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

binary image comparison with local dissimilarity quantification in this paper we present a method for binary image comparison for binary images intensity information is poor and shape extraction is often difficult therefore binary images have to be compared without using feature extraction due to the fact that different scene patterns can be present in the images we propose a modified hausdorff distance hd locally measured in an adaptive way the resulting set of measures is richer than a single global measure the local hd measures result in a local dissimilarity map ldmap including the dissimilarity spatial layout a classification of the images in function of their similarity is carried out on the ldmaps using a support vector machine the proposed method is tested on a medieval illustration database and compared with other methods to show its efficiency

the image foresting transform theory algorithms and applications the image foresting transform ift is a graph based approach to the design of image processing operators based on connectivity it naturally leads to correct and efficient implementations and to a better understanding of how different operators relate to each other we give here a precise definition of the ift and a procedure to compute it a generalization of dijkstra s algorithm with a proof of correctness we also discuss implementation issues and illustrate the use of the ift in a few applications

three dimensional euclidean distance transformation and its application to shortest path planning in this paper we present a novel method to obtain the three dimensional euclidean distance transformation edt in two scans of the image the shortest path can be extracted based on the distance maps using the minimum value tracing the edt is obtained correctly and efficiently in a constant time for arbitrary types of images including the existence of obstacles by adopting the new dynamically rotational mathematical morphology we not only guarantee the collision free in the shortest path but also reduce the time complexity dramatically

new algorithms for euclidean distance transformation of an n dimensional digitized picture with applications abstract in this paper we propose a new method to obtain the euclidean distance transformation and the voronoi diagram based on the exact euclidean metric for an n dimensional picture we present four algorithms to perform the transformation which are constructed by the serial composition of n dimensional filters when performed by a general purpose computer they are faster than the method by h yamada for a two dimensional picture those algorithms require only one n dimensional array for storing input output pictures and a single one dimensional array for a work area if an input picture needs not be preserved

a linear time algorithm for computing exact euclidean distance transforms of binary images in arbitrary dimensions a sequential algorithm is presented for computing the exact euclidean distance transform dt of a k dimensional binary image in time linear in the total number of voxels n the algorithm which is based on dimensionality reduction and partial voronoi diagram construction can be used for computing the dt for a wide class of distance functions including the l sub p and chamfer metrics at each dimension level the dt is computed by constructing the intersection of the voronoi diagram whose sites are the feature voxels with each row of the image this construction is performed efficiently by using the dt in the next lower dimension the correctness and linear time complexity are demonstrated analytically and verified experimentally the algorithm may be of practical value since it is relatively simple and easy to implement and it is relatively fast not only does it run in o n time but the time constant is small a simple modification of the algorithm computes the weighted euclidean dt which is useful for images with anisotropic voxel dimensions a parallel version of the algorithm runs in o n p time with p processors

skeletonization based on error reduction the accuracy of a non pixel based skeletonization method is largely dependent on the contour information chosen as input when using a constrained delaunay triangulation to construct an object s skeleton a number of contour pixels must be chosen as a basis for triangulation this paper presents a new method of selecting these contour pixels a new method for measuring skeletonization error is proposed which quantifies the deviation of a skeleton segment from the true medial axis of a stroke in an image the goal of the proposed algorithm is to reduce this error to an acceptable level whilst retaining the superior efficiencies of previous non pixel based techniques experimental results show that the proposed method is adept at following the medial axis of an image and is capable of producing a skeleton that is confirmed by a human s perception of the image it is also computationally efficient and robust against noise

adaptive beamforming algorithms with robustness against jammer motion the performance of adaptive array algorithms is known to degrade in rapidly moving jammer environments this degradation occurs due to the jammer motion that may bring the jammers out of the sharp notches of the adapted pattern we develop the robust modifications of the sample matrix inversion smi algorithm loaded smi lsmi algorithm and eigenvector projection ep algorithm by means of artificial broadening of the null width in the jammer directions for this purpose data dependent sidelobe derivative constraints that do not require any a priori information about the jammer directions are used

