morphological decomposition of 2 d binary shapes into modestly overlapped octagonal and disk components one problem with several leading morphological shape representation algorithms is the heavy overlapping among the representative disks of the same size a shape component formed by grouping connected disk centers may use many heavily overlapping disks to represent a simple shape part sometimes these representative disks form complicated structures a generalized skeleton transform was recently introduced which allows a shape to be represented as a collection of modestly overlapped octagonal shape parts however the generalized skeleton transform needs to be applied many times furthermore an octagonal component is not easily matched up with another octagonal component in this paper we describe a octagon fitting algorithm which identifies a special maximal octagon for each image point in a given shape this transform leads to the development of two new shape decomposition algorithms these algorithms are more efficient to implement the octagon fitting algorithm only needs to be applied once the components generated are better characterized mathematically the disk components used in the second decomposition algorithm are more primitive than octagons and easily matched up with other disk components from another shape the experiments show that the new decomposition algorithms produce as efficient representations as the old algorithm for both exact and approximate cases a simple shape matching algorithm using disk components is also demonstrated

morphological shape decomposition a technique for decomposing a binary shape into a union of simple binary shapes is presented the decomposition is shown to be unique and invariant to translation rotation and scaling the techniques used in the decomposition are based on mathematical morphology the shape description produced can be used in object recognition and in binary image coding

a moment based unified approach to image feature detection in this paper a novel model based approach is proposed for generating a set of image feature maps or primal sketches for each type of feature a piecewise smooth parametric model is developed to characterize the local intensity function in an image projections of the intensity profile onto a set of orthogonal zernike moment generating polynomials are used to estimate model parameters and in turn generate the desired feature map a small set of moment based detectors is identified that can extract various kinds of primal sketches from intensity as well as range images one main advantage of using parametric model based techniques is that it is possible to extract complete information i e model parameters about the underlying image feature which is desirable in many high level vision tasks experimental results are included to demonstrate the effectiveness of proposed feature detectors

an efficient algorithm for decomposing a polygon into star shaped polygons abstract in this paper we show how a theorem in plane geometry can be converted into a o n log n algorithm for decomposing a polygon into star shaped subsets the computational efficiency of this new decomposition contrasts with the heavy computational burden of existing methods

a morphological signature transform for shape description abstract a novel shape description method based on the multiresolution morphological image processing by non convex multiple structuring elements is presented a binary image which contains the object shape to be described is represented by means of a multiresolution pyramid a set of primary structuring elements along with their rotated versions is used the method is based on the successive morphological erosions of the input image at different resolutions by primary and rotated structuring elements the areas of successively eroded images are computed for each structuring element at each pyramid level the obtained set of numbers is arranged into vectors ordered and used as a shape descriptor results are included to show that the method is robust against noise and invariant to both rotation and scale change

an efficient rate distortion optimal shape coding approach utilizing a skeleton based decomposition in this paper we present a new shape coding approach which decouples the shape information into two independent signal data sets the skeleton and the boundary distance from the skeleton the major benefit of this approach is that it allows for a more flexible tradeoff between approximation error and bit budget curves of arbitrary order can be utilized for approximating both the skeleton and distance signals for a given bit budget for a video frame we solve the problem of choosing the number and location of the control points for all skeleton and distance signals of all boundaries within a frame so that the overall distortion is minimized an operational rate distortion ord optimal approach using lagrangian relaxation and a four dimensional direct acyclic graph dag shortest path algorithm is developed for solving the problem to reduce the computational complexity from o n sup 5 to o n sup 3 where n is the number of admissible control points for a skeleton a suboptimal greedy trellis search algorithm is proposed and compared with the optimal algorithm in addition an even more efficient algorithm with computational complexity o n sup 2 that finds an ord optimal solution using a relaxed distortion criterion is also proposed and compared with the optimal solution experimental results demonstrate that our proposed approaches outperform existing ord optimal approaches which do not follow the same decomposition of the source data

robust partial shape classification using invariant breakpoints and dynamic alignment abstract a system for classifying partially occluded noisy shapes in varying positions orientations and dimensions is described an iterative algorithm derived from the colinearity principle is developed to locate invariant breakpoints on a shape contour the set of invariant breakpoints partitions the contour into a sequence of contour segments each contour segment is described by an ordered sequence that represents the euclidean distance between the pixels in the contour segment and the centroid of the region formed by connecting the end points of the contour segment by a straight line two stages of dynamic alignment with the appropriate constraints are formulated to determine shape similarity the first stage gives a distance measure of contour segment similarity and in the second stage the intersegment distances are used to optimally align contour segments so that a final measure of shape similarity is obtained the performance of the system is demonstrated by considering the classification of aircraft shapes belonging to four classes and classification results are presented as functions of noise and occlusion levels the results indicate that reasonable classification is obtained for noisy shapes with 0 to 30 occlusion

morphological decomposition of 2 d binary shapes into conditionally maximal convex polygons mathematical morphology is an approach to image analysis based on the geometric concept of shape and size naturally it provides a very effective tool for shape analysis in this paper we present a morphological shape segmentation algorithm that decomposes a 2 d two dimensional binary shape into a collection of restricted convex polygons we use simple morphological operations to extract shape information from different skeleton subsets to form a group of conditionally maximal convex polygonal shape components then a set of more meaningful and natural convex polygonal components are constructed from these maximal components the resulting algorithm is very simple and the decomposition is always unique the components produced have well defined mathematical characterizations and they seem to be in good agreement with the nature structures of the given shapes the shape segments produced can be used to construct structural shape description and for other shape analysis purposes

fuzzy artmap classification of invariant features derived using angle of rotation from a neural network conventional regular moment functions have been proposed as pattern sensitive features in image classification and recognition applications but conventional regular moments are only invariant to translation rotation and equal scaling it is shown that the conventional regular moment invariants remain no longer invariant when the image is scaled unequally in the x and y axis directions we address this problem by presenting a technique to make the regular moment functions invariant to unequal scaling however the technique produces a set of features that are only invariant to translation unequal equal scaling and reflection they are not invariant to rotation to make them invariant to rotation moments are calculated with respect to the principal axis of the image to perform this the exact angle of rotation must be known but the method of using the second order moments to determine this angle will also be inclusive of an undesired tilt angle therefore in order to correctly determine the amount of rotation the tilt angle which differs for different scaling factors in the x and y axis directions for the particular image must be obtained in order to solve this problem a neural network using the back propagation learning algorithm is trained to estimate the tilt angle of the image and from this the amount of rotation for the image can be determined next the new moments are derived and a fuzzy artmap network is used to classify these images into their respective classes sets of experiments involving images rotated and scaled unequally in the x and y axis directions are carried out to demonstrate the validity of the proposed technique

