shape retrieval using triangle area representation and dynamic space warping in this paper we present a shape retrieval method using triangle area representation for nonrigid shapes with closed contours the representation utilizes the areas of the triangles formed by the boundary points to measure the convexity concavity of each point at different scales or triangle side lengths this representation is effective in capturing both local and global characteristics of a shape invariant to translation rotation and scaling and robust against noise and moderate amounts of occlusion in the matching stage a dynamic space warping dsw algorithm is employed to search efficiently for the optimal least cost correspondence between the points of two shapes then a distance is derived based on the optimal correspondence the performance of our method is demonstrated using four standard tests on two well known shape databases the results show the superiority of our method over other recent methods in the literature

angular pattern and binary angular pattern for shape retrieval in this paper we propose two novel shape descriptors angular pattern ap and binary angular pattern bap and a multiscale integration of them for shape retrieval both ap and bap are intrinsically invariant to scale and rotation more importantly being global shape descriptors the proposed shape descriptors are computationally very efficient while possessing similar discriminability as state of the art local descriptors as a result the proposed approach is attractive for real world shape retrieval applications the experiments on the widely used mpeg 7 and tari 1000 data sets demonstrate the effectiveness of the proposed method in comparison with existing methods

asymptotic fields in frequency and time domains generated by a point source at the horizontal interface between vertically uniaxial media for a point current source placed at the interface between two half space media investigation is made of the far zone asymptotic fields in the frequency domain and their transient waveforms the media are electrically uniaxial with the uniaxis normal to the interface the leading order fields contributed by the stationary phase points serve as good approximations well off the critical angles near the critical angles the uniform asymptotic techniques need to be employed for a proper approximation unlike the ordinary wave the extraordinary wave cannot be correctly described merely by taking into account the proximity of the stationary and branch points except in some rare cases consideration must also be given to the combined effect associated with the pole introduced in the formulation the validities of the asymptotic approximations are examined in the time domain by comparing the asymptotic field waveforms with the wavenumber synthetic waveforms around the critical angle of the extraordinary wave

co transduction for shape retrieval in this paper we propose a new shape object retrieval algorithm namely co transduction the performance of a retrieval system is critically decided by the accuracy of adopted similarity measures distances or metrics in shape object retrieval ideally intraclass objects should have smaller distances than interclass objects however it is a difficult task to design an ideal metric to account for the large intraclass variation different types of measures may focus on different aspects of the objects for example measures computed based on contours and skeletons are often complementary to each other our goal is to develop an algorithm to fuse different similarity measures for robust shape retrieval through a semisupervised learning framework we name our method co transduction which is inspired by the co training algorithm given two similarity measures and a query shape the algorithm iteratively retrieves the most similar shapes using one measure and assigns them to a pool for the other measure to do a re ranking and vice versa using co transduction we achieved an improved result of 97 72 bull s eye measure on the mpeg 7 data set over the state of the art performance we also present an algorithm called tri transduction to fuse multiple input similarities and it achieved 99 06 on the mpeg 7 data set our algorithm is general and it can be directly applied on input similarity measures metrics it is not limited to object shape retrieval and can be applied to other tasks for ranking retrieval

image retrieval based on multi texton histogram this paper presents a novel image feature representation method called multi texton histogram mth for image retrieval mth integrates the advantages of co occurrence matrix and histogram by representing the attribute of co occurrence matrix using histogram it can be considered as a generalized visual attribute descriptor but without any image segmentation or model training the proposed mth method is based on julesz s textons theory and it works directly on natural images as a shape descriptor meanwhile it can be used as a color texture descriptor and leads to good performance the proposed mth method is extensively tested on the corel dataset with 15000 natural images the results demonstrate that it is much more efficient than representative image feature descriptors such as the edge orientation auto correlogram and the texton co occurrence matrix it has good discrimination power of color texture and shape features

iconic indexing by 2 d strings in this paper we describe a new way of representing a symbolic picture by a two dimensional string a picture query can also be specified as a 2 d string the problem of pictorial information retrieval then becomes a problem of 2 d subsequence matching we present algorithms for encoding a symbolic picture into its 2 d string representation reconstructing a picture from its 2 d string representation and matching a 2 d string with another 2 d string we also prove the necessary and sufficient conditions to characterize ambiguous pictures for reduced 2 d strings as well as normal 2 d strings this approach thus allows an efficient and natural way to construct iconic indexes for pictures