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

efficient euclidean distance transform algorithm of binary images in arbitrary dimensions in this paper we propose an efficient algorithm i e pbedt for short to compute the exact euclidean distance transform edt of a binary image in arbitrary dimensions the pbedt is based on independent scan and implemented in a recursive way i e the edt of a d dimensional image is able to be computed from the edts of its d 1 dimensional sub images in each recursion all of the rows in the current dimensional direction are processed one by one the points in the current processing row and their closest feature points in d 1 dimensional sub images can be shown in a euclidean plane by using the geometric properties of the perpendicular bisector the closest feature points of d 1 dimensional sub images are easily verified so as to lead to the edt of a d dimensional image after eliminating the invalid points the time complexity of the pbedt algorithm is linear in the amount of both image points and dimensions with a small coefficient compared with the state of the art edt algorithms the pbedt algorithm is much faster and more stable in most cases

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

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

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

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

robust hausdorff distance matching algorithms using pyramidal structures abstract this paper proposes two hausdorff distance hd matching algorithms in which robust hd measures are implemented in pyramidal structures by computer simulations the matching performance of the conventional hd measures and the proposed robust hd matching algorithms using pyramidal structures is compared with real images which are degraded by noise and occlusions

linear time euclidean distance transform algorithms two linear time and hence asymptotically optimal algorithms for computing the euclidean distance transform of a two dimensional binary image are presented the algorithms are based on the construction and regular sampling of the voronoi diagram whose sites consist of the unit feature pixels in the image the first algorithm which is of primarily theoretical interest constructs the complete voronoi diagram the second more practical algorithm constructs the voronoi diagram where it intersects the horizontal lines passing through the image pixel centers extensions to higher dimensional images and to other distance functions are also discussed

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

a list processing approach to compute voronoi diagrams and the euclidean distance transform we propose an efficient voronoi transform algorithm for constructing voronoi diagrams using segment lists of rows a significant feature of the algorithm is that it takes segments rather than pixels as the basic units to represent and propagate the nearest neighbor information the segment lists are dynamically updated as they are scanned a distance map can then be easily computed from the segment list representation of the voronoi diagram experimental results have demonstrated its high efficiency extension of the algorithm to higher dimensions is also discussed

on orbit damage assessment for large space structures the need for monitoring the dynamic characteristics of large structural systems for the purpose of assessing the potential degradation of structural properties has been established this paper develops a theory for assessing the occurrence location and extent of potential damage utilizing on orbit response measurements the feasibility of the method is demonstrated using a simple structural system as an example

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

weight evaluation for features via constrained data pairscan t linkq facing the massive amount of data appearing on the web automatic analysis tools have become essential for web users to discover valuable information online precise similarity measurement plays a decisive role in enabling analysis tools to acquire high quality performances because different features contribute diversely to similarity calculation it is necessary to utilize weight to measure feature s contribution and import it into similarity measurement to accurately assign feature s weight constrained data pairs provided by users are usually imported into the weight evaluation procedure whereas conventional plans all fail to consider two challenges a asymmetrical distribution of constrained data pairs and b inconsistency contained by constrained data pairs if these two issues occur conventional plans are incompetent at addressing them or are even unable to work thus this paper proposes a novel constraint based weight evaluation to address these two issues for the former constrained data pairs are partitioned into several equivalent classes and distributing parameters are assigned to constrained data pairs to balance their distributions for the latter constrained data pairs are connected one after another and belief values are thereby formed to indicate their probability of being inconsistent experimental results demonstrate that this type of evaluation is independent of any algorithm with this evaluation similarities can be calculated more accurately

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

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

morphological filters part i their set theoretic analysis and relations to linear shift invariant filters this paper examines the set theoretic interpretation of morphological filters in the framework of mathematical morphology and introduces the representation of classical linear filters in terms of morphological correlations which involve supremum infimum operations and additions binary signals are classified as sets and multilevel signals as functions two set theoretic representations of signals are reviewed filters are classified as set processing sp or function processing fp conditions are provided for certain fp filters that pass binary signals to commute with signal thresholding because then they can be analyzed and implemented as sp filters the basic morphological operations of set erosion dilation opening and closing are related to minkowski set operations and are used to construct fp morphological filters emphasis is then given to analytically and geometrically quantifying the similarities and differences between morphological filtering of signals by sets and functions the latter case allows the definition of morphological convolutions and correlations toward this goal various properties of fp morphological filters are also examined linear shift invariant filters due to their translation invariance are uniquely characterized by their kernel which is a special collection of input signals increasing linear filters are represented as the supremum of erosions by their kernel functions if the filters are also discrete and have a finite extent impulse response they can be represented as the supremum of erosions only by their minimal with respect to a signal ordering kernel functions stable linear filters can be represented as the sum of at most two weighted suprema of erosions these results demonstrate the power of mathematical morphology as a unifying approach to both linear and nonlinear signal shaping strategies