a template polynomial approach for image processing and visual recognition abstract a polynomial approach to the representation of gray images for machine vision is described an algebraic system is developed where a polynomial in two variables with real coefficients represents a gray image and it is shown that most of the standard image processing tasks like smoothing edge detection rotation and magnification can be done by operating certain polynomials called template polynomials this method is also applied to connected component labelling shape decomposition template matching and the skeletonization of a gray image without a priori thresholding a technique is developed to decompose a template and do parallel processing

morphological reversible contour representation in this paper a novel morphological reversible contour representation of discrete binary images is proposed a binary image is represented by a set of nonoverlapping multilevel contours and a residual image in this proposed representation the total number of pixels representing an image is far less than the total number of pixels obtained by the seed based morphological contour skeleton lossless representation the proposed contour representation is simple unique and general without restrictions on the binary image to be represented the resulting multicontour image component is robust to noise an efficient differential chain contour coding scheme is employed to further compress the represented image the proposed method yields very low bit rates compared to the existing morphological techniques an automatic filling procedure which properly fills a proper multicontour image according to its topological structure without need of seed points is proposed

segmenting dot patterns by voronoi diagram concavity this correspondence defines a signed distance called internal concavity on paths of the voronoi diagram of a dot pattern an algorithm using internal concavity to segment dot patterns is described the segmentation algorithm produces subsets of the dirichlet tessellation delaunay triangulation of the dot pattern

non linear alignment of neural net outputs for partial shape classification abstract a neural network approach to the partial shape classification problem is derived although neural networks are generally robust static pattern classifiers they are not effective in classifying patterns with inherent temporal variations in order to compensate for temporal variations resulting from random partial occlusion a multi neural network system which includes a dynamic alignment procedure at the neural net outputs is proposed in formulating the dynamic alignment stage a similarity measure between an input and the neural net outputs is defined combining the robustness of neural networks with the non linear alignment capability of dynamic alignment results in a classifier which can tolerate high degrees of random noise and random occlusion in shapes

classification of invariant image representations using a neural network a neural network nn based approach for classification of images represented by translation scale and rotation invariant features is presented the utilized network is a multilayer perceptron mlp classifier with one hidden layer back propagation learning is used for its training two types of features are used moment invariants derived from geometrical moments of the image and features based on zernlike moments which are the mapping of the image onto a set of complex orthogonal polynomials the performance of the mlp is compared to the bayes nearest neighbor and minimum mean distance statistical classifiers through extensive experimentation with noiseless as well as noisy binary images of all english characters 26 classes the following conclusions are reached 1 the mlp outperforms the other three classifiers especially when noise is present 2 the nearest neighbor classifier performs about the same as the nn for the noiseless case 3 the nn can do well even with a very small number of training samples 4 the nn has a good degree of fault tolerance and 5 the zernlike moment based features possess strong class separability power and are more powerful than moment invariants

a generalized discrete morphological skeleton transform with multiple structuring elements for the extraction of structural shape components a common problem shared by several leading morphological shape representation algorithms is that there is much overlapping among the representative disks of the same size a shape component represented by a group of connected disk centers sometimes uses many heavily overlapping representative disks to represent a relatively simple shape part a shape component may also contain a large number of representative disks that form a complicated structure we introduce a generalized discrete morphological skeleton transform that uses eight structuring elements to generate skeleton subsets so that no two skeletal points from the same skeleton subset are adjacent to each other each skeletal point represents a shape part that is in general an octagon with four pairs of parallel opposing sides the number of representative points needed to represent a given shape is significantly lower than that in the standard skeleton transform a collection of shape components needed to build a structural representation is easily derived from the generalized skeleton transform each shape component covers a significant area of the given shape and severe overlapping is avoided the given shape can also be accurately approximated using a small number of shape components

interpolation of 3 d binary images based on morphological skeletonization the morphological skeleton interpolation msi algorithm is presented it is an efficient shape based interpolation method used for interpolating slices in a three dimensional 3 d binary object it is based on morphological skeletonization which is used for two dimensional 2 d slice representation the proposed morphological skeleton matching process provides translation rotation and scaling information at the same time the interpolated slices preserve the shape of the original object slices when the slices have similar shapes it can also modify the shape of an object when the successive slices do not have similar shapes applications on artificial and real data are also presented

three dimensional surface mesh segmentation using curvedness based region growing approach a new parameter free graph morphology based segmentation algorithm is proposed to address the problem of partitioning a 3d triangular mesh into disjoint submeshes that correspond to the physical parts of the underlying object curvedness which is a rotation and translation invariant shape descriptor is computed at every vertex in the input triangulation iterative graph dilation and morphological filtering of the outlier curvedness values result in multiple disjoint maximally connected submeshes such that each submesh contains a set of vertices with similar curvedness values and vertices in disjoint submeshes have significantly different curvedness values experimental evaluations using the triangulations of a number of complex objects demonstrate the robustness and the efficiency of the proposed algorithm and the results prove that it compares well with a number of state of the art mesh segmentation algorithms

two dimensional object recognition using a two dimensional polar transform abstract a two dimensional 2d transform is proposed for the classification of planar objects with a centroid referenced polar representation it samples the multiple intersections of n radii with the object using the mass center translation invariance is achieved and with an appropriate amplitude normalization the transform is also made invariant to scaling the modules of its 2d fast fourier transform coefficients which are rotation invariant are used as the feature vector simultaneously translation scaling and rotation parameters are estimated the high performance of this algorithm is shown with computer simulations and its advantages and disadvantages are analysed in comparison with existing methods

improved moment invariants for shape discrimination abstract moment invariants have been frequently used as features for shape recognition they are computed based on the information provided by both the shape boundary and its interior region although several fast algorithms for computing traditional moment invariants have been proposed none has ever shown the theoretical results of moment invariants computed based on the shape boundary only this paper proposes improved moment invariants computed using the shape boundary only which tremendously reduces computations the new moment invariants called improved moment invariants are mathematically proved to be invariant to scaling translation and rotation graphical plots of the first two improved moment invariants for six country maps and four industrial tools using improved moment invariants are also given the results suggest that improved moment invariants can be used as effective features for shape discrimination or recognition

