shape smoothing using medial axis properties a shape smoothing algorithm is presented which uses properties of the medial axis to define segments of the shape border and their prominence relative to the local radius of the shape prominence values are used to classify axes as either major or minor and minor axes are then deleted an augmented medial axis transform is also defined using an approximate euclidean distance transform and medial axis interpolation and linking

on the generation of skeletons from discrete euclidean distance maps the skeleton is an important representation for shape analysis a common approach for generating discrete skeletons takes three steps 1 computing the distance map 2 detecting maximal disks from the distance map and 3 linking the centers of maximal disks cmds into a connected skeleton algorithms using approximate distance metrics are abundant and their theory has been well established however the resulting skeletons may be inaccurate and sensitive to rotation in this paper we study methods for generating skeletons based on the exact euclidean metric we first show that no previous algorithms identify the exact set of discrete maximal disks under the euclidean metric we then propose new algorithms and show that they are correct to link cmds into connected skeletons we examine two prevalent approaches connected thinning and steepest ascent we point out that the connected thinning approach does not work properly for euclidean distance maps only the steepest ascent algorithm produces skeletons that are truly medially placed the resulting skeletons have all the desirable properties they have the same simple connectivity as the figure they are well centered they are insensitive to rotation and they allow exact reconstruction the effectiveness of our algorithms is demonstrated with numerous examples

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

an adaptive active contour model for highly irregular boundaries abstract snake is an active contour model for representing image contours in this paper we propose an efficient active contour model which can represent highly irregular boundaries the algorithm includes an adaptive force along the contour and adjusts the number of points for the snake according to the desired boundary a better stopping criterion based on the area of a closed contour is devised furthermore in this method a contour can break automatically to represent the contours of multiple objects experiments show that this method can extract object s boundaries accurately and efficiently

medial axis transformation of a planar shape the medial axis transformation is a means first proposed by blum to describe a shape in this paper we present a 0 n log n algorithm for computing the medial axis of a planar shape represented by an n edge simple polygon the algorithm is an improvement over most previously known results interms of both efficiency and exactness and has been implemented in fortran some computer plotted output of the program are also shown in the paper

skeleton based morphological coding of binary images this paper presents new properties of the discrete morphological skeleton representation of binary images along with a novel coding scheme for lossless binary image compression that is based on these properties following a short review of the theoretical background two sets of new properties of the discrete morphological skeleton representation of binary images are proved the first one leads to the conclusion that only the radii of skeleton points belonging to a subset of the ultimate erosions are needed for perfect reconstruction this corresponds to a lossless sampling of the quench function the second set of new properties is related to deterministic prediction of skeletonal information in a progressive transmission scheme based on the new properties a novel coding scheme for binary images is presented the proposed scheme is suitable for progressive transmission and fast implementation computer simulations also presented show that the proposed coding scheme substantially improves the results obtained by previous skeleton based coders and performs better than classical coders including run length huffman quadtree and chain coders for facsimile images its performance can be placed between the modified read mr method k 4 and modified modified read mmr method

some self dual codes invariant under the hall janko group abstract we construct self dual codes of length 100 invariant under the hall janko group j 2 we also construct a 2 100 22 168 design with the automorphism group j 2 2 which is the extension of j 2 by its outer automorphism

optimum design of chamfer distance transforms the distance transform has found many applications in image analysis chamfer distance transforms are a class of discrete algorithms that offer a good approximation to the desired euclidean distance transform at a lower computational cost they can also give integer valued distances that are more suitable for several digital image processing tasks the local distances used to compute a chamfer distance transform are selected to minimize an approximation error a new geometric approach is developed to find optimal local distances this new approach is easier to visualize than the approaches found in previous work and can be easily extended to chamfer metrics that use large neighborhoods a new concept of critical local distances is presented which reduces the computational complexity of the chamfer distance transform without increasing the maximum approximation error

