a multistage optimal active contour model energy minimizing active contour models or snakes can be used in many applications such as edge detection motion tracking image matching computer vision and three dimensional 3 d reconstruction we present a novel snake that is superior both in accuracy and convergence speed over previous snake algorithms high performance is achieved by using spline representation and dividing the energy minimization process into multiple stages the first stage is designed to optimize the convergence speed in order to allow the snake to quickly approach the minimum energy state the second stage is devoted to snake refinement and to local minimization of energy thereby driving the snake to a quasiminimum energy state the third stage uses the bellman 1957 optimality principle to fine tune the snake to the global minimum energy state this three stage scheme is optimized for both accuracy and speed

invariant properties of straight homogeneous generalized cylinders and their contours a fundamental group in computer vision is the recovery of three dimensional shape from image data while this problem is in general underconstrained the authors show that it can be simplified in the case where the objects being viewed are generalized cylinders they consider the class of straight homogeneous generalized cylinders shgcs without any further assumption on the viewing direction or the precise shape of these objects they present a rigorous mathematical study of the geometry of shgcs and characterize their gaussian curvature and occluding contours and use these results to prove several new invariant properties of the contours of shgcs these properties are in turn used in two implemented algorithms for recovering shgc descriptions from image contours several examples of segmentation of real images are given other applications are also discussed

perceptual grouping for generic recognition we address the problem of recognition of generic objects from a single intensity image this precludes the use of purely geometric methods which assume that models are geometrically and precisely designed instead we propose to use descriptions in terms of features and their qualitative geometric relationships to succeed it is clear that these features need to be high level rather than points or lines we propose to detect groups using perceptual organization criteria such as proximity symmetry parallelism and closure the detection of these features is performed in an efficient way using proximity indexing since many groups are created we also perform selection of relevant groups by organizing them into sets of similar perceptual content finally we present an implementation of a recognition system using these sets as primitives it is an efficient colored graph matching algorithm using the adjacency matrix representation of a graph using indexing we retrieve matching hypotheses which are verified against each other with respect to topological constraints groups of consistent hypotheses represent detected model instances in a scene the complete system is illustrated on real images we also discuss further extensions

hierarchical decomposition and axial shape description a method for producing a segmented axial description of a given shape together with a hierarchical decomposition of the shape into its parts is presented the novelty of this approach lies in the combination of several competing approaches and tools into a unified scheme and an efficient implementation producing natural descriptions smooth local symmetries are used for the axial description of parts which are suggested by curvature sign changes parallel symmetries are used to provide information on global relationships within the shape this information is used for parsing shape into a hierarchy of parts this approach uses both region and contour information can handle shapes with corners and addresses the issue of local versus global information the issue of scale and the notion of part the method is computationally efficient robust and stable results that show that it provides an intuitive shape description are included

displacement operator based decompositions of matrices using circulants or other group matrices abstract we show how an arbitrary square matrix can be expressed as sums of products of circulant and upper or lower triangular toeplitz matrices and as sums of products of matrices derived from finite groups group matrices and matrices which are close to group matrices the results obtained are interesting from several points of view they lead to different methods for computing linear transforms using ffts or fast convolution algorithms to faster methods for solving toeplitz systems to potential methods for mapping linear transforms to parallel computer architectures with interconnection scheme given by the group graph of a finite group and possibly to matrix theoretic methods for expressing relationship between finite groups

line drawing interpretation bilateral symmetry results previously derived by the author are used to investigate the implication of bilateral symmetry in line drawings it is shown that the line drawing of an orthographically protected surface of revolution exhibits bilateral symmetry about the projection of its axis of revolution irrespective of the viewing direction barring one exception a bilaterally symmetric line drawing is necessarily the orthographic projection of a local surface of revolution whenever its symmetry axis continues to be the projection of a fixed line in space under perturbation of viewpoint the axis of revolution is the invariant preimage of the symmetry axis various line drawing causes are detailed which facilitate the deduction of invariant preimages of symmetry axes and consequently of local surfaces of revolution

robust detection of skewed symmetries by combining local and semi local affine invariants abstract affine invariant feature vector ip and shen image vision comput 16 2 1998 135 146 that captures both local and semi local geometric features around each point of the object boundary is applied here for the detection of skewed symmetries based on the affine invariant shape representation the problem of detecting symmetry axes has been formulated as a problem of detecting lines with known orientations in a local similarity matrix of an object since the feature vector extracts sufficient local and semi local shape information for every point along the object boundary the process of checking symmetric point pairs is thus robust against both noises and deformations moreover our technique is able to detect all the local reflectional symmetries contained in the object various experimental results have shown the robustness and effectiveness of our method in detecting skewed symmetries from both self symmetric objects and generalized objects

