sequences of complex numbers an analogous framework is developed for the multiresolution analysis of finite length sequences of elements from arbitrary fields attention is restricted to sequences of length 2 sup n for n a positive integer so that the resolution may be recursively halved to completion as in finite length fourier analysis a cyclic group structure of the index set of such sequences is exploited to characterize the transforms of interest for the particular cases of complex and finite fields

image representations using multiscale differential operators differential operators have been widely used for multiscale geometric descriptions of images the efficient computation of these differential operators is always desirable moreover it has not been clear whether such representations are invertible for certain applications it is usually required that such representations should be invertible so that one can facilitate the processing of information in the transform domain and then recover it in this paper such problems are studied we consider multiscale differential representations of images using different types of operators such as the directional derivative operators and laplacian operators in particular we provide a general approach to represent images by their multiscale and multidirectional derivative components for practical implementation efficient pyramid like algorithms are derived using the spline technique for both the the composition and reconstruction of images it is shown that using these representations various meaningful geometric information of images can be extracted at multiple scales therefore these representations can be used for edge based image processing purposes furthermore the intrinsic relationships of the proposed representations with the compact wavelet models and some classical multiscale approaches are also elucidated in the paper

self similarity properties of natural images resemble those of turbulent flows we show that the statistics of an edge type variable in natural images exhibits self similarity properties which resemble those of local energy dissipation in turbulent flows our results show that selfsimilarity and extended self similarity hold remarkably for the statistics of the local edge variance and that the very same models can be used to predict all of the associated exponents these results suggest using natural images as a laboratory for testing more elaborate scaling models of interest for the statistical description of turbulent flows the properties we have exhibited are relevant for the modeling of the early visual system they should be included in models designed for the prediction of receptive fields s0031 9007 97 05190 9

curvature estimation in oriented patterns using curvilinear models applied to gradient vector fields curved oriented patterns are dominated by high frequencies and exhibit zero gradients on ridges and valleys existing curvature estimators fail here the characterization of curved oriented patterns based on translation invariance lacks an estimation of local curvature and yields a biased curvature dependent confidence measure using parameterized curvilinear models we measure the amount of local gradient energy along the model gradient as a function of model curvature minimizing the residual energy yields a closed form solution for the local curvature estimate and the corresponding confidence measure we show that simple curvilinear models are applicable in the analysis of a wide variety of curved oriented patterns

recognition of occluded objects with heuristic search abstract this paper presents a new heuristic search based approach for recognition of partially obscured planar shapes based on a general scheme for representing the planar shapes in terms of their contour segments a state space formulation is obtained for the recognition problem the search in the state space is guided by an admissible heuristic function which is not dependent upon the features actually used for representing the shapes some schemes for toning up the efficiency of the method are also discussed a study of the method was carried out by experimenting with some typical objects and results of experimentation are presented

a fast parallel algorithm for blind estimation of noise variance a blind noise variance algorithm that recovers the variance of noise in two steps is proposed the sample variances are computed for square cells tessellating the noise image several tessellations are applied with the size of the cells increasing fourfold for consecutive tessellations the four smallest sample variance values are retained for each tessellation and combined through an outlier analysis into one estimate the different tessellations thus yield a variance estimate sequence the value of the noise variance is determined from this variance estimate sequence the blind noise variance algorithm is applied to 500 noisy 256 256 images in 98 of the cases the relative estimation error was less than 0 2 with an average error of 0 06 application of the algorithm to differently sized images is also discussed

a theory for multiresolution signal decomposition the wavelet representation multiresolution representations are effective for analyzing the information content of images the properties of the operator which approximates a signal at a given resolution were studied it is shown that the difference of information between the approximation of a signal at the resolutions 2 sup j 1 and 2 sup j where j is an integer can be extracted by decomposing this signal on a wavelet orthonormal basis of l sup 2 r sup n the vector space of measurable square integrable n dimensional functions in l sup 2 r a wavelet orthonormal basis is a family of functions which is built by dilating and translating a unique function psi x this decomposition defines an orthogonal multiresolution representation called a wavelet representation it is computed with a pyramidal algorithm based on convolutions with quadrature mirror filters wavelet representation lies between the spatial and fourier domains for images the wavelet representation differentiates several spatial orientations the application of this representation to data compression in image coding texture discrimination and fractal analysis is discussed