a rotation invariant rule based thinning algorithm for character recognition this paper presents a novel rule based system for thinning the unique feature that distinguishes our thinning system is that it thins symbols to their central lines this means that the shape of the symbol is preserved it also means that the method is rotation invariant the system has 20 rules in its inference engine these rules are applied simultaneously to each pixel in the image therefore the system has the advantages of symmetrical thinning and speed the results show that the system is very efficient in preserving the topology of symbols and letters written in any language

a note on self dual group codes we classify group algebras over galois rings containing self dual ideals i e ideals c which satisfy c c sup spl perp with respect to the natural nondegenerate bilinear form given on group algebras

snakes active contour models a snake is an energy minimizing spline guided by external constraint forces and influenced by image forces that pull it toward features such as lines and edges snakes are active contour models they lock onto nearby edges localizing them accurately scale space continuation can be used to enlarge the capture region surrounding a feature snakes provide a unified account of a number of visual problems including detection of edges lines and subjective contours motion tracking and stereo matching we have used snakes successfully for interactive interpretation in which user imposed constraint forces guide the snake near features of interest

detection of 3 d simple points for topology preserving transformations with application to thinning the problems of 3 d digital topology preservation under binary transformations and 3 d object thinning are considered in this correspondence first the authors establish the conditions under which transformation of an object voxel to a non object voxel or its inverse does not affect the image topology an efficient algorithm to detect a simple point has been proposed on the basis of those conditions in this connection some other interesting properties of 3 d digital geometry are also discussed using these properties and the simple point detection algorithm the authors have proposed an algorithm to generate a surface skeleton so that the topology of the original image is preserved the shape of the image is maintained as much as possible and the results are less affected by noise

object matching with hierarchical skeletons the skeleton of an object provides an intuitive and effective abstraction which facilitates object matching and recognition however without any human interaction traditional skeleton based descriptors and matching algorithms are not stable for deformable objects specifically some fine grained topological and geometrical features would be discarded if the skeleton was incomplete or only represented significant visual parts of an object moreover the performance of skeleton based matching highly depends on the quality and completeness of skeletons in this paper we propose a novel object representation and matching algorithm based on hierarchical skeletons which capture the shape topology and geometry through multiple levels of skeletons for object representation we reuse the pruned skeleton branches to represent the coarse and fine grained shape topological and geometrical features moreover this can improve the stability of skeleton pruning without human interaction we also propose an object matching method which considers both global shape properties and fine grained deformations by defining singleton and pairwise potentials for similarity computation between hierarchical skeletons our experiments attest our hierarchical skeleton based method a significantly better performance than most existing shape based object matching methods on six datasets achieving a 99 21 bulls eye score on the mpeg7 shape dataset highlightsit represents the coarse and fine grained shape topological and geometrical features it improves the stability of skeleton pruning without human interaction it considers both global and fine shape properties by different potential functions it achieves a better performance than most existing methods on six datasets experiments attest our method a better performance than most related approaches we achieve a 99 21 bulls eye score on the mpeg7 shape dataset

subharmonics for convex nonautonomous hamiltonian systems on etudie des solutions periodiques du systeme hamiltonien jx h t x ou j est la matrice symplectique standard et h c 2 r r 2n r est t periodique en la premiere variable pour tout t x h t x note le gradient partiel par rapport a la seconde variable

extremal binary self dual codes in this correspondence we investigate binary extremal self dual codes numerous extremal self dual codes and interesting self dual codes with minimum weight d 14 and 16 are constructed in particular the first extremal type i 86 43 16 code and new extremal self dual codes with weight enumerators which were not previously known to exist for lengths 40 50 52 and 54 are constructed we also determine the possible weight enumerators for extremal type i codes of lengths 66 100