empirical test for cellular automaton models of traffic flow based on a detailed microscopic test scenario motivated by recent empirical studies of single vehicle data several cellular automaton models for traffic flow are compared we find three levels of agreement with the empirical data 1 models that do not reproduce even qualitatively the most important empirical observations 2 models that are on a macroscopic level in reasonable agreement with the empirics and 3 models that reproduce the empirical data on a microscopic level as well our results are not only relevant for applications but also shed light on the relevant interactions in traffic flow

shape from contour straight homogeneous generalized cylinders and constant cross section generalized cylinders we analyze the properties of straight homogeneous generalized cylinders shgcs and constant cross section generalized cylinders cgcs and derive the types of symmetries that the limb boundaries and cross sections of these objects produce on the image plane the constraints on the 3d shape of the objects are formulated based on the symmetries and from the geometry of the projection models finally the methods that recover the 3d shape from the image of their contours are discussed and recovered surfaces are shown for sample objects

detecting symmetries in polynomial bezier curves in a recent article alcazar 2014 presents algorithms for detecting central and mirror symmetries in planar polynomial curves expressed with proper parameterization in the monomial i e power basis however for practical purposes in computer graphics and cagd the usual choice is the bernstein bezier representation because of its superior numerical and geometric characteristics we point out that in this form and for properly parameterized curves detecting symmetry amounts to simply checking that the bezier points exhibit pairwise symmetry this result is a direct consequence of well known properties of the bezier representation namely its symmetry affine invariance and uniqueness for proper parameterizations detecting the existence of a symmetric segment in a bezier curve also amounts to a simple task by analysing the last non vanishing derivatives finally these results carry over in a straightforward manner to symmetries in euclidean space

signature detection and matching for document image retrieval as one of the most pervasive methods of individual identification and document authentication signatures present convincing evidence and provide an important form of indexing for effective document image processing and retrieval in a broad range of applications however detection and segmentation of free form objects such as signatures from clustered background is currently an open document analysis problem in this paper we focus on two fundamental problems in signature based document image retrieval first we propose a novel multiscale approach to jointly detecting and segmenting signatures from document images rather than focusing on local features that typically have large variations our approach captures the structural saliency using a signature production model and computes the dynamic curvature of 2d contour fragments over multiple scales this detection framework is general and computationally tractable second we treat the problem of signature retrieval in the unconstrained setting of translation scale and rotation invariant nonrigid shape matching we propose two novel measures of shape dissimilarity based on anisotropic scaling and registration residual error and present a supervised learning framework for combining complementary shape information from different dissimilarity metrics using lda we quantitatively study state of the art shape representations shape matching algorithms measures of dissimilarity and the use of multiple instances as query in document image retrieval we further demonstrate our matching techniques in offline signature verification extensive experiments using large real world collections of english and arabic machine printed and handwritten documents demonstrate the excellent performance of our approaches

b spline contour representation and symmetry detection the detection of edges is only one of many steps in the understanding of images further processing necessarily involves grouping operations between contours we present a representation of edge contours by approximating b splines and show that such a representation facilitates the extraction of symmetries between contours our representation is rich compact stable and does not critically depend on feature extraction we turn our attention to the detection of three types of symmetries skew symmetries and parallel symmetries which have proven to be of great importance in inferring shape from contour and smooth local symmetries which have been used for planar shape description we show that our representation facilitates the computation of these symmetries

generating and generalizing models of visual objects abstract we report on initial experiments with an implemented learning system whose inputs are images of two dimensional shapes the system first builds semantic network descriptions of shapes based on brady s smoothed local symmetry representation it learns shape models from them using a substantially modified version of winston s analogy program a generalization of gray coding enables the representation to be extended and also allows a single operation called ablation to achieve the effects of many standard induction heuristics the program can learn disjunctions and can learn concepts using only positive examples we discuss learnability and the pervasive importance of representational hierarchies

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

parametric reconstruction of generalized cylinders from limb edges the three dimensional 3 d reconstruction of generalized cylinders gcs is an important research field in computer vision one of the main difficulties is that some contour features in images cannot be reconstructed by traditional stereovision because they do not correspond to reflectance discontinuities of surface in space in this paper we present a novel parametric approach for the 3 d reconstruction of circular generalized cylinders cgcs only from the limb edges of cgcs in two images instead of exploiting the invariant and quasiinvariant properties of some specific subclasses of gcs in projections our reconstruction is achieved by some general assumptions on gcs and can therefore be applied to a broader subclass of gcs in order to improve robustness we perform the extraction and labeling of the limb edge interactively and estimate the epipolar geometry between two images by an optimal algorithm then for different types of gcs three kinds of symmetries parallel symmetry skew symmetry and local smooth symmetry are employed to compute the symmetry of limb edges the surface points corresponding to limb edges in images are reconstructed by integrating the recovered epipolar geometry and the properties induced from the assumptions that we make on the gcs finally a homography based method is exploited to further refine the 3 d description of the gc with a coplanar curved axis