multiscale hybrid linear models for lossy image representation in this paper we introduce a simple and efficient representation for natural images we view an image in either the spatial domain or the wavelet domain as a collection of vectors in a high dimensional space we then fit a piece wise linear model i e a union of affine subspaces to the vectors at each downsampling scale we call this a multiscale hybrid linear model for the image the model can be effectively estimated via a new algebraic method known as generalized principal component analysis gpca the hybrid and hierarchical structure of this model allows us to effectively extract and exploit multimodal correlations among the imagery data at different scales it conceptually and computationally remedies limitations of many existing image representation methods that are based on either a fixed linear transformation e g dct wavelets or an adaptive uni modal linear transformation e g pca or a multimodal model that uses only cluster means e g vq we will justify both quantitatively and experimentally why and how such a simple multiscale hybrid model is able to reduce simultaneously the model complexity and computational cost despite a small overhead of the model our careful and extensive experimental results show that this new model gives more compact representations for a wide variety of natural images under a wide range of signal to noise ratios than many existing methods including wavelets we also briefly address how the same hybrid linear modeling paradigm can be extended to be potentially useful for other applications such as image segmentation

optimal feedback production planning in a stochastic n machine flowshop we consider a production planning problem in an n machine flowshop subject to breakdown and repair of machines and to non negativity constraints on work in process the machine capacities and demand processes are assumed to be finite state markov chains the problem is to choose the rates of production on the n machines over time to minimize the expected discounted cost of production and inventory backlog over an infinite horizon it is formulated as a stochastic dynamic programming problem we show that the value function of the problem is locally lipschitz and is a solution to a dynamic programming equation together with a certain boundary condition we provide an interpretation of the boundary condition we also prove a verification theorem and derive the optimal feedback control policy in terms of the directional derivatives of the value function finally we obtain a deterministic optimal control problem that is equivalent to the stochastic production planning problem under consideration

optimal pyramidal and subband decompositions for hierarchical coding of noisy and quantized images optimal hierarchical coding is sought for progressive or scalable image transmission by minimizing the variance of the error difference between the original image and its lower resolution renditions the optimal according to the above criterion pyramidal and subband image coders are determined for images subject to corruption by quantization or transmission noise given arbitrary analysis filters and assuming adequate knowledge of the noise statistics optimal synthesis filters are found the optimal analysis filters are subsequently determined leading to formulas for globally optimal structures for pyramidal and subband image decompositions experimental results illustrate the implementation and performance of the optimal coders

b spline snakes a flexible tool for parametric contour detection we present a novel formulation for b spline snakes that can be used as a tool for fast and intuitive contour outlining we start with a theoretical argument in favor of splines in the traditional formulation by showing that the optimal curvature constrained snake is a cubic spline irrespective of the form of the external energy field unfortunately such regularized snakes suffer from slow convergence speed because of a large number of control points as well as from difficulties in determining the weight factors associated to the internal energies of the curve we therefore propose an alternative formulation in which the intrinsic scale of the spline model is adjusted a priori this leads to a reduction of the number of parameters to be optimized and eliminates the need for internal energies i e the regularization term in other words we are now controlling the elasticity of the spline implicitly and rather intuitively by varying the spacing between the spline knots the theory is embedded into a multiresolution formulation demonstrating improved stability in noisy image environments validation results are presented comparing the traditional snake using internal energies and the proposed approach without internal energies showing the similar performance of the latter several biomedical examples of applications are included to illustrate the versatility of the method

