pairwise rotation invariant co occurrence local binary pattern designing effective features is a fundamental problem in computer vision however it is usually difficult to achieve a great tradeoff between discriminative power and robustness previous works shown that spatial co occurrence can boost the discriminative power of features however the current existing co occurrence features are taking few considerations to the robustness and hence suffering from sensitivity to geometric and photometric variations in this work we study the transform invariance ti of co occurrence features concretely we formally introduce a pairwise transform invariance pti principle and then propose a novel pairwise rotation invariant co occurrence local binary pattern pricolbp feature and further extend it to incorporate multi scale multi orientation and multi channel information different from other lbp variants pricolbp can not only capture the spatial context co occurrence information effectively but also possess rotation invariance we evaluate pricolbp comprehensively on nine benchmark data sets from five different perspectives e g encoding strategy rotation invariance the number of templates speed and discriminative power compared to other lbp variants furthermore we apply pricolbp to six different but related applications texture material flower leaf food and scene classification and demonstrate that pricolbp is efficient effective and of a well balanced tradeoff between the discriminative power and robustness

beyond diffusion process nss is proposed to replace the role of diffusion process to capture the geometry of the underlying manifold in shape and image retrieval nss is more precise than diffusion process and more robust to noise nss is computed more efficiently than diffusion process and it no longer needs an iterative process to guarantee the retrieval precision we obtain state of the art retrieval performance on several benchmark datasets measuring the similarity between two instances reliably shape or image is a challenging problem in shape and image retrieval in this paper a simple yet effective method called neighbor set similarity nss is proposed which is superior to both traditional pairwise similarity and diffusion process nss makes full use of contextual information to capture the geometry of the underlying manifold and obtains a more precise measure than the original pairwise similarity moreover based on nss we propose a powerful fusion process to utilize the complementarity of different descriptors to further enhance the retrieval performance the experimental results on mpeg 7 shape dataset n s image dataset and orl face dataset demonstrate the effectiveness of the proposed method in addition the time complexity of nss is much lower than diffusion process which suggests that nss is more suitable for large scale image retrieval than diffusion process

hierarchical string cuts a translation rotation scale and mirror invariant descriptor for fast shape retrieval this paper presents a novel approach for both fast and accurately retrieving similar shapes a hierarchical string cuts hscs method is proposed to partition a shape into multiple level curve segments of different lengths from a point moving around the contour to describe the shape gradually and completely from the global information to the finest details at each hierarchical level the curve segments are cut by strings to extract features that characterize the geometric and distribution properties in that particular level of details the translation rotation scale and mirror invariant hsc descriptor enables a fast metric based matching to achieve the desired high accuracy encouraging experimental results on four databases demonstrated that the proposed method can consistently achieve higher or similar retrieval accuracies than the state of the art benchmarks with a more than 120 times faster speed this may suggest a new way of developing shape retrieval techniques in which a high accuracy can be achieved by a fast metric matching algorithm without using the time consuming correspondence optimization strategy

learning compositional shape models of multiple distance metrics by information projection this paper presents a novel compositional contour based shape model by incorporating multiple distance metrics to account for varying shape distortions or deformations our approach contains two key steps 1 contour feature generation and 2 generative model pursuit for each category we first densely sample an ensemble of local prototype contour segments from a few positive shape examples and describe each segment using three different types of distance metrics these metrics are diverse and complementary with each other to capture various shape deformations we regard the parameterized contour segment plus an additive residual epsilon as a basic subspace namely epsilon ball in the sense that it represents local shape variance under the certain distance metric using these epsilon balls as features we then propose a generative learning algorithm to pursue the compositional shape model which greedily selects the most representative features under the information projection principle in experiments we evaluate our model on several public challenging data sets and demonstrate that the integration of multiple shape distance metrics is capable of dealing various shape deformations articulations and background clutter hence boosting system performance

bag of contour fragments for robust shape classification shape representation is a fundamental problem in computer vision current approaches to shape representation mainly focus on designing low level shape descriptors which are robust to rotation scaling and deformation of shapes in this paper we focus on mid level modeling of shape representation we develop a new shape representation called bag of contour fragments bcf inspired by classical bag of words bow model in bcf a shape is decomposed into contour fragments each of which is then individually described using a shape descriptor e g the shape context descriptor and encoded into a shape code finally a compact shape representation is built by pooling shape codes in the shape shape classification with bcf only requires an efficient linear svm classifier in our experiments we fully study the characteristics of bcf show that bcf achieves the state of the art performance on several well known shape benchmarks and can be applied to real image classification problem highlightsa new shape representation is proposed by encoding contour fragments in shape the proposed shape representation is compact yet informative the proposed shape representation is robust to shape deformation and conclusion we obtain the state of the art shape classification performance on several bench mark datasets

dali deformation and light invariant descriptor recent advances in 3d shape analysis and recognition have shown that heat diffusion theory can be effectively used to describe local features of deforming and scaling surfaces in this paper we show how this description can be used to characterize 2d image patches and introduce dali a novel feature point descriptor with high resilience to non rigid image transformations and illumination changes in order to build the descriptor 2d image patches are initially treated as 3d surfaces patches are then described in terms of a heat kernel signature which captures both local and global information and shows a high degree of invariance to non linear image warps in addition by further applying a logarithmic sampling and a fourier transform invariance to photometric changes is achieved finally the descriptor is compacted by mapping it onto a low dimensional subspace computed using principal component analysis allowing for an efficient matching a thorough experimental validation demonstrates that dali is significantly more discriminative and robust to illuminations changes and image transformations than state of the art descriptors even those specifically designed to describe non rigid deformations