multiscale symmetric part detection and grouping skeletonization algorithms typically decompose an object s silhouette into a set of symmetric parts offering a powerful representation for shape categorization however having access to an object s silhouette assumes correct figure ground segmentation leading to a disconnect with the mainstream categorization community which attempts to recognize objects from cluttered images in this paper we present a novel approach to recovering and grouping the symmetric parts of an object from a cluttered scene we begin by using a multiresolution superpixel segmentation to generate medial point hypotheses and use a learned affinity function to perceptually group nearby medial points likely to belong to the same medial branch in the next stage we learn higher granularity affinity functions to group the resulting medial branches likely to belong to the same object the resulting framework yields a skeletal approximation that is free of many of the instabilities that occur with traditional skeletons more importantly it does not require a closed contour enabling the application of skeleton based categorization systems to more realistic imagery

finding axes of symmetry from potential fields this paper addresses the problem of detecting axes of bilateral symmetry in images in order to achieve robustness to variation in illumination only edge gradient information is used to overcome the problem of edge breaks a potential field is developed from the edge map which spreads the information in the image plane pairs of points in the image plane are made to vote for their axes of symmetry with some confidence values to make the method robust to overlapping objects only local features in the form of taylor coefficients are used for quantifying symmetry we define an axis of symmetry histogram which is used to accumulate the weighted votes for all possible axes of symmetry to reduce the computational complexity of voting a hashing scheme is proposed wherein pairs of points whose potential fields are too asymmetric are pruned by not being counted for the vote experimental results indicate that the proposed method is fairly robust to edge breaks and is able to detect symmetries even when only 0 05 of the possible pairs are used for voting

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

the curvature primal sketch in this paper we introduce a novel representation of the significant changes in curvature along the bounding contour of planar shape we call the representation the curvature primal sketch because of the close analogy to the primal sketch representation advocated by marr for describing significant intensity changes we define a set of primitive parameterized curvature discontinuities and derive expressions for their convolutions with the first and second derivatives of a gaussian we describe an implemented algorithm that computes the curvature primal sketch by matching the multiscale convolutions of a shape and illustrate its performance on a set of tool shapes several applications of the representation are sketched

affine invariant detection of perceptually parallel 3d planar curves abstract the problem of parallelism detection between two curves has been formulated in this paper as a line detection problem within an affine invariant local similarity matrix computed for the two curves each element of this matrix gives an affine invariant measure of local parallelism for any pair of curve segments along the two curves this approach enables the detection of a pair of parallel 3d planar curves as well as parallel 2d curves under general affine transform two descriptors were also used here to provide a multi resolution representation of a curve since these two descriptors provide sufficient local and semi local shape information at every feature point on the curves the process of detecting parallelism is thus robust against both noise and deformations moreover the proposed technique allows all significant pairs of parallel segments within any two curves in the scene to be detected experiments on detecting randomly affine transformed curves which are obtained from natural images or artificially generated images have demonstrated the effectiveness of the technique

high resolution numerical approximation of traffic flow problems with variable lanes and free flow velocities this paper develops macroscopic traffic flow models for a highway section with variable lanes and free flow velocities that involve spatially varying flux functions to address this complex physical property we develop a riemann solver that derives the exact flux values at the interface of the riemann problem based on this solver we formulate godunov type numerical schemes to solve the traffic flow models numerical examples that simulate the traffic flow around a bottleneck that arises from a drop in traffic capacity on the highway section are given to illustrate the efficiency of these schemes

cellular automaton model for mixed traffic flow with motorcycles abstract a single lane cellular automaton model is proposed to simulate mixed traffic with motorcycles by performing numerical simulations under the periodic boundary condition some density flow relations and the lane changing behavior of motorcycles are investigated in detail it is found that the maximum car flow decreases because of the lane changing behavior of motorcycles the maximum total flow increases first and then decreases with increasing motorcycle density moreover the transition of the total flow from the free flow to the congested flow is smooth in this model the lane changing rate of motorcycles will decrease to zero finally with the increase of the car density but its evolutionary trend is considerably complex another interesting fact is that with the increase of the motorcycle density the lane changing rate increases first and decreases later this phenomenon is very similar to the findings in other papers on multi lane car flows the lane changing is almost of no use in increasing the flow of motorcycles as the motorcycle density is small but it distinctly causes the increase in the flow of motorcycles when the motorcycle density is sufficiently large and in this density regime the flow of motorcycles gradually decreases to the one given with the nagel schreckenberg model for motorcycles with the increase of the car density the simulation results indicate that it is necessary to set a barrier or a lane for separating the motorcycle flow from the car flow except in some special density regime