from discrepancy to declustering near optimal multidimensional declustering strategies for range queries declustering schemes allocate data blocks among multiple disks to enable parallel retrieval given a declustering scheme d its response time with respect to a query q rt q is defined to be the maximum number of data blocks of the query stored by the scheme in any one of the disks if q is the number of data blocks in q and m is the number of disks then rt q is at least q m one way to evaluate the performance of d with respect to a set of range queries q is to measure its additive error the maximum difference of rt q from q m over all range queries q q in this article we consider the problem of designing declustering schemes for uniform multidimensional data arranged in a d dimensional grid so that their additive errors with respect to range queries are as small as possible it has been shown that for a fixed dimension d 2 any declustering scheme on an md grid a grid with length m on each dimension will always incur an additive error with respect to range queries of log m when d 2 and logd 1 2 m when d 2 asymptotically optimal declustering schemes exist for 2 dimensional data however the best general upper bound known so far for the worst case additive errors of d dimensional declustering schemes d 3 is o md 1 which is large when compared to the lower bound in this article we propose two declustering schemes based on low discrepancy points in d dimensions when d is fixed both schemes have an additive error of o logd 1 m with respect to range queries provided that certain conditions are satisfied the first scheme requires that the side lengths of the grid grow at a rate polynomial in m while the second scheme requires d 2 and m pt where d p c c a constant and t is a positive integer such that t d 1 2 these are the first multidimensional declustering schemes with additive errors proven to be near optimal

on the decomposition of binary shapes into meaningful parts abstract a novel decomposition scheme for binary shapes is proposed based on a newly developed notion of maximal approximately convex subpart macs macss are first derived from concepts of integral geometry and it is argued that macss are the simplest possible constituents of a decomposition an algorithm is developed that utilizes the notion of macss to achieve a decomposition into possibly overlapping parts the developed algorithm is based on concepts of mathematical morphology which have been extended by an elongation and a fattening operation the validity of the chosen approach is shown by applying it to several examples synthetic as well as real objects thus corroborating as well the validity of the initial concept of macss

hyperelliptic quasi periodic and soliton solutions of the nonlinear schrodinger equation on considere la construction de solutions par des methodes de geometrie algebriques et en particulier par les fonctions theta hyperelliptiques

morphological residual representations of signals a general approach for residual representation of one dimensional 1 d and two dimensional 2 d signals is defined signals are reconstructed as a sum of components that are recursively determined by using a constructive transform several morphological constructive transforms are proposed and their corresponding representations are discussed the use of residual representations in signal and image compression is investigated with promising results

efficient morphological shape representation mathematical morphology is well suited to capturing geometric information hence morphology based approaches have been popular for object shape representation the two primary morphology based approaches the morphological skeleton and the morphological shape decomposition msd each represent an object as a collection of disjoint sets a practical shape representation scheme though should give a representation that is computationally efficient to use unfortunately little work has been done for the morphological skeleton and the msd to address efficiency we propose a flexible search based shape representation scheme that typically gives more efficient representations than the morphological skeleton and msd our method decomposes an object into a number of simple components based on homothetics of a set of structuring elements to form the representation the components are combined using set union and set difference operations we use three constituent component types and a thorough cost based search strategy to find efficient representations we also consider allowing object representation error which may yield even more efficient representations

effective integration of the nonlinear vector schrodinger equation abstract a comprehensive algebro geometric integration of the two component nonlinear vector schrodinger equation manakov system is developed the allied spectral variety is a trigonal riemann surface which is described explicitly and the solutions of the equations are given in terms of functions of the surface the final formulae are effective in the sense that all entries like transcendental constants in exponentials winding vectors etc are expressed in terms of the prime form of the curve and well algorithmized operations on them that made the result available for direct calculations in applied problems implementing the manakov system the simplest solutions in jacobian functions are given as a particular case of general formulae and are discussed in detail

a generalized morphological skeleton transform using both internal and external skeleton points the morphological skeleton transform mst is a leading morphological shape representation scheme in the mst a given shape is represented as the union of all the maximal disks contained in the shape the concept of external skeleton points and external maximal disks has been used for shape description and characterization purposes in this paper we develop a generalized morphological skeleton transform that combines the concepts of internal and external maximal disks into a unified framework in this framework a shape is described in terms of disk components that need to be added as well as disk components that need to be removed the procedures and formulae describing the extraction of the disk components and the reconstruction of the original shape from these components are developed the correctness of the procedures and formulae is established this new framework seems to provide a more powerful and more natural way of modeling the approximation and reconstruction of binary shapes using primitive shape components

a new shape decomposition scheme for graph based representation nowadays the part based representation of a given shape plays a significant role in shape related applications such as those involving content based retrieval object recognition and so on in this paper to represent both 2 d and 3 d shapes as a relational structure i e a graph a new shape decomposition scheme which recursively performs constrained morphological decomposition cmd is proposed the cmd method adopts the use of the opening operation with the ball shaped structuring element and weighted convexity to select the optimal decomposition for the sake of providing a compact representation the merging criterion is applied using the weighted convexity difference therefore the proposed scheme uses the split and merge approach finally we present experimental results for various modified 2 d shapes as well as 3 d shapes represented by triangular meshes based on the experimental results it is believed that the decomposition of a given shape coincides with that based on human insight for both 2 d and 3 d shapes and also provides robustness to scaling rotation noise shape deformation and occlusion

efficient morphological shape representation with overlapping disk components this paper proposes a new morphological shape representation algorithm in which a two dimensional 2 d binary shape is represented as a union of certain disks contained in the given shape the representative disks of different sizes may overlap but excessive overlapping between them is avoided the algorithm combines the advantages of the morphological skeleton transform mst and the morphological shape decomposition msd the representative disks have simple and well defined mathematical characterizations the algorithm is simple and efficient to implement the experimental results show that the number of representative disks used by our algorithm is significant lower than that used by the msd the overlapping level between the representative disks is much lower than that of the mst a simple procedure can be used to combine the representative disks into more meaningful shape components these shape components seem to correspond better to the natural shape parts than those generated by the msd it is also possible to build a good approximation for a given shape using only a small number of major components

fast computation of geometric moments using a symmetric kernel this paper presents a novel set of geometric moments with symmetric kernel sgm obtained using an appropriate transformation of image coordinates by using this image transformation the computational complexity of geometric moments gm is reduced significantly through the embedded symmetry and separability properties in addition it minimizes the numerical instability problem that occurs in high order gm computation the novelty of the method proposed in this paper lies in the transformation of gm kernel from interval 0 to interval 1 1 the transformed gm monomials are symmetry at the origin of principal cartesian coordinate axes and hence possess symmetrical property the computational complexity of sgm is reduced significantly from order o n 4 using the original form of computation to order o n 3 for the proposed symmetry separable approach experimental results show that the percentage of reduction in computation time of the proposed sgm over the original gm is very significant at about 75 0 and 50 0 for square and non square images respectively furthermore the invariant properties of translation scaling and rotation in hu s moment invariants are maintained the advantages of applying sgm over gm in zernike moments computation in terms of efficient representation and computation have been shown through experimental results