equivalence and symmetries for variable coefficient linear heat type equations i a systematic and unified approach to transformations and symmetries of a class of variable coefficient heat type linear partial differential equations pdes is presented the complete symmetry group classification is re performed in the current context a useful criterion which is necessary and sufficient for being reducible to the standard heat equation by point transformations is established a similar criterion is also valid for the equations to have a four or six dimensional symmetry group nontrivial symmetry groups in this situation the basis elements are listed in terms of coefficients a number of illustrative examples are given in particular some applications from the recent literature are re examined in our new approach multidimensional parabolic pdes of heat and schrodinger type are also considered

review of shape representation and description techniques more and more images have been generated in digital form around the world there is a growing interest in 1nding images in large collections or from remote databases in order to 1nd an image the image has to be described or represented by certain features shape is an important visual feature of an image searching for images using shape features has attracted much attention there are many shape representation anddescription techniques in the literature in this paper we classify and review these important techniques we examine implementation procedures for each technique and discuss its advantages and disadvantages some recent research results are also included and discussed in this paper finally we identify some promising techniques for image retrieval according to standard principles

invariant image recognition by zernike moments the problem of rotation scale and translation invariant recognition of images is discussed a set of rotation invariant features are introduced they are the magnitudes of a set of orthogonal complex moments of the image known as zernike moments scale and translation invariance are obtained by first normalizing the image with respect to these parameters using its regular geometrical moments a systematic reconstruction based method for deciding the highest order zernike moments required in a classification problem is developed the quality of the reconstructed image is examined through its comparison to the original one the orthogonality property of the zernike moments which simplifies the process of image reconstruction make the suggest feature selection approach practical features of each order can also be weighted according to their contribution to the reconstruction process the superiority of zernike moment features over regular moments and moment invariants was experimentally verified

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

frequency and time domain asymptotic fields near the critical cone in fluid fluid configuration near the critical cone of a point source placed at the interface between two half space fluid media investigation is made of the asymptotic fields in the frequency domain and their synthetic wave forms in the time domain while the leading order and the head wave components give a good description of the true fields well off the critical cone the uniform asymptotic ua analysis has to be made for the approximation near the critical cone the ua analysis splits into two cases depending on the medium densities and wave speeds for case 1 the ua1 approximation is employed that takes into account the proximity of the stationary phase point to the branch point in case 2 the ua2 approximation is employed in which consideration is also given to the proximity of the stationary point to the pole and to the combined effect of the stationary point the branch point and the pole the validities of the asymptotic fields are checked in the time domain by comparing the asymptotic field wave forms against the wave number synthetic wave forms the ua fields show good accuracy and causal behaviors with the causality of the ua2 fields previously unreported in the literature

ecds an effective shape signature using electrical charge distribution on the shape abstract motivated by the fact that electrical charge distributions are almost the same for similar shapes but not vice versa when shapes reach their electrical equilibrium condition we propose a novel shape signature based on the electrical charge distribution on the shape ecds compared to other shape signatures ecds has the following interesting properties 1 ecds is a local measure but computed in a global manner thus it is more robust to noise and shape variations 2 ecds is articulation insensitive and therefore exhibits better performance by the introduction of generalized coulomb potentials this allows it to better match shapes whose parts can move independently such as scissors 3 the sum of ecds remains constant during the process of reaching electrical equilibrium which does favor some applications numerous experiments have been done on several public shape databases mpeg 7 database articulated shape data set kimia silhouettes and eth 80 data set demonstrating that ecds has the above properties and compares well with other shape descriptors in many kinds of shape retrieval and recognition tasks

uniform asymptotic expansion of an integral with a saddle point a pole and a branch point the paper is concerned with an asymptotic behaviour of a contour integral with three critical points a saddle point a pole and a branch point two leading terms of a uniform asymptotic expansion of the integral have been effectively constructed the expansion remains valid as its critical points approach one another or coalesce in the special case that the saddle point is bounded away from one of the remaining critical points or from both the expansion reduces to simpler in form quasiuniform and non uniform expansions respectively with the aid of the non uniform expansion the integral has been interpreted as describing three different waves each one associated with a corresponding critical point