attributed string matching with merging for shape recognition a new structural approach to shape recognition using attributed string matching with merging is proposed after illustrating the disadvantages of conventional symbolic string matching using changes deletions and insertions attributed strings are suggested for matching each attributed string is an ordered sequence of shape boundary primitives each representing a basic boundary structural unit line segment with two types of numerical attributes length and direction a new type of primitive edit operation called merge is then introduced which can be used to combine and then match any number of consecutive boundary primitives in one shape with those in another the resulting attributed string matching with merging approach is shown useful for recognizing distorted shapes experimental results prove the feasibility of the proposed approach for general shape recognition some possible extensions of the approach are also included

two dimensional object recognition through two stage string matching a two stage string matching method for the recognition of two dimensional 2 d objects is proposed in this work the first stage is a global cyclic string matching the second stage is a local matching with local dissimilarity measure computing the dissimilarity measure function of the input shape and the reference shape are obtained by combining the global matching cost and the local dissimilarity measure the proposed method has the advantage that there is no need to set any parameter in the recognition process experimental results indicate that the hostage string matching approach significantly improves the recognition rates compared to the one stage string matching method

optimal control of production rate in a failure prone manufacturing system we address the problem of controlling the production rate of a failure prone manufacturing system so as to minimize the discounted inventory cost where certain cost rates are specified for both positive and negative inventories and there is a constant demand rate for the commodity produced the underlying theoretical problem is the optimal control of a continuous time system with jump markov disturbances with an infinite horizon discounted cost criterion we use two complementary approaches first proceeding informally and using a combination of stochastic coupling linear system arguments stable and unstable eigenspaces renewal theory parametric optimization etc we arrive at a conjecture for the optimal policy then we address the previously ignored mathematical difficulties associated with differential equations with discontinuous right hand sides singularity of the optimal control problem smoothness and validity of the dynamic programming equation etc to give a rigorous proof of optimality of the conjectured policy it is hoped that both approaches will find uses in other such problems also we obtain the complete solution and show that the optimal solution is simply characterized by a certain critical number which we call the optimal inventory level if the current inventory level exceeds the optimal one should not produce at all if less one should produce at the maximum rate while if exactly equal one should produce exactly enough to meet demand we also give a simple explicit formula for the optimal inventory level

statistics of natural images scaling in the woods we study the statistics of an ensemble of images taken in the woods distributions of local quantities such as contrast are scale invariant and have nearly exponential tails power spectra exhibit scaling with a nontrivial exponent these data limit the information content of natural images and point to the importance of gain control strategies in visual processing

stereo correspondence by surface reconstruction an algorithm that solves the computational stereo correspondence and the surface reconstruction is presented the algorithm integrates the reconstruction process in the correspondence analysis by means of multipass attribute matching and disparity refinement in the matching process the requirement of attribute similarity is relaxed with the pass number while the requirement for agreement between the predicted and the measured disparity is tightened disparity discontinuities and occluded areas are detected by analyzing the partial derivatives of the reconstructed disparity surface results on synthetic and on real stereo image pairs are reported

microcanonical multifractal formalism a geometrical approach to multifractal systems part i singularity analysis multifractal formalism in the microcanonical framework has proved to be a valuable approach to understand and analyze complex signals typically associated with natural phenomena in scale invariant systems in this paper we discuss the multifractal microcanonical formalism in a comprehensive unified way including new theoretical proofs and validation tests on real signals so completing some known gaps in the foundations of this theory we also review the latest advances and describe the present perspectives in this field some technical details on the implementation of involved algorithms and relevant open issues are also discussed

image representation using block pattern models and its image processing applications an image representation scheme using a set of block pattern models bpms consisting of three categories constant oriented and irregular is introduced algorithms for model classification model parameter estimation and image reconstruction from model parameters are presented and these provide the necessary vehicles for applying the proposed representation scheme to various image processing tasks the applications of the proposed models in image coding image zooming and image smoothing are described satisfactory coded images have been obtained at bit rates between 0 5 approximately 0 6 b p p bits per pixel with a high rate realization and between 0 3 approximately 0 5 b p p with a low rate realization the high rate realization has a simple structure suitable for real time implementation the methods for image zooming and smoothing are similar where both adapt the processing for each pixel according to the model of its neighborhood by using directional filters in oriented regions edges and lines are rendered sharper in a smoother manner than with conventional linear filtering approaches which leads to significant improvement in perceived image quality