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

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

histograms analysis for image retrieval abstract this paper analyzes the use of histograms of low level image features such as color and luminance as descriptors for image retrieval purposes a novel definition of histogram capacity curve taking into account the density distribution of histograms in the corresponding spaces is proposed and used to quantify the effectiveness of image descriptors and histogram dissimilarities in image retrieval applications the results permit the design of scalable image retrieval systems which make optimal use of computational and storage resources

morphological iterative closest point algorithm this work presents a method for the registration of three dimensional 3 d shapes the method is based on the iterative closest point icp algorithm and improves it through the use of a 3 d volume containing the shapes to be registered the voronoi diagram of the model shape points is first constructed in the volume then this is used for the calculation of the closest point operator this way a dramatic decrease of the computational cost is achieved

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

information geometry for landmark shape analysis unifying shape representation and deformation shape matching plays a prominent role in the comparison of similar structures we present a unifying framework for shape matching that uses mixture models to couple both the shape representation and deformation the theoretical foundation is drawn from information geometry wherein information matrices are used to establish intrinsic distances between parametric densities when a parameterized probability density function is used to represent a landmark based shape the modes of deformation are automatically established through the information matrix of the density we first show that given two shapes parameterized by gaussian mixture models gmms the well known fisher information matrix of the mixture model is also a riemannian metric actually the fisher rao riemannian metric and can therefore be used for computing shape geodesics the fisher rao metric has the advantage of being an intrinsic metric and invariant to reparameterization the geodesic computed using this metric establishes an intrinsic deformation between the shapes thus unifying both shape representation and deformation a fundamental drawback of the fisher rao metric is that it is not available in closed form for the gmm consequently shape comparisons are computationally very expensive to address this we develop a new riemannian metric based on generalized phi entropy measures in sharp contrast to the fisher rao metric the new metric is available in closed form geodesic computations using the new metric are considerably more efficient we validate the performance and discriminative capabilities of these new information geometry based metrics by pairwise matching of corpus callosum shapes we also study the deformations of fish shapes that have various topological properties a comprehensive comparative analysis is also provided using other landmark based distances including the hausdorff distance the procrustes metric landmark based diffeomorphisms and the bending energies of the thin plate tps and wendland splines

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

computing distance transformations in convex and non convex domains abstract it is shown that the well known two pass sequential local transformation algorithm for computing a distance transformation in rectangular domains may fail in some convex integer domains but that a four pass algorithm is sufficient in all two dimensional convex domains for non convex domains the number of passes necessary is shown to be generally greater two propagation algorithms for computing the distance transformation are described and shown theoretically and experimentally to be computationally more efficient than the sequential local transformation algorithm in non convex domains of complex shape the relationship of the distance transformation in non convex domains to some more general transformations is explored

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

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

theory and application of covariance matrix tapers for robust adaptive beamforming we unify several seemingly disparate approaches to robust adaptive beamforming through the introduction of the concept of a covariance matrix taper cmt this is accomplished by recognizing that an important class of adapted pattern modification techniques are realized by the application of a conformal matrix taper to the original sample covariance matrix from the schur product theorem for positive semi definite matrices and kolmogorov s existence theorem we further establish that cmts are in fact the solution to a minimum variance optimum beamformer associated with an auxiliary stochastic process that is related to the original by a hadamard schur product this allows us to gain deeper insight into the design of both existing pattern modification techniques and new cmts that can for example simultaneously address several different design constraints such as pattern distortion due to insufficient sample support and weights mismatch due to nonstationary interference a new two dimensional 2 d cmt for space time adaptive radar applications designed to provide more robust clutter cancellation is also introduced since the cmt approach only involves a single matrix haddamard product it is also inherently low complexity the practical utility of the cmt approach is illustrated through its application to both spatial and spatio temporal adaptive beamforming examples