numerical stability of fast computation algorithms of zernike moments abstract a detailed comparative study of the numerical stability of the recursive algorithms widely used to calculate the zernike moments of an image is presented in this paper while many papers introducing fast algorithms for the computation of zernike moments have been presented in the literature there is not any work studying the numerical behaviour of these methods these algorithms have been in the past compared to each other only according to their computational complexity without been given the appropriate attention as far as their numerical stability is concerned being the most significant part of the algorithms reliability the present contribution attempts to fill this gap in the literature since it mainly demonstrates that the usefulness of a recursive algorithm is defined not only by its low computational complexity but most of all by its numerical robustness this paper exhaustively compares some well known recursive algorithms for the computation of zernike moments and sets the appropriate conditions in which each algorithm may fall in an unstable state the experiments show that any of these algorithms can be unstable under some conditions and thus the need to develop more stable algorithms is of major importance

shape decomposition and representation using a recursive morphological operation abstract this paper presents a recursive morphological operation developed in order to perform efficient shape representation this operation uses a structuring element as a geometrical primitive to evaluate the shape of an object it results in a set of loci of the translated structuring elements that are included in the object but which do not overlap the analysis of its computational complexity shows that it is usually less time consuming than morphological erosion by using this operation an object decomposition algorithm is then developed for shape representation it decomposes an object into a union of simple and non overlapping object components the object is represented by the sizes and loci of its object components this representation is information preserving shift and scale invariant and non rebundant it has been compared with skeletons morphological decomposition chain codes and quatrees in terms of compression ability and image processing facility experimental results shows that it is very compact especially if information loss is allowed because of the non overlap between object components many image processing tasks can be easily performed by directly using this shape representation

ordered structural shape matching with primitive extraction by mathematical morphology abstract structural shape matching procedures begin by decomposing the shapes to be matched into primitive parts and extracting the properties of and relationships among these primitives the resultant structural descriptions are matched to structural models usually via a tree search whose time is exponential in the number of primitives in this paper we introduce a new fast method of structural shape matching called ordered structural matching which has polynomial time complexity instead of exponential the approach presented also uses mathematical morphology to rapidly decompose the shapes into primitives to be used in the matching the primitives so produced are pieces of the original shape but not necessarily those pieces that a human would select the method has been tested on the toy task of determining which plastic shapes match the shapes of the holes in a child s six sided toy box it is also directly applicable to the inspection and manipulation of certain airplane parts

accurate calculation of zernike moments zernike moments zms are very effective global image descriptors which are used in many digital image processing applications the digitization process compromises the accuracy of the moments and therefore several of its properties are affected there are two major discretization errors namely the geometric error and numerical integration error in this paper we propose two new algorithms which eliminate these errors the first algorithm performs the exact computation of geometric moments gms over a unit disk and then uses gms to zms relationship to compute the latter this algorithm is computationally more expensive and it becomes numerically instable for higher order moments therefore we develop a second algorithm based on gaussian quadrature numerical integration the second algorithm reduces both the errors simultaneously and its accuracy increases as the degree of gaussian quadrature numerical integration increases the proposed algorithms are observed to provide very accurate zms which result in improved image reconstruction reduction in reconstruction error and improvement in rotation and scale invariance exhaustive experiments are provided to support improved accuracy of zms and time complexity analysis is performed for the existing and the proposed methods

isospectral hamiltonian flows in finite and infinite dimensions the approach to isospectral hamiltonian flow introduced in part i is further developed to include integration of flows with singular spectral curves the flow on finite dimensional ad invariant poisson submanifolds of the dual widetilde gl r of the positive part of the loop algebra widetilde gl r is obtained through a generalization of the standard method of linearization on the jacobi variety of the invariant spectral curves these curves are embedded in the total space of a line bundlet p1 c allowing an explicit analysis of singularities arising from the structure of the image of a moment map tilde j r m n r times m n r to widetilde gl r from the space of rank r deformations of a fixedn n matrixa it is shown how the linear flow of line bundles e t to tilde s over a suitably desingularized curve tilde s may be used to determine both the flow of matricial polynomialsl and the hamiltonian flow in the spacemn r mn r in terms of functions the resulting flows are proved to be completely integrable the reductions to subalgebras developed in part i are shown to correspond to invariance of the spectral curves and line bundles e t to tilde s under certain linear or anti linear involutions the integration of two examples from part i is given to illustrate the method the rosochatius system and the cnls coupled non linear schrodinger equation

reasoning about pictures and similarity retrieval for image information systems based on sk set knowledge representation spatial reasoning and similarity retrieval are two important functions of any image information system good spatial knowledge representation for images is necessary to adequately support these two functions in this paper we propose a new spatial knowledge representation called the sk set based on morphological skeleton theories spatial reasoning algorithms which achieve more accurate results by directly analysing skeletons are described sk set facilitates browsing and progressive visualization we also define four new types of similarity measures and propose a similarity retrieval algorithm for performing image retrieval moreover using sk set as a spatial knowledge representation will reduce the storage space required by an image database significantly

genus two finite gap solutions to the vector nonlinear schrodinger equation a recently published article presents a technique used to derive explicit formulae for odd genus solutions to the vector nonlinear schrodinger equation in another article solutions of genus two are derived using a different approach which assumes a separable ansatz in this communication the extension of the first technique to the even genus case is discussed and this extension is carried out explicitly for genus two furthermore a birational mapping is found between the spectral curves that arise in the two approaches

on stability of distance measures for event sequences induced by level crossing sampling while shannon s paradigm of sampling is based on equidistant points in time triggered by a clock level crossing sampling schemes are based on the evaluation of the input signal s amplitude three types of level crossing concepts are considered a absolute level crossings b absolute level crossings with hysteretic quantization that ignores repeated crossings and c thresholding changes the latter is also referred to as send on delta such event driven sampling principles are encountered in asynchronous event based data acquisition of wireless sensor networks in order to reduce the amount of data transfer and energy consumption in event based imaging in order to realize high dynamic range image acquisition or in biology in terms of neuronal spike trains the paper addresses the similarity between the event sequences which encode the quantized signals resulting from such event based sampling concepts it is shown that such event driven sampling principles induce instability effects when using dissimilarity measures which are state of the art in this context as an alternative metric hermann weyl s discrepancy norm is introduced by which such instability effects can be avoided