discounted stochastic fluid programs we consider optimal control problems for stochastic fluid models of the following type suppose z t is a continuous time markov chain with finite state space as long asz t z the dynamics of the system at timet are given by a functionb z u i whereu is a control we have to choose a cost rate functionc is given depending on the state and the action we want to control the system in such a way as to minimize the expected discounted cost over an infinite horizon we will call a problem of this type astochastic fluid program sfp they typically appear in production and telecommunication systems we formulate the optimization problem as a discrete time markov decision process and give conditions under which an optimal stationary policy exists furthermore we show how to solve sfps numerically using kushner s approximating markov chain approach last but not least we apply our results to a multiproduct manufacturing system without backlog

significance linked connected component analysis for wavelet image coding the success in wavelet image coding is mainly attributed to a recognition of the importance of data organization and representation there have been several very competitive wavelet coders developed namely shapiro s 1993 embedded zerotree wavelets ezw servetto et al s 1995 morphological representation of wavelet data mrwd and said and pearlman s see ieee trans circuits syst video technol vol 6 p 245 50 1996 set partitioning in hierarchical trees spiht we develop a novel wavelet image coder called significance linked connected component analysis slcca of wavelet coefficients that extends mrwd by exploiting both within subband clustering of significant coefficients and cross subband dependency in significant fields extensive computer experiments on both natural and texture images show convincingly that the proposed slcca outperforms ezw mrwd and spiht for example for the barbara image at 0 25 b pixel slcca outperforms ezw mrwd and spiht by 1 41 db 0 32 db and 0 60 db in psnr respectively it is also observed that slcca works extremely well for images with a large portion of texture for eight typical 256 spl times 256 grayscale texture images compressed at 0 40 b pixel slcca outperforms spiht by 0 16 db 0 63 db in psnr this performance is achieved without using any optimal bit allocation procedure thus both the encoding and decoding procedures are fast

robust symbolic representation for shape recognition and retrieval a new method for shape recognition and retrieval is proposed here the suggested algorithm is based on several steps the algorithm analyzes the contour of pairs of shapes their contours are recovered and represented by a pair of n points obtained by linear interpolation given two points p i and q j from the two shapes the cost of their matching is evaluated by using the shape context and by using dynamic programming the best matching between the point sets is obtained dynamic programming not only recovers the best matching but also identifies occlusions i e points in the two shapes which cannot be properly matched given the correspondence between the two point sets the two contours are aligned using procrustes analysis after alignment each contour is transformed into a string of symbols and a modified version of edit distance is used to compute the similarity between strings of symbols finally recognition and retrieval are obtained by a simple nearest neighbor procedure the algorithm has been tested on a large set of shape databases kimia mpeg 7 natural silhouette database gesture database marine database swedish leaf database diatom database eth 80 3d object database providing performances for both in recognition and in retrieval superior to most of previously proposed approaches

the laplacian pyramid as a compact image code we describe a technique for image encoding in which local operators of many scales but identical shape serve as the basis functions the representation differs from established techniques in that the code elements are localized in spatial frequency as well as in space pixel to pixel correlations are first removed by subtracting a lowpass filtered copy of the image from the image itself the result is a net data compression since the difference or error image has low variance and entropy and the low pass filtered image may represented at reduced sample density further data compression is achieved by quantizing the difference image these steps are then repeated to compress the low pass image iteration of the process at appropriately expanded scales generates a pyramid data structure the encoding process is equivalent to sampling the image with laplacian operators of many scales thus the code tends to enhance salient image features a further advantage of the present code is that it is well suited for many image analysis tasks as well as for image compression fast algorithms are described for coding and decoding