periodic solutions for second order systems with not uniformly coercive potential abstract the existence and multiplicity of periodic solutions are obtained for the nonautonomous second order systems with locally coercive potential that is f t x as x for a e t in some positive measure subset of 0 t by using an analogy of egorov s theorem the properties of subadditive functions the least action principle and a three critical point theorem proposed by brezis and nirenberg

a skeleton family generator via physics based deformable models this paper presents a novel approach for object skeleton family extraction the introduced technique utilizes a 2 d physics based deformable model that parameterizes the objects shape deformation equations are solved exploiting modal analysis and proportional to model physical characteristics a different skeleton is produced every time generating in this way a family of skeletons the theoretical properties and the experiments presented demonstrate that obtained skeletons match to hand labeled skeletons provided by human subjects even in the presence of significant noise and shape variations cuts and tears and have the same topology as the original skeletons in particular the proposed approach produces no spurious branches without the need of any known skeleton pruning method

path similarity skeleton graph matching this paper proposes a novel graph matching algorithm and applies it to shape recognition based on object silhouettes the main idea is to match skeleton graphs by comparing the geodesic paths between skeleton endpoints in contrast to typical tree or graph matching methods we do not consider the topological graph structure our approach is motivated by the fact that visually similar skeleton graphs may have completely different topological structures the proposed comparison of geodesic paths between endpoints of skeleton graphs yields correct matching results in such cases the skeletons are pruned by contour partitioning with discrete curve evolution which implies that the endpoints of skeleton branches correspond to visual parts of the objects the experimental results demonstrate that our method is able to produce correct results in the presence of articulations stretching and contour deformations

hierarchic voronoi skeletons abstract robust and time efficient skeletonization of a planar shape which is connectivity preserving and based on euclidean metrics can be achieved by first regularizing the voronoi diagram vd of a shape s boundary points i e by removal of noise sensitive parts of the tessellation and then by establishing a hierarchic organization of skeleton constituents each component of the vd is attributed with a measure of prominence which exhibits the expected invariance under geometric transformations and noise the second processing step a hierarchic clustering of skeleton branches leads to a multiresolution representation of the skeleton termed skeleton pyramid

a new algorithm for line image vectorization in this paper a new approach which differentiates from the conventional thinning algorithms in vectorizing a raster line image called maximal inscribing circle mic is used this region based vectorization algorithm takes the ensemble of pixels within the line segments collectively as legitimate candidates in deciding the vectorized representation an iterative procedure is outlined and the criteria for merging short straight line segments into the corresponding curve representation are described this method cannot only segment the lines and junctions construct their spatial relationships in a computation efficient manner but also retain their line width

skeletonization of ribbon like shapes based on a new wavelet function a wavelet based scheme to extract skeleton of ribbon like shape is proposed in this paper where a novel wavelet function plays a key role in this scheme which possesses three significant characteristics namely 1 the position of the local maximum moduli of the wavelet transform with respect to the ribbon like shape is independent of the gray levels of the image 2 when the appropriate scale of the wavelet transform is selected the local maximum moduli of the wavelet transform of the ribbon like shape produce two new parallel contours which are located symmetrically at two sides of the original one and have the same topological and geometric properties as that of the original shape 3 the distance between these two parallel contours equals to the scale of the wavelet transform which is independent of the width of the shape this new scheme consists of two phases 1 generation of wavelet skeleton based on the desirable properties of the new wavelet function symmetry analyses of the maximum moduli of the wavelet transform is described midpoints of all pairs of contour elements can be connected to generate a skeleton of the shape which is defined as wavelet skeleton 2 modification of the wavelet skeleton thereafter a set of techniques are utilized for modifying the artifacts of the primary wavelet skeleton the corresponding algorithm is also developed in this paper experimental results show that the proposed scheme is capable of extracting exactly the skeleton of the ribbon like shape with different width as well as different gray levels the skeleton representation is robust against noise and affine transformation