global shape analysis by k syntactic similarity the k syntactic similarity approach is couched in graphical representation terms and its ability to provide global recognition capability while retaining a low time complexity is explored one potential application domain that of composite shape decomposition into approximately convex subshapes is described this is shown to be equivalent to finding cycles within a particular graph the approach yields valid decompositions in many cases of interest and is capable of identifying those cases where additional semantic considerations are necessary for proper analysis the permissible graph structures representing composite shapes given a reasonable set of relations are determined experimental results on nonideal data are given

improved bounds and schemes for the declustering problem the declustering problem is to allocate given data on parallel working storage devices in such a manner that typical requests find their data evenly distributed on the devices using deep results from discrepancy theory we improve previous work of several authors concerning range queries to higher dimensional data we give a declustering scheme with an additive error of od logd 1m independent of the data size where d is the dimension m the number of storage devices and d 1 does not exceed the smallest prime power in the canonical decomposition of m into prime powers in particular our schemes work for arbitrary m in dimensions two and three for general d they work for all m d 1 that are powers of two concerning lower bounds we show that a recent proof of a d log d 1 2m bound contains an error we close the gap in the proof and thus establish the bound

discrete active models and applications abstract optimization processes based on active models play central roles in many areas of computational vision as well as computational geometry unfortunately current models usually require highly complex and sophisticated mathematical machinery and at the same time they suffer from a number of limitations which impose restrictions on their applicability in this paper a simple class of discrete active models called migration processes mps is presented the processes are based on iterated averaging over neighborhoods defined by constant geodesic distance it is demonstrated that the mp model a system of self organizing active particles has a number of advantages over previous models both parametric active models snakes and implicit contour evolution models due to the generality of the mp model the process can be applied to derive natural solutions to a variety of optimization problems including defining minimal surface patches given their boundary curves finding shortest paths joining sets of points and decomposing objects into primitive parts

decomposition of arbitrarily shaped morphological structuring elements for image processing systems that have a limited size of region of support say 3 spl times 3 direct implementation of morphological operations by a structuring element larger than the prefixed size is impossible the decomposition of morphological operations by a large structuring element into a sequence of recursive operations each using a smaller structuring element enables the implementation of large morphological operations in this paper the authors present the decomposition of arbitrarily shaped convex or concave structuring elements into 3 spl times 3 elements optimized with respect to the number of 3 spl times 3 elements the decomposition is based on the concept of factorization of a structuring element into its prime factors for a given structuring element all its corresponding 3 spl times 3 prime concave factors are first determined from the set of the prime factors the decomposability of the structuring element is then established and subsequently the structuring element is decomposed into a smallest possible set of 3 spl times 3 elements examples of optimal decomposition and structuring elements that are not decomposable are presented

asymptotically optimal declustering schemes for 2 dim range queries declustering techniques have been widely adopted in parallel storage systems e g disk arrays to speed up bulk retrieval of multidimensional data a declustering scheme distributes data items among multiple disks thus enabling parallel data access and reducing query response time we measure the performance of any declustering scheme as its worst case additive deviation from the ideal scheme the goal thus is to design declustering schemes with as small an additive error as possible we describe a number of declustering schemes with additive error o log m for 2 dimensional range queries where m is the number of disks these are the first results giving o logm upper bound for all values of m our second result is a lower bound on the additive error it is known that except for a few stringent cases additive error of any 2 dimensional declustering scheme is at least one we strengthen this lower bound to logm d 1 2 for d dimensional schemes and to logm for 2 dimensional schemes thus proving that the 2 dimensional schemes described in this paper are asymptotically optimal these results are obtained by establishing a connection to geometric discrepancy we also present simulation results to evaluate the performance of these schemes in practice

region extraction from complex shapes an algorithm is described which extracts primitive regions i e convex spiral shaped and biconcave lens from complex shapes the interior region bounded by the shape is decomposed by first slicing it into a set of convex subregions and then rotating and dissolving the various boundaries between subregions until a satisfactory decomposition is obtained the same algorithm also is used to decompose the exterior region between the shape and its convex hull the algorithm has been implemented as an algol w computer program for the univac 90 80 and results of running the program are presented for a wide variety of complex shapes these results compare favorably with the experience reported by previous programs

a discrepancy measure for improved clustering a discrepancy measure is proposed to improve the clustering of patterns which experience non linear distortions the discrepancy measure is an outcome of a non linear alignment procedure which optimally aligns the elements of patterns in order to minimize the dissimilarity between the patterns the k means clustering algorithm is modified to use the discrepancy measure to compute the similarity between patterns and the cluster centers a series of clustering experiments were conducted on identical data using the modified and standard k means algorithm the results obtained show that clustering performance of the modified algorithm is significantly superior to that of the standard algorithm

periodic solutions of the kdv equation in this paper we construct a large family of special solutions of the kdv equation which are periodic in x and almost periodic in t these solutions lie on n dimensional tori very likely they are dense among all solutions the special solutions are characterized variationally they minimize fn u subject to the constraints fj u aj j 1 n 1 here fj denote the remarkable sequence of conserved functionals discovered by kruskal and zabusky the above minimum problem was originally suggested by them in exploring the manifold of solutions of this minimum problem we make essential use of gardner s discovery that these functionals are in involution with respect to a suitable poisson bracket gardner greene kruskal and miura have shown that the eigenvalues of the schrodinger operator are conserved functionals if the potential is a function of t and satisfies the kdv equation in section 6 a new set of conserved quantities is constructed which serve as a link between the eigenvalues of the schrodinger operator and the fj another result in section 6 is a slight sharpening of an earlier result of the author and j moser for the special solutions constructed above all but 2n 1 eigenvalues of the schrodinger operator are double the simplest class of special solutions n 1 are cnoidal waves in an appendix m hyman describes the results of computing numerically the next simplest case n 2 these calculations show that the shape of these solutions recurs exactly after a finite time in a shifted position the theory verifies this fact

bounded gray level morphology and its applications to image representation morphological skeletonization and decomposition are two well known schemes for binary image representation but they are not compact for gray level images in this correspondence bounded gray level morphology is used to improve their performances for gray level image representation experimental results show that bounded gray level morphology efficiently reduces the number of skeleton points and the entropy of morphological decomposition

efficient morphological shape representation by varying overlapping levels among representative disks abstract the morphological skeleton transform the morphological shape decomposition and the overlapped morphological shape decomposition are three basic morphological shape representation schemes in this paper we propose a new way of generalizing these basic representation algorithms to improve representational efficiency in all three basic algorithms a fixed overlapping policy is used to control the overlapping relationships among representative disks of different sizes in our new algorithm different overlapping policies are used to generate shape components that have different overlapping relationships among themselves the overlapping policy is selected dynamically according to local shape features experiments show that compared to the three basic algorithms our algorithm produces more efficient representations with lower numbers of representative points