turnpike sets and their analysis in stochastic production planning problems this paper considers optimal infinite horizon stochastic production planning problems with capacity and demand to be finite state markov chains the existence of the optimal feedback control is shown with the aid of viscosity solutions to the dynamic programming equations turnpike set concepts are introduced to characterize the optimal inventory levels it is proved that the turnpike set is an attractor set for the optimal trajectories provided that the capacity is assumed to be fixed at a level exceeding the maximum possible demand conditions under which the optimal trajectories enter the convex closure of the set in finite time are given the structure of turnpike sets is analyzed last but not least it is shown that the turnpike sets exhibit a monotone property with respect to capacity and demand it turns out that the monotonicity property helps in solving the optimal production problem numerically and in some cases analytically

a class of reduced complexity viterbi detectors for partial response continuous phase modulation partial response continuous phase modulation cpm gives constant envelope digital modulation schemes with excellent power spectra both narrow main lobe and low spectral tails can be achieved when these signals are detected in an optimum coherent maximum likelihood sequence detector viterbi detector power efficient schemes can also be designed sometimes at the expense of receiver complexity this paper describes a general class of simple viterbi detectors with reduced complexity compared to the optimum case the key idea is that the approximate receiver is based on a less complex cpm scheme than the transmitted scheme the asymptotically optimum reduced complexity receiver is found for a variety of transmitted schemes and various complexity reduction factors for a specific class of receivers and modulation indexes a new distance measure is introduced for the performance analysis smooth schemes based on raised cosine pulses are analyzed and simulated for the case of simplified reception a graceful performance degradation occurs with the reduction of complexity

singularity spectrum of fractal signals from wavelet analysis exact results the multifractal formalism for singular measures is revisited using the wavelet transform for bernoulli invariant measures of some expanding markov maps the generalized fractal dimensions are proved to be transition points for the scaling exponents of some partition functions defined from the wavelet transform modulus maxima the generalization of this formalism to fractal signals is established for the class of distribution functions of these singular invariant measures it is demonstrated that the hausdorff dimensiond h of the set of singularities of holder exponenth can be directly determined from the wavelet transform modulus maxima the singularity spectrum so obtained is shown to be not disturbed by the presence in the signal of a superimposed polynomial behavior of ordern provided one uses an analyzing wavelet that possesses at leastn n vanishing moments however it is shown that ac behavior generally induces a phase transition in thed h singularity spectrum that somewhat masks the weakest singularities this phase transition actually depends on the numbern of vanishing moments of the analyzing wavelet its observation is emphasized as a reliable experimental test for the existence of nonsingular behavior in the considered signal these theoretical results are illustrated with numerical examples they are likely to be valid for a large class of fractal functions as suggested by recent applications to fractional brownian motions and turbulent velocity signals

a computational approach to edge detection this paper describes a computational approach to edge detection the success of the approach depends on the definition of a comprehensive set of goals for the computation of edge points these goals must be precise enough to delimit the desired behavior of the detector while making minimal assumptions about the form of the solution we define detection and localization criteria for a class of edges and present mathematical forms for these criteria as functionals on the operator impulse response a third criterion is then added to ensure that the detector has only one response to a single edge we use the criteria in numerical optimization to derive detectors for several common image features including step edges on specializing the analysis to step edges we find that there is a natural uncertainty principle between detection and localization performance which are the two main goals with this principle we derive a single operator shape which is optimal at any scale the optimal detector has a simple approximate implementation in which edges are marked at maxima in gradient magnitude of a gaussian smoothed image we extend this simple detector using operators of several widths to cope with different signal to noise ratios in the image we present a general method called feature synthesis for the fine to coarse integration of information from operators at different scales finally we show that step edge detector performance improves considerably as the operator point spread function is extended along the edge

the multifractal structure of contrast changes in natural images from sharp edges to textures we present a formalism that leads naturally to a hierarchical description of the different contrast structures in images providing precise definitions of sharp edges and other texture components within this formalism we achieve a decomposition of pixels of the image in sets the fractal components of the image such that each set contains only points characterized by a fixed strength of the singularity of the contrast gradient in its neighborhood a crucial role in this description of images is played by the behavior of contrast differences under changes in scale contrary to naive scaling ideas where the image is thought to have uniform transformation properties field 1987 each of these fractal components has its own transformation law and scaling exponents a conjecture on their biological relevance is also given