a ridge following algorithm for finding the skeleton of a fuzzy image abstract a typical method for finding the skeleton of a grayscale image is to threshold the image then thin the result with one of several binary thinning algorithms this process loses information in the intensity dimension by reducing all intensities to either one of two values the loss of intensity information causes the skeleton of non uniform grayscale images to be centrally located within the thresholded image but may not lie along the maximum intensity ridge line in this paper we propose a method that avoids thresholding instead we transform the grayscale image into a fuzzy set and use the degree of membership in the underlying object to find the skeleton along the maximum intensity ridge line topographical labeling methods find a ridge line by topographically labeling pixels the ride line is the union of peak ridge and saddle point pixels these methods require preprocessing or postprocessing to find connected single pixel skeletons we show the results of our algorithm on images varying in uniformity from a gaussian smoothed binary rectangle to a scanned image of a grayscale object we compare results with the threshold and thin and topographical labeling methods

multiple instance subspace learning via partial random projection tree for local reflection symmetry in natural images local reflection symmetry detection in nature images is a quite important but challenging task in computer vision the main obstacle is both the scales and the orientations of symmetric structure are unknown the multiple instance learning mil framework sheds lights onto this task owing to its capability to well accommodate the unknown scales and orientations of the symmetric structures however to differentiate symmetry vs non symmetry remains to face extreme confusions caused by clutters scenes and ambiguous object structures in this paper we propose a novel multiple instance learning framework for local reflection symmetry detection named multiple instance subspace learning misl which instead learns a group of models respectively on well partitioned subspaces to obtain such subspaces we propose an efficient dividing strategy under mil setting named partial random projection tree prpt by taking advantage of the fact that each sample bag is represented by the proposed symmetry features computed at specific scale and orientation combinations instances encouraging experimental results on two datasets demonstrate that the proposed local reflection symmetry detection method outperforms current state of the arts highlightswe perform clustering on samples represented by multiple instances we learn a group of mil classifiers on subspaces we report state of the arts results on the symmetry detection benchmark

fast homotopy preserving skeletons using mathematical morphology two algorithms for skeletonization of 2 d binary images each of which explicitly separates the two major aspects of skeletonization are described the identification of points critical to shape representation and the identification of further points necessary to preserve homotopy sets of points critical to shape representation are found by eroding the original image i with a nested sequence of structuring elements e sub i by choosing appropriate e sub i and d a structuring element either algorithm is capable of producing a variety of skeletons corresponding to different distance functions a sufficient condition is given for the original image to be reconstructed from the skeleton in the case of the first algorithm there are few restrictions on the set of structuring elements it uses a simple search strategy to find points whose removal would alter homotopy the second faster algorithm has a more constructional approach to finding points necessary for preserving homotopy which limits it to a more restricted set of structuring elements than the first algorithm however it may still be used with a variety of distance functions

subharmonics for not uniformly coercive hamiltonian systems abstract in this paper we prove the existence of subharmonic solutions with prescribed minimal period for the hamiltonian system u t j h t u t when the hamiltonian h is subquadratic with unbounded gradient and not uniformly coercive

subharmonic solutions with prescribed minimal period for nonautonomous hamiltonian systems on etablit un resultat de multiplicite pour une certaine classe de systemes hamiltoniens periodiques en temps

the multiresolution gradient vector field skeleton many algorithms suppress skeleton associated with boundary perturbation by preventing their formation or by costly branch pruning this work proposes a novel concept of structural and textural skeletons the former is associated with the general shape structure and the latter with boundary perturbations these skeletons remain disconnected to facilitate gross shape matching without the need for branch pruning they are extracted from a multiresolution gradient vector field that is efficiently generated within a pyramidal framework experimental results show that these skeletons are scale and rotation invariant they are less affected by boundary noise compared to skeletons extracted by popular iterative and non iterative techniques

subharmonic solutions for nonautonomous sublinear second order hamiltonian systems some existence theorems are obtained for subharmonic solutions of nonautonomous second order hamiltonian systems by the minimax methods in critical point theory