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

modal parameter identification using simulated evolution a global optimization algorithm based on the darwinian evolutionary theory is implemented for the identification of modal parameters of linear vibrating structures the capability of the evolutionary search method in locating the global minimum among numerous local minima is demonstrated the modal parameter identification procedure is based on the concept of modal sweep according to which modes of a structure are identified individually and iteratively a fast recursive algorithm is also developed for forward response calculation of a linear oscillator to lessen the computational burden of using simulated evolution in the iterative identification process the proposed modal parameter identification approach does not require any initial estimate of parameter values simulation results show that the approach is effective and reliable in identifying dominant modes under noisy conditions

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

a new structural damage identification method a new method is presented to provide an insight in to the characterizations of structural damages the present algorithm makes use of an original finite element model and a subset of measured eigenvalues and eigenvectors the proposed method detects damages in a decoupled fashion first a theory is developed to determine the number of damaged elements with the damage number determined the localization and quantification algorithms are then developed a plane truss structure is analyzed as a numerical example to verify the present method results show that the method is accurate and robust in structural damage identification when the number of measured modes is more than the number of damaged elements with or without noise

decomposition of additively separable structuring elements with applications abstract the techniques of decomposing gray scale structuring elements with emphasis on the additively separable structuring elements are presented based on the concept of additively separable we proposed the square euclidean distance as the measure in the distance transformation since the structuring element corresponding to square euclidean distance is additively separable the developed techniques can be applied to decompose the structuring element into successive dilation of small structuring elements with window size 3 3

distance driven skeletonization in voxel images a distance driven method to compute the surface and curve skeletons of 3d objects in voxel images is described the method is based on the use of the weighted distance transform on the detection of anchor points and on the application of topology preserving removal operations the obtained surface and curve skeletons are centered within the object have the same topology as the object and have unit thickness the object can be almost completely recovered from the surface skeleton since this includes almost all of the centers of maximal balls of the object hence the surface skeleton is a faithful representation in turn though only partial recovery is possible from the curve skeleton this still provides an appealing representation of the object

multiple acceptable solutions in structural model improvement this paper examines the question as to whether it is possible to obtain the correct discrete linear analytical model of an actual structure by the use of analysis and test data it is shown that no such correct model exists an illustration of an application is shown where multiple acceptable and very different analytical models are all representative of the structure the implications regarding methods of improving analytical models and detecting damage are discussed

comparing face images using the modified hausdorff distance abstract we introduce a novel methodology applicable to face matching and fast screening of large facial databases the proposed shape comparison method operates on edge maps and derives holistic similarity measures yet it does not require solving the point correspondence problem while the use of edge images is important to introduce robustness to changes in illumination the lack of point to point matching delivers speed and tolerance to local non rigid distortions in particular we propose a face similarity measure derived as a variant of the hausdorff distance by introducing the notion of a neighborhood function n and associated penalties p experimental results on a large set of face images demonstrate that our approach produces excellent recognition results even when less than 3 of the original grey scale face image information is stored in the face database gallery these results implicate that the process of face recognition may start at a much earlier stage of visual processing than it was earlier suggested we argue that edge like retinal images of faces are initially screened at a glance without the involvement of high level cognitive functions thus delivering high speed and reducing computational complexity

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

morphological filters part ii their relations to median order statistic and stack filters this paper extends the theory of median order statistic os and stack filters by using mathematical morphology to analyze them and by relating them to those morphological erosions dilations openings closings and open closings that commute with thresholding the max min representation of os filters is introduced by showing that any median or other os filter is equal to a maximum of erosions moving local minima and also to a minimum of dilations moving local maxima thus os filters can be computed by a closed formula that involves a max min on prespecified sets of numbers and no sorting stack filters are established as the class of filters that are composed exactly of a finite number of max min operations the kernels of median os and stack filters are collections of input signals that uniquely represent these filters due to their translation invariance the max min functional definitions of these nonlinear iliters is shown to be equivalent to a maximum of erosions by minimal with respect to a signal ordering kernel elements and also to a minimum of dilations by minimal kernel elements of dual filters the representation of stack filters based on their minimal kernel elements is proven to be equivalent to their representation based on irreducible sum of products expressions of boolean functions it is also shown that median filtering and its iterations of any signal by convex 1 d windows is bounded below by openings and above by closings a signal is a root fixed point of the median iff it is a root of both an opening and a closing the open closing and clos opening yield median roots in one pass suppress impulse noise similarly to the median can discriminate between positive and negative noise impulses and are computationally less complex than the median some similar results are obtained for 2 d median filtering