edges transitions and criticality in this article various notions of edges encountered in digital image processing are reviewed in terms of compact representation or completion we show that critical exponents defined in statistical physics lead to a much more coherent definition of edges consistent across the scales in acquisitions of natural phenomena such as high resolution natural images or turbulent acquisitions edges belong to the multiscale hierarchy of an underlying dynamics they are understood from a statistical perspective well adapted to fit the case of natural images numerical computation methods for the evaluation of critical exponents in the non ergodic case are recalled which apply for the vast majority of natural images we study the framework of reconstructible systems in a microcanonical formulation show how it redefines edge completion and how it can be used to evaluate and assess quantitatively the adequation of edges as candidates for compact representations we study with particular attention the case of turbulent data in which edges in the classical sense are particularly challenged tests are conducted and evaluated on a standard database for natural images we test the newly introduced compact representation as an ideal candidate for evaluating turbulent cascading properties of complex images and we show better reconstruction performance than the classical tested methods highlightsclassical edge detection algorithms are reviewed in terms of completion a new edge detection scheme based on multiscale hierarchical classification assessing the consistency of edges across scales evaluating edge performance through the framework of reconstructible systems comparing the performance with classical edge operators

reconstructing images from their most singular fractal manifold real world images are complex objects difficult to describe but at the same time possessing a high degree of redundancy a previous on the statistical properties of natural images reveals that natural images can be viewed through different partitions which are essentially fractal in nature one particular fractal component related to the most singular sharpest transitions in the image seems to be highly informative about the whole scene we show how to decompose the image into their fractal components we see that the most singular component is related to but not coincident with the edges of the objects present in the scenes we propose a new simple method to reconstruct the image with information contained in that most informative component we see that the quality of the reconstruction is strongly dependent on the capability to extract the relevant edges in the determination of the most singular set we discuss the results from the perspective of coding proposing this method as a starting point for future developments

markov decision processes with slow scale periodic decisions we consider a class of discrete time dynamic decision making models which we refer to as periodically time inhomogeneous markov decision processes ptmdps in these models the decision making horizon can be partitioned into intervals calledslow scale cycles ofn 1 epochs the transition law and reward function are time homogeneous over the firstn epochs of each slow scale cycle but distinct at the final epoch the motivation for such models is in applications where decisions of different nature are taken at different time scales i e many low level decisions are made between less frequent high level ones for the ptmdp model we consider the problem of optimizing the expected discounted reward when rewards devalue by a discount factor at the beginning of each slow scale cycle whenn is large initially stationary policies i s p s are natural candidates for optimal policies similar to turnpike policies an initially stationary policy uses the same decision rule for some large number of epochs in each slow scale cycle followed by a relatively short planning horizon of time varying decision rules in this paper we characterize the form of the optimal value as a function ofn establish conditions ensuring the existence of near optimal i s p s and characterize their structure our analysis deals separately with the cases where the time homogeneous part of the system has state dependent and state independent optimal average reward as we illustrate the results in these two distinct cases are qualitatively different

symbol error probability bounds for coherently viterbi detected continuous phase modulated signals recently the minimum euclidean distance and bandwidth properties of continuous phase modulated cpm signals have been considered it has also been shown that for rational modulation indexes a state description of these signals is possible and that the viterbi algorithm va can be used for demodulation in this paper the performance analysis of cpm systems is extended to obtain bounds on the symbol error probability when the va is used the calculation of these bounds is based on the transfer function technique which has been generalized from numerical comparisons of the upper and lower bounds it is concluded that the minimum euclidean distance is a good performance measure for a broad class of cpm signals even when the symbol error probability is as large as 10 2