shape detection from line drawings with local neighborhood structure an object detection method from line drawings is presented the method adopts the local neighborhood structure as the elementary descriptor which is formed by grouping several nearest neighbor lines curves around one reference with this representation both the appearance and the geometric structure of the line drawing are well described the detection algorithm is a hypothesis test scheme the top k most similar local structures in the drawing are firstly obtained for each local structure of the model and the transformation parameters are estimated for each of the k candidates such as object center scale and rotation factors by treating each estimation result as a point in the parameter space a dense region around the ground truth is then formed provided that there exist a model in the drawing the mean shift method is used to detect the dense regions and the significant modes are accepted as the occurrence of object instances

shape vocabulary a robust and efficient shape representation for shape matching in this paper a learning based shape descriptor for shape matching is demonstrated formulated in a bag of words like framework the proposed method summarizes the local features extracted from certain shape to generate a integrated representation it contributes to the speed up of shape matching since the distance metric in the vector space analysis can be directly applied to compare the constructed global descriptors eliminating the time consuming stage of local feature matching similar to the philosophy in spatial pyramid matching a strategy for feature division is applied in the phase of encoded feature pooling and vocabulary learning which helps to construct a more discriminative descriptor incorporating both global and local information also a local contour based feature extraction method is designed for 2d shapes while significant properties of the local contours are inspected for the design of feature division rules the designed local feature extraction method and the feature division rules manage to reduce the variances of shape representation due to the changes in rotation in addition to 2d shape we also present a simple and natural method to extend the proposed method to the scenario of 3d shape representation the proposed shape descriptor is validated on several benchmark data sets for evaluating 2d and 3d shape matching algorithms and it is observed that the investigated shape descriptor maintains superior discriminative power as well as high time efficiency

binary partition tree as an efficient representation for image processing segmentation and information retrieval this paper discusses the interest of binary partition trees as a region oriented image representation binary partition trees concentrate in a compact and structured representation a set of meaningful regions that can be extracted from an image they offer a multiscale representation of the image and define a translation invariant 2 connectivity rule among regions as shown in this paper this representation can be used for a large number of processing goals such as filtering segmentation information retrieval and visual browsing furthermore the processing of the tree representation leads to very efficient algorithms finally for some applications it may be interesting to compute the binary partition tree once and to store it for subsequent use for various applications in this context the paper shows that the amount of bits necessary to encode a binary partition tree remains moderate

galilei invariant gauge symmetries in fokker planck dynamics with logarithmic diffusion and drift terms a tensorial approach to galilean invariance is utilized together with lie symmetries of differential equations in order to derive equations of fokker planck type containing a logarithmic diffusion tensor and drift term the formalism is based on the projection from an extended by one space like dimension minkowski manifold to the usual newtonian spacetime so that non relativistic models are described by manifestly covariant lagrangians in this paper we obtain the fokker planck equations from the euler lagrange equations with the extended manifold by using a specific choice of the gauge condition we work in 1 1 spacetime and carry out the analysis for both abelian and non abelian symmetries

a class of fokker planck equations with logarithmic factors in diffusion and drift terms the x2 ln x dependence of the diffusion coefficient in the fokker planck equation is retrieved by means of symmetry arguments exact solutions of the equation with logarithmic factors in coefficients are presented algebraic and log algebraic solutions are found for some values of exponents they seem to be analogues on an interval of log normal distributions

fast computation of a contrast invariant image representation this paper sets out a new representation of an image which is contrast independent the image is decomposed into a tree of shapes based on connected components of level sets which provides a full and nonredundant representation of the image a fast algorithm to compute the tree the fast level lines transform fllt is explained in detail some simple and direct applications of this representation are shown

structure integral transform versus radon transform a 2d mathematical tool for invariant shape recognition in this paper we present a novel mathematical tool structure integral transform sit for invariant shape description and recognition different from the radon transform rt which integrates the shape image function over a 1d line in the image plane the proposed sit builds upon two orthogonal integrals over a 2d k cross dissecting structure spanning across all rotation angles by which the shape regions are bisected in each integral the proposed sit brings the following advantages over the rt 1 it has the extra function of describing the interior structural relationship within the shape which provides a more powerful discriminative ability for shape recognition 2 the shape regions are dissected by the k cross in a coarse to fine hierarchical order that can characterize the shape in a better spatial organization scanning from the center to the periphery and 3 it is easier to build a completely invariant shape descriptor the experimental results of applying sit to shape recognition demonstrate its superior performance over the well known radon transform and the well known shape contexts and the polar harmonic transforms