optimal image and video closure by superpixel grouping detecting independent objects in images and videos is an important perceptual grouping problem one common perceptual grouping cue that can facilitate this objective is the cue of contour closure reflecting the spatial coherence of objects in the world and their projections as closed boundaries separating figure from background detecting contour closure in images consists of finding a cycle of disconnected contour fragments that separates an object from its background searching the entire space of possible groupings is intractable and previous approaches have adopted powerful perceptual grouping heuristics such as proximity and co curvilinearity to constrain the search we introduce a new formulation of the problem by transforming the problem of finding cycles of contour fragments to finding subsets of superpixels whose collective boundary has strong edge support few gaps in the image our cost function a ratio of a boundary gap measure to area promotes spatially coherent sets of superpixels moreover its properties support a global optimization procedure based on parametric maxflow extending closure detection to videos we introduce the concept of spatiotemporal closure analogous to image closure we formulate our spatiotemporal closure cost over a graph of spatiotemporal superpixels our cost function is a ratio of motion and appearance discontinuity measures on the boundary of the selection to an internal homogeneity measure of the selected spatiotemporal volume the resulting approach automatically recovers coherent components in images and videos corresponding to objects object parts and objects with surrounding context providing a good set of multiscale hypotheses for high level scene analysis we evaluate both our image and video closure frameworks by comparing them to other closure detection approaches and find that they yield improved performance

unsupervised contour representation and estimation using b splines and a minimum description length criterion this paper describes a new approach to adaptive estimation of parametric deformable contours based on b spline representations the problem is formulated in a statistical framework with the likelihood function being derived from a region based image model the parameters of the image model the contour parameters and the b spline parameterization order i e the number of control points are all considered unknown the parameterization order is estimated via a minimum description length mdl type criterion a deterministic iterative algorithm is developed to implement the derived contour estimation criterion the result is an unsupervised parametric deformable contour it adapts its degree of smoothness complexity number of control points and it also estimates the observation image model parameters the experiments reported in the paper performed on synthetic and real medical images confirm the adequate and good performance of the approach

automated b spline curve representation incorporating mdl and error minimizing control point insertion strategies the main issues of developing an automatic and reliable scheme for spline fitting are discussed and addressed in this paper which are not fully covered in previous papers or algorithms the proposed method incorporates b spline active contours the minimum description length mdl principle and a novel control point insertion strategy based on maximizing the potential for energy reduction maximization perm a comparison of test results shows that it outperforms one of the better existing methods

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

irregular shape symmetry analysis theory and application to quantitative galaxy classification this paper presents a set of imperfectly symmetric measures based on a series of geometric transformation operations for quantitatively measuring the amount of symmetry of arbitrary shapes the definitions of both bilateral symmetricity and rotational symmetricity give new insight into analyzing the geometrical property of a shape and enable characterizing arbitrary shapes in a new way we developed a set of criteria for quantitative galaxy classification using our proposed irregular shape symmetry measures our study has demonstrated the effectiveness of the proposed method for the characterization of the shape of the celestial bodies the concepts described in the paper are applicable to many fields such as mathematics artificial intelligence digital image processing robotics biomedicine etc

recovery of the three dimensional shape of an object from a single view given a single picture which is a projection of a three dimensional scene onto the two dimensional picture plane we usually have definite ideas about the 3 d shapes of objects to do this we need to use assumptions about the world and the image formation process since there exist a large number of shapes which can produce the same picture the purpose of this paper is to identify some of these assumptions mostly geometrical ones by demonstrating how the theory and techniques which exploit such assumptions can provide a systematic shape recovery method the method consists of two parts the first is the application of the origami theory which models the world as a collection of plane surfaces and recovers the possible shapes qualitatively the second is the technique of mapping image regularities into shape constraints for recovering the probable shapes quantitatively actual shape recovery from a single view is demonstrated for the scenes of an object such as a box and a chair given a single image the method recovers the 3 d shapes of an object in it and generates images of the same object as we would see it from other directions

a machine learning approach for acquiring descriptive classification rules of shape contours we devise a method to generate descriptive classification rules of shape contours by using inductive learning the classification rules are represented in the form of logic programs we first transform input objects from pixel representation into predicate representation the transformation consists of preprocessing feature extraction and symbolic transformation we then use foil which is an indictive logic programming system to produce classification rules experiments on two sets of data were performed to justify our proposed method