content adaptive mesh representation of images using binary space partitions the interest in content adaptive mesh generation of images has been arising lately due to its wide area of applications in image processing the major issue is to represent an image with a low number of pixels while preserving its content these pixels or the nonuniform samples are then used to generate a mesh that approximates the corresponding image this work presents a novel method based on binary space partitions in combination with three clustering schemes to approximate an image with a mesh the algorithm has the ability to simultaneously reduce the number of pixels and generate the mesh approximation the idea is to assume each triangle of the mesh as a plane consequently it will be possible to reconstruct the inlying pixels with planar equations defined from the three nodes of each triangle if a triangle s equation does not have the ability to reconstruct the pixels lying within up to a predefined error it is split into two new triangles tested on several real images the proposed method leads to reduced size meshes in a fast manner while retaining the visual quality of the reconstructed images in addition it is parallelizable due to the property of binary space partitions which facilitates its application in real time scenarios

equilateral polygon approximation of closed contours numerous algorithms have been suggested for computing polygonal approximations of closed contours we present an algorithm which as a unique feature creates polygons which are equilateral that is whose edges are all of the same length this allows one dimensional shape descriptions to be derived using the interior polygon angles conceptually the algorithm is an optimization framework for finding the minimum energy configuration of a mechanical system of particles and springs that represent the contour points the polygon vertices and their interaction in practice the dominant points are detected on the gaussian smoothed contour and used to seed an initial polygon nonlinear programming is then used to minimize the system energy subject to the constraint that adjacent vertices must be equidistant the objective function is the sum of a curvature weighted distance between each vertex and a set of contour points associated therewith experimental results are given for closed contours obtained from grey scale images

simulated symbol error probability for a matched filter differential detector with variable delay for continuous phase modulation a matched filter differential detector for continuous phase modulation is proposed and simulated error probability for this detector is presented the detector consists of a conventional differential detector operating with a delay a bank of matched filters and a viterbi processor to perform sequence decision the author shows that quaternary schemes outperform binary schemes when the schemes are compared in a power bandwidth tradeoff schemes that lose about 3 4 db compared to coherently detected minimum shift keying msk at 10 sup 3 on a gaussian channel but with a bandwidth of about 0 6 times the msk bandwidth are presented

forms of optimal solutions for separated continuous linear programs this paper discusses the nature of optimal solutions for a class of continuous linear programs called separated continuous linear programs it is shown that under various different assumptions on the problem data there exist optimal solutions that are piecewise constant piecewise polynomial or more generally piecewise analytic these results are reminiscent of bang bang results in linear optimal control

flexible syntactic matching of curves and its application to automatic hierarchical classification of silhouettes curve matching is one instance of the fundamental correspondence problem our flexible algorithm is designed to match curves under substantial deformations and arbitrary large scaling and rigid transformations a syntactic representation is constructed for both curves and an edit transformation which maps one curve to the other is found using dynamic programming we present extensive experiments where we apply the algorithm to silhouette matching in these experiments we examine partial occlusion viewpoint variation articulation and class matching where silhouettes of similar objects are matched based on the qualitative syntactic matching we define a dissimilarity measure and we compute it for every pair of images in a database of 121 images we use this experiment to objectively evaluate our algorithm first we compare our results to those reported by others second we use the dissimilarity values in order to organize the image database into shape categories the veridical hierarchical organization stands as evidence to the quality of our matching and similarity estimation

multiscaling and information content of natural color images naive scale invariance is not a true property of natural images natural monochrome images possess a much richer geometrical structure which is particularly well described in terms of multiscaling relations this means that the pixels of a given image can be decomposed into sets the fractal components of the image with well defined scaling exponents turiel and parga neural comput 12 763 2000 here it is shown that hyperspectral representations of natural scenes also exhibit multiscaling properties observing the same kind of behavior a precise measure of the informational relevance of the fractal components is also given and it is shown that there are important differences between the intrinsically redundant red green blue system and the decorrelated one defined in ruderman cronin and chiao j opt soc am a 15 2036 1998

empirical evidences of a common multifractal signature in economic biological and physical systems abstract recent developments in microcanonical multifractal formalism have lead to a sensible improvement in the numerical techniques for the determination of the multifractal characteristics of real signals with the aid of these techniques we have found empirical evidence of a common multifractal signature in six very different systems ranging from stock market time series to sea surface temperature records these systems are not only found to be multifractal but their singularity spectra are coincident we propose an explanation of this striking coincidence in terms of a cascade process and analyze its consequences