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

a width independent fast thinning algorithm the skeleton of a digital figure can often be regarded as a convenient alternative to the figure itself it is useful both to diminish drastically the amount of data to be handled and to simplify the computational procedures required for description and classification purposes thinning a digital figure down to its skeleton is a time consuming process when conventional sequential computers are employed the procedure we propose allows one to speed up the thinning transformation and to get a well shaped skeleton after cleaning of the input picture has been performed the pixels of the figure are labeled according to their distance from the background and a set whose pixels are symmetrically placed with respect to distinct contour parts of the figure is found this set is then given a linear structure by applying topology preserving removal operations finally a pruning step regarding branches not relevant in the framework of the problem domain completes the process the resulting skeleton is a labeled set of pixels which is shown to possess all the required properties particularly those concerning connectedness topology and shape moreover the original figure can almost completely be recovered by means of a reverse distance transformation only a fixed and small number of sequential passes through the picture is necessary to achieve the goal the computational effort is rather modest and the use of the proposed algorithm turns out to be more advantageous the greater the width of the figure to be thinned

simulating the grassfire transform using an active contour model a method for shape description of planar objects that integrates both region and boundary features is presented the method is an implementation of a 2d dynamic grassfire that relies on a distance surface on which elastic contours minimize an energy function the method is based on an active contour model numerous implementation aspects of the shape description method were optimized a euclidean metric was used for optimal accuracy and the active contour model permits bypassing some of the discretization limitations inherent in using a digital grid noise filtering was performed on the basis of both contour feature measures and region measures that is curvature extremum significance and ridge support respectively to obtain robust shape descriptors other improvements and variations of the algorithmic implementation are proposed

the groupwise medial axis transform for fuzzy skeletonization and pruning medial representations of shapes are useful due to their use of an object centered coordinate system that directly captures intuitive notions of shape such as thickness bending and elongation however it is well known that an object s medial axis transform mat is unstable with respect to small perturbations of its boundary this instability results in additional unwanted branches in the skeletons which must be pruned in order to recover the portions of the skeletons arising purely from the uncorrupted shape information almost all approaches to skeleton pruning compute a significance measure for each branch according to some heuristic criteria and then prune the least significant branches first current approaches to branch significance computation can be classified as either local solely using information from a neighborhood surrounding each branch or global using information about the shape as a whole in this paper we propose a third groupwise approach to branch significance computation we develop a groupwise skeletonization framework that yields a fuzzy significance measure for each branch derived from information provided by the group of shapes we call this framework the groupwise medial axis transform g mat we propose and evaluate four groupwise methods for computing branch significance and report superior performance compared to a recent leading method we measure the performance of each pruning algorithm using denoising classification and within class skeleton similarity measures this research has several applications including object retrieval and shape analysis

permutation groups and binary self orthogonal codes abstract let g be a permutation group on an n element set we study the binary code c g defined as the dual code of the code spanned by the sets of fixed points of involutions of g we show that any g invariant self orthogonal code of length n is contained in c g many self orthogonal codes related to sporadic simple groups including the extended golay code are obtained as c g some new self dual codes invariant under sporadic almost simple groups are constructed

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

disconnected skeleton shape at its absolute scale we present a new skeletal representation along with a matching framework to address the deformable shape recognition problem the disconnectedness arises as a result of excessive regularization that we use to describe a shape at an attainably coarse scale our motivation is to rely on stable properties the shape instead of inaccurately measured secondary details the new representation does not suffer from the common instability problems of the traditional connected skeletons and the matching process gives quite successful results on a diverse database of 2d shapes an important difference of our approach from the conventional use of skeleton is that we replace the local coordinate frame with a global euclidean frame supported by additional mechanisms to handle articulations and local boundary deformations as a result we can produce descriptions that are sensitive to any combination of changes in scale position orientation and articulation as well as invariant ones