shape matching and object recognition using shape contexts we present a novel approach to measuring similarity between shapes and exploit it for object recognition in our framework the measurement of similarity is preceded by 1 solving for correspondences between points on the two shapes 2 using the correspondences to estimate an aligning transform in order to solve the correspondence problem we attach a descriptor the shape context to each point the shape context at a reference point captures the distribution of the remaining points relative to it thus offering a globally discriminative characterization corresponding points on two similar shapes will have similar shape contexts enabling us to solve for correspondences as an optimal assignment problem given the point correspondences we estimate the transformation that best aligns the two shapes regularized thin plate splines provide a flexible class of transformation maps for this purpose the dissimilarity between the two shapes is computed as a sum of matching errors between corresponding points together with a term measuring the magnitude of the aligning transform we treat recognition in a nearest neighbor classification framework as the problem of finding the stored prototype shape that is maximally similar to that in the image results are presented for silhouettes trademarks handwritten digits and the coil data set

polynomial time metrics for attributed trees we address the problem of comparing attributed trees and propose four novel distance measures centered around the notion of a maximal similarity common subtree the proposed measures are general and defined on trees endowed with either symbolic or continuous valued attributes and can be applied to rooted as well as unrooted trees we prove that our measures satisfy the metric constraints and provide a polynomial time algorithm to compute them this is a remarkable and attractive property since the computation of traditional edit distance based metrics is in general np complete at least in the unordered case we experimentally validate the usefulness of our metrics on shape matching tasks and compare them with an approximation of edit distance

retrieval of similar pictures on pictorial databases abstract in this paper we suggest a method of retrieving iconic pictures in a pictorial database based upon the spatial relationship among the objects in the picture this special kind of database query problem is generally known as a spatial match retrieval problem we transform each picture or query into a set of ordered triples o i o j r ij s where o i and o j are two symbolic objects and r ij is the spatial relationship between o i and o j then we construct a hashing table for all o i o j r ij s of all the pictures in the pictorial database by searching the preconstructed hashing table for all of the o i o j r ij s associated with a query the pictures satisfying that query can be easily determined

connected filtering based on multivalued component trees in recent papers a new notion of component graph was introduced it extends the classical notion of component tree initially proposed in mathematical morphology to model the structure of gray level images component graphs can indeed model the structure of any gray level or multivalued images we now extend the anti extensive filtering scheme based on component trees to make it tractable in the framework of component graphs more precisely we provide solutions for building a component graph reducing it based on selection criteria and reconstructing a filtered image from a reduced component graph in this paper we first consider the cases where component graphs still have a tree structure they are then called multivalued component trees the relevance and usefulness of such multivalued component trees are illustrated by applicative examples on hierarchically classified remote sensing images

computationally efficient wavelet affine invariant functions for shape recognition an affine invariant function for object recognition is constructed from wavelet coefficients of the object boundary in previous works undecimated dyadic wavelet transform was used to construct affine invariant functions in this paper an algorithm based on decimated wavelet transform is developed to compute an affine invariant function as a result computational complexity is reduced without decreasing recognition performance experimental results are presented

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

perceptually motivated shape context which uses shape interiors in this paper we identify some of the limitations of current day shape matching techniques we provide examples of how contour based shape matching techniques cannot provide a good match for certain visually similar shapes to overcome this limitation we propose a perceptually motivated variant of the well known shape context descriptor we identify that the interior properties of the shape play an important role in object recognition and develop a descriptor that captures these interior properties we show that our method can easily be augmented with any other shape matching algorithm we also show from our experiments that the use of our descriptor can significantly improve the retrieval rates

reconstruction of binary shapes from blurred images via hankel structured low rank matrix recovery with the dominance of digital imaging systems we are often dealing with discrete domain samples of an analog image due to physical limitations all imaging devices apply a blurring kernel on the input image before taking samples to form the output pixels in this paper we focus on the reconstruction of binary shape images from few blurred samples this problem has applications in medical imaging shape processing and image segmentation our method relies on representing the analog shape image in a discrete grid much finer than the sampling grid we formulate the problem as the recovery of a rank r matrix that is formed by a hankel structure on the pixels we further propose efficient admm based algorithms to recover the low rank matrix in both noiseless and noisy settings we also analytically investigate the number of required samples for successful recovery in the noiseless case for this purpose we study the problem in the random sampling framework and show that with mathcal o r log 4 n 1 n 2 random samples where the size of the image is assumed to be n 1 times n 2 we can guarantee the perfect reconstruction with high probability under mild conditions we further prove the robustness of the proposed recovery in the noisy setting by showing that the reconstruction error in the noisy case is bounded when the input noise is bounded simulation results confirm that our proposed method outperform the conventional total variation minimization in the noiseless settings