fast computation of exact zernike moments using cascaded digital filters zernike moments have been extensively used and have received much research attention in a number of fields object recognition image reconstruction image segmentation edge detection and biomedical imaging however computation of these moments is time consuming thus we present a fast computation technique to calculate exact zernike moments by using cascaded digital filters the novelty of the method proposed in this paper lies in the computation of exact geometric moments directly from digital filter outputs without the need to first compute geometric moments the mathematical relationship between digital filter outputs and exact geometric moments is derived and then they are used in the formulation of exact zernike moments a comparison of the speed of performance of the proposed algorithm with other state of the art alternatives shows that the proposed algorithm betters current computation time and uses less memory

third order moment spectrum and weighted fuzzy classifier for robust 2 d object recognition abstract in this paper a robust position scale and rotation invariant system for the recognition of closed 2 d noise corrupted images using the bispectral features of a contour sequence and the weighted fuzzy classifier are derived the higher order spectrum based on third order moment called a bispectrum is applied to the contour sequences of an image to extract a 15 dimensional feature vector for each of the 2 d images this bispectral feature vector which is invariant to shape translation scale and rotation transformation can be used to represent a 2 d planar image and is fed into a weighted fuzzy classifier for the recognition process the experiments with eight different shapes of aircraft images are presented to illustrate the high performance of the proposed system even when the image is significantly corrupted by noise

shape codification indexing and retrieval using the quad tree structure the author presents in this paper a new approach for indexing and content based image retrieval based on the quad tree structure the 3d objects are represented by their silhouettes and codified following the filling rate of each quadrant at different levels of the quad tree subdivision the author proposes a modified linear codification for silhouettes this method improves the processing time because in opposite to the traditional algorithms the author s algorithm has not a processing time that is proportional to the number of pixels in the image as the same descriptor may characterize a set of different shapes the author proposes also efficient similarity measures to distinguish different objects having the same index in order to apply the approach to the retrieval process

shape description and recognition using the high order morphological pattern spectrum abstract shape analysis and recognition is an important issue in modern image processing and computer vision it needs to solve three problems possibility sensitivity and robustness to deal with the third one this paper proposes the high order morphological pattern hp spectrum which relies upon the difference between two different sized alternating sequential morphological transformations on the original image the hp spectrum is characterized by the translating invariance and rotating invariance for the isotropic structuring element it is also proved that the higher order components of hp spectrum for a noisy image are exactly identical to these for the noise free image under certain conditions also the results of the experiments conducted have shown that the hp spectrum shows the strongest robustness in a noisy environment

isospectral hamiltonian flows in finite and infinite dimensions i generalized moser systems and moment maps into loop algebras a moment map jr jia gl r is constructed from the poisson manifold j a of rank r perturbations of a fixed n xn matrix a to the dual r f e positive part of the formal loop algebra i r g r c 1 the adler kostant symes theorem is used to give hamiltonians which generate commutative isospectral flows on g r the pull back of these hamiltonians by the moment map gives rise to commutative isospectral hamiltonian flows in j a the latter may be identified with flows on finite dimensional coadjoint orbits in g and linearized on the jacobi variety of an invariant spectral curve xr which generically is an r sheeted riemann surface reductions of j a are derived corresponding to subalgebras of gl r c and sl r c determined as the fixed point set of automorphism groupes generated by involutions i e jdl the classical algebras as well as reductions to twisted subalgebras of s r c the theory is illustrated by a number of examples of finite dimensional isospectral flows defining integrable hamiltonian systems and their embeddings as finite gap solutions to integrable systems of pde s

morphological decomposition of 2 d binary shapes into convex polygons a heuristic algorithm in many morphological shape decomposition algorithms either a shape can only be decomposed into shape components of extremely simple forms or a time consuming search process is employed to determine a decomposition in this paper we present a morphological shape decomposition algorithm that decomposes a two dimensional 2 d binary shape into a collection of convex polygonal components a single convex polygonal approximation for a given image is first identified this first component is determined incrementally by selecting a sequence of basic shape primitives these shape primitives are chosen based on shape information extracted from the given shape at different scale levels additional shape components are identified recursively from the difference image between the given image and the first component simple operations are used to repair certain concavities caused by the set difference operation the resulting hierarchical structure provides descriptions for the given shape at different detail levels the experiments show that the decomposition results produced by the algorithm seem to be in good agreement with the natural structures of the given shapes the computational cost of the algorithm is significantly lower than that of an earlier search based convex decomposition algorithm compared to nonconvex decomposition algorithms our algorithm allows accurate approximations for the given shapes at low coding costs

extraction of the euclidean skeleton based on a connectivity criterion abstract the skeleton is essential for general shape representation the commonly required properties of a skeletonization algorithm are that the extracted skeleton should be accurate robust to noise position and rotation able to reconstruct the original object and able to produce a connected skeleton in order to preserve its topological and hierarchical properties however the use of a discrete image presents a lot of problems that may influence the extraction of the skeleton moreover most of the methods are memory intensive and computationally intensive and require a complex data structure in this paper we propose a fast efficient and accurate skeletonization method for the extraction of a well connected euclidean skeleton based on a signed sequential euclidean distance map a connectivity criterion is proposed which can be used to determine whether a given pixel is a skeleton point independently the criterion is based on a set of point pairs along the object boundary which are the nearest contour points to the pixel under consideration and its 8 neighbors our proposed method generates a connected euclidean skeleton with a single pixel width without requiring a linking algorithm or iteration process experiments show that the runtime of our algorithm is faster than the distance transformation and is linearly proportional to the number of pixels of an image

darboux coordinates and liouville arnold integration in loop algebras darboux coordinates are constructed on rational coadjoint orbits of the positive frequency part tilde mathfrak g of loop algebras these are given by the values of the spectral parameters at the divisors corresponding to eigenvector line bundles over the associated spectral curves defined within a given matrix representation a liouville generating function is obtained in completely separated form and shown through the liouvile arnold integration method to lead to the abel map linearization of all hamiltonian flows induced by the spectral invariants as illustrative examples the caseg sl 2 together with its real forms is shown to reproduce the classical integration methods for finite dimensional systems defined on quadrics with the liouville generating function expressed in hyperellipsoidal coordinates forg sl 3 the method is applied to the computation of quasi periodic solutions of the two component coupled nonlinear schrodinger equation a case which requires further symplectic constraints in order to deal with singularities in the spectral data at