robust wideband adaptive beamforming with null broadening and constant beamwidth in the cases of rapidly moving interference and look direction error robustness and output signal to interference and noise ratio sinr of conventional wideband adaptive beamforming methods are degraded severely in order to solve these problems a robust wideband adaptive beamforming with null broadening and constant beamwidth is proposed we first propose a taper matrix constructed by adding virtual interferences for null broadening where the reference frequency and number of virtual interferences of taper matrix are determined based on numerical methods this is followed by reconstructing the array covariance matrix based on taper matrix spatial response variation srv constraint is then applied for a constant beamwidth over the entire frequency band finally the adaptive weight vector for null broadening and constant beamwidth is obtained by using lagrange multiplier method the effectiveness of proposed method is verified by numerical simulations

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

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 mathematical morphology approach to euclidean distance transformation a distance transformation technique for a binary digital image using a gray scale mathematical morphology approach is presented applying well developed decomposition properties of mathematical morphology one can significantly reduce the tremendous cost of global operations to that of small neighborhood operations suitable for parallel pipelined computers first the distance transformation using mathematical morphology is developed then several approximations of the euclidean distance are discussed the decomposition of the euclidean distance structuring element is presented the decomposition technique employs a set of 3 by 3 gray scale morphological erosions with suitable weighted structuring elements and combines the outputs using the minimum operator real valued distance transformations are considered during the processes and the result is approximated to the closest integer in the final output image

adaptive wideband beamforming with frequency invariance constraints a response variation rv element is introduced to control the consistency of an adaptive wideband beamformer s response over the frequency range of interest by incorporating the rv element into the linearly constrained minimum variance lcmv beamformer we develop a novel linearly constrained beamformer with an improved output signal to interference plus noise ratio sinr compared to both the traditional formulation and the eigenvector based formulation due to an increased number of degrees of freedom for interference suppression in addition two novel wideband beamformers robust against look direction estimation errors are also proposed as a further application of the rv element one is designed by imposing a constraint on the rv element and simultaneously limiting the magnitude response of the beamformer within a pre defined angle range at a reference frequency the other one is obtained by combining the rv element and the worst case performance optimization method both of them are reformulated in a convex form as the second order cone soc programming problem and solved efficiently using interior point method compared with the original robust methods a more efficient and effective control over the beamformer s response at the look direction region is achieved with an improved overall performance

damage detection in elastic structures using vibratory residual forces and weighted sensitivity a methodology is presented for detecting structural damage in elastic structures by nondestructiv e means measured modal test data along with a correlated analytical structural model are used to locate potentially damaged regions using residual modal force vectors and to conduct a weighted sensitivity analysis to assess the extent of mass and or stiffness variations where damage is characterized as a stiffness reduction the current approach is unique among other approaches in that it accounts for 1 variations in system mass system stiffness and mass center locations 2 perturbations of both the natural frequencies and modal vectors and 3 statistical confidence factors for the structural parameters and potential experimental instrumentation error moreover this procedure can be used with either full or reduced models a wide variety of numerical examples are presented that show that the current method provides a precise indication of both the location and the extent of structural damage lexible space structures launch vehicles and satellites are susceptible to structural damage over their operating lives from impact operating loads and fatigue undetected and uncorrected damage can lead to structural deterioration of their members and consequently jeopardize the flight safety of the structure thus numerous damage inspection methods and monitoring procedures have been developed examples include x ray ultrasonic testing magnetic resonance coin tap dye penetration and visual inspection these methods can be time consuming and are local assessments often requir ing the exposure of structural elements to the inspector and equipment for detecting damage as a monitoring system for detecting damage of spacecraft in orbit i e space station freedom none of these methods are appropriate an alterna tive approach which formed the basis for our current study is to recognize the fact that modal vibration test data struc tural natural frequencies and mode shapes characterize the state of the structure 1 therefore postflight and in flight e g monitoring data can be used to distinguish whether changes damage have occurred to the structure by comparing these data with a set of baseline data modal testing as a means of inspection has several advantages direct exposure of struc tural elements is not required and at the same time more of the complete structure can be inspected in one modal test by having appropriately placed sensors the consequences of this are a reduction in schedule and cost the use of vibration test data to locate structural damage has been attempted to evaluate the integrity of offshore oil and gas platforms 2 3 composite laminates 4 continuum struc tures 5 8 and recently large space structures 9 11 the early ana lytical and experimental approaches2 3 had limited success as a result of inadequate instrumentation and addressing only fre quency shifts associated with stiffness changes while ignoring changes in the modal vectors the continuum based meth ods5 8 provide valuable insight into the magnitude of fre quency shifts but their usefulness is severely limited to simple structures bars beams plates with unrealistic boundary con