on the log normal diffusion process the log normal conditional density function is the delta function initial condition solution of a four parameter fokker planck equation it defines a diffusion process over the open first quadrant of the x t plane this process reaches a nonzero steady state as t increases indefinitely if the drift parameter is positive the process may be monotonic or by expansion and contraction breathing if the drift parameter is negative the process goes to zero by expansion and contraction towards x 0 as t increases indefinitely

learning context sensitive shape similarity by graph transduction shape similarity and shape retrieval are very important topics in computer vision the recent progress in this domain has been mostly driven by designing smart shape descriptors for providing better similarity measure between pairs of shapes in this paper we provide a new perspective to this problem by considering the existing shapes as a group and study their similarity measures to the query shape in a graph structure our method is general and can be built on top of any existing shape similarity measure for a given similarity measure a new similarity is learned through graph transduction the new similarity is learned iteratively so that the neighbors of a given shape influence its final similarity to the query the basic idea here is related to pagerank ranking which forms a foundation of google web search the presented experimental results demonstrate that the proposed approach yields significant improvements over the state of art shape matching algorithms we obtained a retrieval rate of 91 61 percent on the mpeg 7 data set which is the highest ever reported in the literature moreover the learned similarity by the proposed method also achieves promising improvements on both shape classification and shape clustering

shape similarity measure based on correspondence of visual parts a cognitively motivated similarity measure is presented and its properties are analyzed with respect to retrieval of similar objects in image databases of silhouettes of 2d objects to reduce influence of digitization noise as well as segmentation errors the shapes are simplified by a novel process of digital curve evolution to compute our similarity measure we first establish the best possible correspondence of visual parts without explicitly computing the visual parts then the similarity between corresponding parts is computed and aggregated we applied our similarity measure to shape matching of object contours in various image databases and compared it to well known approaches in the literature the experimental results justify that our shape matching procedure gives an intuitive shape correspondence and is stable with respect to noise distortions

geometry based image retrieval in binary image databases in this paper a geometry based image retrieval system is developed for multiobject images we model both shape and topology of image objects using a structured representation called curvature tree ct the hierarchy of the ct reflects the inclusion relationships between the image objects to facilitate shape based matching triangle area representation tar of each object is stored at the corresponding node in the ct the similarity between two multiobject images is measured based on the maximum similarity subtree isomorphism mssi between their cts for this purpose we adopt a recursive algorithm to solve the mssi problem and a very effective dynamic programming algorithm to measure the similarity between the attributed nodes our matching scheme agrees with many recent findings in psychology about the human perception of multiobject images experiments on a database of 13 500 real and synthesized medical images and the mpeg 7 ce 1 database of 1 400 shape images have shown the effectiveness of the proposed method

2 d object recognition using invariant contour descriptor and projective refinement abstract this paper presents an efficient model based recognition method to recognize 2 d objects and to obtain correspondences between models and scene boundaries with a subpixel positioning error as a shape signature for a contour we propose a descriptor consisting of five point invariants which are used to index a hash table also we propose a projective refinement as a verification method to compute exact correspondences between models and scene contour points this method repeatedly computes projective transformation using a weighted pseudo inverse we present an error model for five point invariants which are used to define a similarity between two descriptors to determine a searching bound in indexing and to obtain the weights in the projective refinement in experiments using seriously distorted images of forty models this method led to the recognition of planar curved objects a transformation using the correspondence between the model and scene points on contours was also obtained

scale based description and recognition of planar curves and two dimensional shapes the problem of finding a description at varying levels of detail for planar curves and matching two such descriptions is posed and solved in this paper a number of necessary criteria are imposed on any candidate solution method path based gaussian smoothing techniques are applied to the curve to find zeros of curvature at varying levels of detail the result is the generalized scale space image of a planar curve which is invariant under rotation uniform scaling and translation of the curve these properties make the scale space image suitable for matching the matching algorithm is a modification of the uniform cost algorithm and finds the lowest cost match of contours in the scale space images it is argued that this is preferable to matching in a so called stable scale of the curve because no such scale may exist for a given curve this technique is applied to register a landsat satellite image of the strait of georgia b c manually corrected for skew to a map containing the shorelines of an overlapping area