invariant planar shape recognition using dynamic alignment abstract closed planar shapes are modelled by an ordered sequence that represents the euclidean distance between the centroid and all contour pixels of the shape shapes belonging to the same class have similar sequences hence a procedure for classifying shapes is based on the degree of similarity between these sequences in order to determine the similarity between sequences a dynamic alignment process is developed to find the best correspondence between the sequences optimum alignment is obtained by expanding segments of the sequences to minimize a dissimilarity function between the sequences normalization with respect to scaling and rotation is described and an example illustrating the use of dynamic alignment for the classification of noisy shapes is presented

the stationary equations of a coupled nonlinear schrodinger system abstract the integrable coupled nonlinear schrodinger cnls equations under periodic boundary conditions are known to possess linearized instabilities in both the focussing and defocussing cases m g forest d w mclaughlin d muraki o c wright non focussing instabilities in coupled integrable nonlinear schrodinger pdes in preparation d j muraki o c wright d w mclaughlin birefringent optical fibers modulational instability in a near integrable system nonlinear processes in physics proceedings of iii postdam v kiev workshop 1991 pp 242 245 o c wright modulational stability in a defocussing coupled nonlinear schrodinger system physica d 82 1995 1 10 whereas the scalar nls equation is linearly unstable only in the focussing case m g forest j e lee geometry and modulation theory for the periodic schrodinger equation in dafermas et al eds oscillation theory computation and methods of compensated compactness i m a math appl 2 1986 35 70 these instabilities indicate the presence of crossed homoclinic orbits similar to those in the phase plane of the unforced duffing oscillator y li d w mclaughlin morse and melnikov functions for nls pde s commun math phys 162 1994 175 214 d w mclaughlin e a overman whiskered tori for integrable pde s chaotic behaviour in near integrable pde s in keller et al eds surveys in applied mathematics vol 1 chapter 2 plenum press new york 1995 the homoclinic orbits and the near homoclinic tori that are connected to the unstable wave trains of the nls and the cnls reside in the finite dimensional phase space of certain stationary equations s p novikov funct anal prilozen 8 3 1974 54 66 of the infinite hierarchy of integrable commuting flows the correct stationary equations must be matched to the unstable torus through the analytic structure of the spectral curves o c wright near homoclinic orbits of the focussing nonlinear schrodinger equation preprint thus in this paper the stationary equations of the cnls are derived and the analytic structure of the trigonal spectral curve is examined providing a basis for further study of the near homoclinic orbits of the cnls system

morse and melnikov functions for nls pde s the theory of the focusing nls equation under periodic boundary conditions together with the floquet spectral theory of its associated zakharov shabat linear operator hat l is developed in sufficient detail for later use in studies of perturbations of the nls equation counting lemmas for the non selfadjoint operator hat l are established which control its spectrum and show that all of its eccentricities are finite in number and must reside within a finite discd in the complex eigenvalue plane the radius of the discd is controlled by theh 1 norm of the potential overrightarrow q for this integrable nls hamiltonian system unstable tori are identified and backlund transformations are then used to construct global representations of their stable and unstable manifolds whiskered tori for the nls pde the floquet discriminant delta lambda overrightarrow q is used to introduce a natural sequence of nls constants of motion f j overrightarrow q equiv delta lambda lambda j c overrightarrow q overrightarrow q where denotes thej th critical point of the floquet discriminant a taylor series expansion of the constants f j overrightarrow q with explicit representations of the first and second variations is then used to study neighborhoods of the whiskered tori in particular critical tori with hyperbolic structure are identified through the first and second variations of f j overrightarrow q which themselves are expressed in terms of quadratic products of eigenfunctions of hat l the second variation permits identification within the disc d of important bifurcations in the spectral configurations of the operator hat l the constant f j overrightarrow q as the height of the floquet discriminant over the critical point admits a natural interpretation as a morse function for nls isospectral level sets this morse interpretation is studied in some detail it is valid globally for the infinite tail f j overrightarrow q j n which is associated with critical points outside the discd within this disc the interpretation is only valid locally with the same obstruction to its global validity as to a global ordering of the spectrum nevertheless this local morse theory together with the backlund representations of the whiskered tori produces extremely clear pictures of the stratification of nls invariant sets near these whiskered tori pictures which are useful in the study of perturbations of nls finally a natural connection is noted between the constants f j overrightarrow q of the integrable theory and melnikov functions for the theory of perturbations of the nls equation this connection generates a simple but general representations of the melnikov functions

on image analysis by the methods of moments various types of moments have been used to recognize image patterns in a number of applications a number of moments are evaluated and some fundamental questions are addressed such as image representation ability noise sensitivity and information redundancy moments considered include regular moments legendre moments zernike moments pseudo zernike moments rotational moments and complex moments properties of these moments are examined in detail and the interrelationships among them are discussed both theoretical and experimental results are presented

comparison between the morphological skeleton and morphological shape decomposition the morphological skeleton and morphological shape decomposition msd are two popular approaches for morphological shape representation each method represents an object as an algebraic combination of a number of components where each component is given by a locus of points dilated by a specified structuring element homothetic this correspondence develops a theoretical comparison between the two methods combining the theoretical results with several representation cost measures we make a concrete comparison of the efficiency of the two methods the results indicate that for complex objects i e objects requiring a full range of homothetic sizes in the morphological skeleton representation the msd represents objects more efficiently than the morphological skeleton for three of four suggested cost measures

some sequential algorithms for a generalized distance transformation based on minkowski operations a generalized distance transformation gdt of binary images and the related medial axis transformation mat are discussed these transformations are defined in a discrete space of arbitrary dimension and arbitrary grids the gdt is based on successive morphological operations using alternatively n arbitrary structuring elements n is called the period of the gdt the gdt differs from the classical distance transformations based on a point to point distance however the well known chessboard city block and hexagonal distance transformations are special cases of the one period gdt whereas the octagonal distance transformation is a special case of the two period gdt in this paper both one and two period gdts are discussed different sequential algorithms are proposed for computing such gdts these algorithms need a maximum of two scannings of the image the computation of the mat is also discussed

a method for shift rotation and scale invariant pattern recognition using the form and arrangement of pattern specific features abstract a new computer based method for visual pattern recognition is described the process extracts shape features from binary edge images represented in either real valued or discrete coordinates both separate and overlapping features are extracted maximizing their completeness and continuity without using templates or mathematical feature descriptions these features and their arrangement are encoded in a shift rotation and scale invariant manner and used to recognize incoming patterns from a set of previously encoded patterns stored in memory new patterns may be automatically classified and stored in memory allowing the system to learn and generalize without operator intervention testing shows the system to be completely shift rotation and scale invariant and insensitive to local image distortion