an efficient uniform cost algorithm applied to distance transforms the uniform cost algorithm is a special case of the a algorithm for finding the shortest paths in graphs in the uniform cost algorithm nodes are expanded in order of increasing cost an efficient version of this algorithm is developed for integer cost values nodes are sorted by storing them at predefined places bucket sort keeping the overhead low the algorithm is applied to general distance transformation a constrained distance transform is an operation which calculates at each pixel of an image the distance to the nearest pixel of a reference set distance being defined as minimum path length the uniform cost algorithm in the constrained case proves to be the best solution for distance transformation it is fast the processing time is independent of the complexity of the image and memory requirements are moderate

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

a skeletonization algorithm by maxima tracking on euclidean distance transform abstract a simple and efficient algorithm using the maxima tracking approach on euclidean distance transform to detect skeleton points is presented the advantages of the skeleton obtained are 1 connectivity preservation 2 single pixel in width and 3 its locations as close as to the most symmetrical axes besides the condition of the least slope change of skeleton is used to ensure the fairness of the digital medial axes with the least effort the algorithm can be modified to eliminate non significant short skeletal branches originating from the object contour while the critical shape informative medial axes are preserved

euclidean skeletons of digital image and volume data in linear time by the integer medial axis transform a general algorithm for computing euclidean skeletons of 2d and 3d data sets in linear time is presented these skeletons are defined in terms of a new concept called the integer medial axis ima transform we prove a number of fundamental properties of the ima skeleton and compare these with properties of the cmd centers of maximal disks skeleton several pruning methods for ima skeletons are introduced constant linear and square root pruning and their properties studied the algorithm for computing the ima skeleton is based upon the feature transform using a modification of a linear time algorithm for euclidean distance transforms the skeletonization algorithm has a time complexity which is linear in the number of input points and can be easily parallelized we present experimental results for several data sets looking at skeleton quality memory usage and computation time both for 2d images and 3d volumes

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

fast 2 d distance transformations the performance of a number of image processing methods depends on the output quality of a distance transformation dt process most of the fast dt methodologies are not accurate whereas other error free dt algorithms are not very fast in this paper a novel fast simple and error free dt algorithm is presented by recording the relative x and y coordinates of the examined image pixels an optimal algorithm can be developed to achieve the dt of an image correctly and efficiently in constant time without any iteration furthermore the proposed method is general since it can be used by any kind of distance function leading to accurate image dts

broad band array design using the asymptotic theory of unequally spaced arrays the problem of designing broadband linear arrays of omnidirectional sensors is addressed attention is restricted to the case of shaded delay and sum beamforming broadbanding is here defined to mean that the beam pattern function has little or no frequency dependence of peak response main lobe width plateau sidelobe level and sinespace separation between the main lobe and the plateau sidelobe the asymptotic theory of unequally spaced arrays is used to derive relationships between beam pattern properties and array properties these relationships are used to translate beam pattern requirements into functional requirements on sensor spacings and amplitude shadings the functional requirements are then used to derive a broadband array design in addition to the design equations the asymptotic theory is used to derive equations for main lobe level sidelobe level beamwidth and signal to noise ratio snr gain in isotropic noise a specific example is presented to clarify the concepts and verify that the design procedure actually works

the efficient algorithms for achieving euclidean distance transformation euclidean distance transformation edt is used to convert a digital binary image consisting of object foreground and nonobject background pixels into another image where each pixel has a value of the minimum euclidean distance from nonobject pixels in this paper the improved iterative erosion algorithm is proposed to avoid the redundant calculations in the iterative erosion algorithm furthermore to avoid the iterative operations the two scan based algorithm by a deriving approach is developed for achieving edt correctly and efficiently in a constant time besides we discover when obstacles appear in the image many algorithms cannot achieve the correct edt except our two scan based algorithm moreover the two scan based algorithm does not require the additional cost of preprocessing or relative coordinates recording