efficient shape matching through model based shape recognition abstract an efficient shape matching method for shape recognition is proposed it first uses a polygonal approximation technique to describe a shape then using the proposed matching algorithm based on some polygonal attributes the dissimilarity measure between an input shape and its reference model is obtained the input shape can be classified into the class model which has the minimum dissimilarity measure with it in addition it can provide the best matching orientation information for the input shape and its model so that further applications such as automated inspection and assembly can be effectively performed the proposed shape matching is invariant to translation rotation and scale changes of a shape experiments using noisy shapes and real images are performed and the recognition results demonstrate that the proposed method is very effective

convex stochastic fluid programs with average cost abstract we consider stochastic fluid programs under the average cost criterion these models have been introduced by the author in press math oper res and are of the following type suppose z t is a continuous time markov chain with finite state space as long as z t z the dynamics of the system at time t are given by a linear function b z a where a is a control we have to choose a convex cost rate function c is given depending on the state and the action we want to control the system in such a way as to minimize the expected average cost such models typically appear in production and telecommunication systems using a vanishing discount approach and a discretization technique we show that the relative value function satisfies a hjb equation and derive a verification theorem last but not least we apply our results to manufacturing systems and network problems

a method for representing shape based on an equivalence relation on polygons abstract it is proved that there is a correspondence between deformations of polygons and a grammar this gives rise to an o n lo g n algorithm to match regions whose connectivity has been changed based on boundary contours this has application to problems in handwriting recognition it is then shown that deformations of polygons can be decomposed into canonical types this gives rise to new types of features to measure symmetry handedness rigidity bending and stretching

on analysis of bi dimensional component decomposition via bemd this paper investigates how the bi dimensional empirical mode decomposition bemd behaves in digital images via two components first some definitions of components are given then the theoretical analysis is presented to show that in digital images there might be sparse extrema sets and the sifting process of bemd converges to the true component provided that the sparse extrema sets do exist also the feature of 2d component in digital images is explored via composite two component signals the three dimensional cubes disclosing the performance of bemd are presented which turn out to be in good agreement with intuition and physical interpretation this paper has also shown that the sampling period the cross angle the amplitude ratio and the frequency ratio between the components will affect the separation of them and some instructive conclusions are achieved as well the theoretical analysis is provided for analyzing the observed behaviors and supported by numerical experiments the main aim of this study is primarily to contribute to a better understanding of the possibilities and limitations offered by bemd in digital images

extraction of dominant points by estimation of the contour fluctuations a new method of dominant points dps extraction is presented for each boundary point the method assigns a support region whose length is individually limited two steps are used to detect dps firstly points having higher curvature value than the estimated fluctuations over the support region are extracted as candidates secondly adjacent candidates are merged and a final elimination step is performed on each region additionally a new error measurement scheme is introduced which takes into account the error due to the polygonalisation and the deviation brought by each dp this error is used to compare our algorithm to other methods

polygonal shape recognition using string matching techniques in this paper we study several aspects of the use of string matching techniques as an approach to the problem of recognizing and classifying polygons several authors have already proposed methods for polygon recognition that are based on string matching in many cases however linear strings are used to represent polygons which makes it difficult to handle different orientations of an object efficiently we can however easily extend the linear string matching techniques to cyclic strings at some small computational cost we will propose a method to represent polygons as cyclic strings and we will show how cyclic string matching techniques can be used for rotation translation and scale independent polygonal shape recognition we will however also point out the limitations of such an approach

multifractal geometry in stock market time series it has been recently noticed that time series of returns in stock markets are of multifractal multiscaling character in that context multifractality has been always evidenced by its statistical signature i e the scaling exponents associated to a related variable however a direct geometrical framework much more revealing about the underlying dynamics is possible in this paper we present the techniques allowing the multifractal decomposition we will show that there exists a particular fractal component the most singular manifold msm which contains the relevant information about the dynamics of the series it is possible to reconstruct the series at a given precision from the msm we analyze the dynamics of the msm which shows revealing features about the evolution of this type of series