a euclidean distance transform using grayscale morphology decomposition a fast and exact euclidean distance transformation using decomposed grayscale morphological operators is presented applied on a binary image a distance transformation assigns each object pixel a value that corresponds to the shortest distance between the object pixel and the background pixels it is shown that the large structuring element required for the euclidean distance transformation can be easily decomposed into 3 spl times 3 windows this is possible because the square of the euclidean distance matrix changes uniformly both in the vertical and horizontal directions a simple extension for a 3d euclidean distance transformation is discussed a fast distance transform for serial computers is also presented acting like thinning algorithms the version for serial computers focuses operations only on the potential changing pixels and propagates from the boundary of objects significantly reducing execution time nonsquare pixels can also be used in this algorithm an example application shape filtering using arbitrary sized circular dilation and erosion is discussed rotation invariant basic morphological operations can be done using this example application

binary shape recognition using the morphological skeleton transform abstract binary image representation by its morphological skeleton transform has been proposed in the past as an information preserving representation in this paper this skeleton representation is adopted as the start point for the development of a binary shape recognition scheme a skeleton matching algorithm is presented that efficiently characterizes the similarity between two skeletons as a distance measure this skeleton matching algorithm resembles the well known from speech processing elastic matching technique

kac moody lie algebras and soliton equations ii lax equations associated with a1 1 the soliton equations associated with sl 2 eigenvalue problems polynomial in the eigenvalue parameter are given a unified treatment they are shown to be generated by a single family of commuting hamiltonians on a subalgebra of the loop algebra of sl 2 the conserved densities and fluxes of the usual anks hierarchy are identified with conserved densities and fluxes for the polynomial eigenvalue problems the hamiltonian structures of the soliton equations associated with the polynomial eigenvalue problems are given a unified treatment

morphological representation of 2 d binary shapes using rectangular components abstract the morphological skeleton transform is a shape representation scheme that decomposes a shape into a union of all maximal homothetics of a structuring element contained in the shape in this paper we develop an algorithm that generalizes the skeleton transform by allowing many different rectangles of different sizes and aspect ratios to be used as shape components the shape components in our representations still have simple and well defined mathematical characterizations the representation is uniquely defined and the algorithm still is simple and efficient to implement experiments show that our representations use significantly less shape components than those produced by the skeleton transform we also describe different ways to derive a new set of rectangular shape components with less overlapping from the original set of rectangles from our representation algorithm

a generalized fuzzy mathematical morphology and its application in robust 2 d and 3 d object representation in this paper the generalized fuzzy mathematical morphology gfmm is proposed based on a novel definition of the fuzzy inclusion indicator fii fii is a fuzzy set used as a measure of the inclusion of a fuzzy set into another that is proposed to be a fuzzy set it is proven that the fii obeys a set of axioms which are proposed to be extensions of the known axioms that any inclusion indicator should obey and which correspond to the desirable properties of any mathematical morphology operation the gfmm provides a very powerful and flexible tool for morphological operations the binary and grayscale mathematical morphologies can be considered as special cases of the proposed gfmm an application for robust skeletonization and shape decomposition of two dimensional 2 d and three dimensional 3 d objects is presented simulation examples show that the object reconstruction from their skeletal subsets that can be achieved by using the gfmm is better than by using the binary mathematical morphology in most cases furthermore the use of the gfmm for skeletonization and shape decomposition preserves the shape and the location of the skeletal subsets and spines

robust automatic target recognition using a localized boundary representation abstract a localized classification approach which includes a localized target boundary representation a set of local features to characterize parts of a target boundary and a feature matching method is developed to classify highly degraded targets each pixel on the target boundary is represented by the perpendicular euclidean distance between the boundary pixel and the chord connecting the end points of a window centered on the boundary pixel the resulting localized representation is quite robust with respect to noise and missing segments in the targets a local feature is the segment of the localized representation between two points selected on the target boundary the two points on the boundary may be specified or randomly selected the reference features of a hypothesized target class are compared with segments of the localized representation of the test target to determine a dissimilarity measure between the hypothesized target class and the test target segments of the test target may also be matched with the reference localized contour sequences of the targets the test target is assigned to a target class using a minimum mismatch rule results from a series of experiments conducted on three targets show that it is possible to classify targets experiencing high levels of noise and high percentages of missing segments in partial targets

a neural network approach to robust shape classification abstract a neural network approach for the classification of closed planar shapes is described the primary foci are the development of an effective representation for planar shapes which may be used in conjunction with neural nets the selection of a suitable neural network structure and determining training methods to increase the degree of robustness in classification a three layer perception using backpropagation is initially trained with contour sequences of noisefree reference shapes and its generalization capability is demonstrated the network is then gradually retrained with increasingly noisy data to improve the robustness of the classifier the advantages and improvement in robustness using this extended training scheme are shown and typical classification results are presented

morphological shape representation abstract a new approach for shape representation is described which provides a general scheme for object description and unifies some of the existing representation techniques the proposed method has the advantage that it is based on the use of simple geometric objects which are intuitively used by humans in their perception of shapes furthermore its unifying framework can be used both in computer graphics and computer vision thus providing a tool to close the existing gap between object modeling and object recognition in certain applications

on elliptic solutions of a coupled nonlinear schrodinger system abstract an explicit formula is obtained for single phase bounded elliptic solutions of the manakov system of integrable coupled nonlinear schrodinger equations in terms of the weierstrass sigma function with a real quasiperiod the parametrization is effective in the sense that the reality conditions are completely characterized for each of the three possible couplings focusing focusing defocusing defocusing and focusing defocusing the manakov soliton is recovered in the soliton limit and the small wave modulation limit is shown to satisfy the linearized dispersion relation of planewave solutions

binary object representation and recognition using the hilbert morphological skeleton transform abstract a binary shape representation called the hilbert morphological skeleton transform hmst is introduced this representation combines the morphological skeleton transform mst with the clustering capabilities of the hilbert transform the hmst preserves the skeleton properties including information preservation progressive visualization and compact representation then an object recognition algorithm the hilbert skeleton matching algorithm hsma is introduced this algorithm performs a single sweep over the hmst s and renders the similarity between them as a distance measure testing the hsma against the skeleton matching algorithm sma and invariant moments revealed that the hsma algorithm achieves slightly better object recognition rates while substantially reducing the complexity in an experiment of 14 400 shape matches the hsma achieved a 90 36 recognition rate as opposed to 89 76 for the sma and 89 49 for invariant moments on the other hand the hsma improved the sma processing more than 40