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

skeleton pruning by contour partitioning with discrete curve evolution in this paper we introduce a new skeleton pruning method based on contour partitioning any contour partition can be used but the partitions obtained by discrete curve evolution dce yield excellent results the theoretical properties and the experiments presented demonstrate that obtained skeletons are in accord with human visual perception and stable even in the presence of significant noise and shape variations and have the same topology as the original skeletons in particular we have proven that the proposed approach never produces spurious branches which are common when using the known skeleton pruning methods moreover the proposed pruning method does not displace the skeleton points consequently all skeleton points are centers of maximal disks again many existing methods displace skeleton points in order to produces pruned skeletons

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

automatic and robust computation of 3d medial models incorporating object variability this paper presents a novel processing scheme for the automatic and robust computation of a medial shape model which represents an object population with shape variability the sensitivity of medial descriptions to object variations and small boundary perturbations are fundamental problems of any skeletonization technique these problems are approached with the computation of a model with common medial branching topology and grid sampling this model is then used for a medial shape description of individual objects via a constrained model fit the process starts from parametric 3d boundary representations with existing point to point homology between objects the voronoi skeleton of each sampled object boundary is partitioned into non branching medial sheets and simplified by a novel pruning algorithm using a volumetric contribution criterion using the surface homology medial sheets are combined to form a common medial branching topology finally the medial sheets are sampled and represented as meshes of medial primitives results on populations of up to 184 biological objects clearly demonstrate that the common medial branching topology can be described by a small number of medial sheets and that even a coarse sampling leads to a close approximation of individual objects

shape skeletonization by identifying discrete local symmetries abstract this paper presents a new skeletonization method based on a novel concept discrete local symmetry a skeleton obtained from discrete local symmetries approaches the skeleton of the underlying continuous shape if the sampling is dense enough discrete local symmetries can be obtained by computing the constrained delaunay triangulation of the underlying image internal triangles of a triangulation are divided into isolated triangles end triangles normal triangles and junction triangles a discrete local symmetry corresponds to an isolated triangle or an end triangle or a normal triangle several measures are taken to remove skeletonization artifacts and suppress image noise the proposed method can produce correct centre lines and junctions it is efficient and robust against noise the method is suitable for skeletonizing high resolution images

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

a robust parallel thinning algorithm for binary images abstract the class of multi pass iterative thinning algorithms is considered a new algorithm in the same class is proposed and is shown on the basis of experimental results to be superior to the existing ones with respect to medial axis representation and robustness some basic properties of thinning like 1 pixel thickness preservation of connectivity for the present algorithm are ensured for which theoretical proofs are also given

hierarchical shape description via the multiresolution symmetric axis transform a method is proposed that produces a shape description in the form of a hierarchy by scale of simple symmetric axis sequences an axis segment that is a child of another has smaller scale and is seen as a branch of its parent the scale value and parent child relationship are induced by following the symmetric axis under successive reduction of resolution the result in two or three dimensions is a figure rather than boundary oriented shape description that has natural segments and is insensitive to noise in the object description the general approach of hierarchy production by following a feature through successive resolution reduction will be presented as will methods of resolution reduction and computer implementation also the relation of this figure based shape description to those based on boundary curvature will be briefly discussed

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

a new upper bound on the minimal distance of self dual codes it is shown that the minimal distance d of a binary self dual code of length n or 74 is at most 2 n 6 10 this bound is a consequence of some new conditions on the weight enumerator of a self dual code obtained by considering a particular translate of the code called its shadow these conditions also enable one to find the highest possible minimal distance of a self dual code for all n or 60 to show that self dual codes with d or 22 with d or 8 exist precisely for n 24 32 and n or 26 and with d or 10 exist precisely for n or 46 and to show that there are exactly eight self dual codes of length 32 with d 8 several of the self dual codes of length 34 have trivial group this appears to be the smallest length where this can happen