entropy rate clustering cluster analysis via maximizing a submodular function subject to a matroid constraint we propose a new objective function for clustering this objective function consists of two components the entropy rate of a random walk on a graph and a balancing term the entropy rate favors formation of compact and homogeneous clusters while the balancing function encourages clusters with similar sizes and penalizes larger clusters that aggressively group samples we present a novel graph construction for the graph associated with the data and show that this construction induces a matroid a combinatorial structure that generalizes the concept of linear independence in vector spaces the clustering result is given by the graph topology that maximizes the objective function under the matroid constraint by exploiting the submodular and monotonic properties of the objective function we develop an efficient greedy algorithm furthermore we prove an approximation bound of 1 2 for the optimality of the greedy solution we validate the proposed algorithm on various benchmarks and show its competitive performances with respect to popular clustering algorithms we further apply it for the task of superpixel segmentation experiments on the berkeley segmentation data set reveal its superior performances over the state of the art superpixel segmentation algorithms in all the standard evaluation metrics

shape classification using the inner distance part structure and articulation are of fundamental importance in computer and human vision we propose using the inner distance to build shape descriptors that are robust to articulation and capture part structure the inner distance is defined as the length of the shortest path between landmark points within the shape silhouette we show that it is articulation insensitive and more effective at capturing part structures than the euclidean distance this suggests that the inner distance can be used as a replacement for the euclidean distance to build more accurate descriptors for complex shapes especially for those with articulated parts in addition texture information along the shortest path can be used to further improve shape classification with this idea we propose three approaches to using the inner distance the first method combines the inner distance and multidimensional scaling mds to build articulation invariant signatures for articulated shapes the second method uses the inner distance to build a new shape descriptor based on shape contexts the third one extends the second one by considering the texture information along shortest paths the proposed approaches have been tested on a variety of shape databases including an articulated shape data set mpeg7 ce shape 1 kimia silhouettes the eth 80 data set two leaf data sets and a human motion silhouette data set in all the experiments our methods demonstrate effective performance compared with other algorithms

heterogeneous feature structure fusion for classification the key to feature fusion for classification is to take advantage of the discriminative and complementary information from different feature sets which can be represented as internal within each feature set or external structures across different feature sets traditional approaches tend to preserve either internal or external structures via certain feature projection some early attempts consider both structures implicitly or indirectly without revealing their relative importance and relevance in feature fusion we propose a new unsupervised heterogeneous structure fusion hsf algorithm that is able to jointly optimize two kinds of structures explicitly and directly via unified feature projection specifically the internal structure is represented based on locality preserving projection lpp and the external structure is captured by canonical correlation analysis cca the objective function of hsf combines two feature structures in a closed form which can be optimized alternately via linear programming and eigenvector methods the hsf solution provides not only the optimal feature projection but also the weights that encode the relative importance between two kinds of feature structures the experimental results on image classification face recognition shape analysis and infrared target recognition demonstrate the effectiveness and efficiency of hsf compared with state of the art methods graphical abstractdisplay omitted highlightsthe external and internal feature structures are jointly optimized for fusion two kinds of feature structures are preserved via a unified feature projection the nonlinear relationship between two kinds of feature structures is revealed the new feature fusion algorithm shows great promise in four classification problems

clifford algebra approach to twistors local particle interpretation or equivalently an enlargement of a structure group to the poincare group at each point of a riemannian space time manifold naturally results in a complexification of the clifford algebra for the tangent minkowski space following crumeyrolle twistor space is identified with an appropriate one sided ideal of this algebra every antiautomorphism of the latter provides a unique projection from the complexified clifford algebra onto the affine complex minkowski space this projection commutes with the action of the poincare group using the above approach three projections the cases of symmetric antisymmetric and hermitian tensors are derived the projection in terms of the antisymmetric decomposable tensors is shown to give the penrose projection

recognizing articulated objects using a region based invariant transform in this paper we present a new method for representing and recognizing objects based on invariants of the object s regions we apply the method to articulated objects in low resolution noisy range images articulated objects such as a back hoe can have many degrees of freedom in addition to the unknown variables of viewpoint recognizing such an object in an image can involve a search in a high dimensional space that involves all these unknown variables here we use invariance to reduce this search space to a manageable size the low resolution of our range images makes it hard to use common features such as edges to find invariants we have thus developed a new featureless method that does not depend on feature detection instead of local features we deal with whole regions of the object we define a transform that converts the image into an invariant representation on a grid based on invariant descriptors of entire regions centered around the grid points we use these region based invariants for indexing and recognition while the focus here is on articulation the method can be easily applied to other problems such as the occlusion of fixed objects

image re ranking and rank aggregation based on similarity of ranked lists in content based image retrieval cbir systems ranking accurately collection images is of great relevance users are interested in the returned images placed at the first positions which usually are the most relevant ones collection images are ranked in increasing order of their distance to the query pattern e g query image defined by users therefore the effectiveness of these systems is very dependent on the accuracy of the distance function adopted in this paper we present a novel context based approach for redefining distances and later re ranking images aiming to improve the effectiveness of cbir systems in our approach distances among images are redefined based on the similarity of their ranked lists conducted experiments involving shape color and texture descriptors demonstrate the effectiveness of our method

a novel shape constrained feature based active contour model for lips mouth segmentation in the wild in this paper we propose a novel joint formulation of feature based active contour fac and prior shape constraints cs for lips mouth segmentation in the wild our proposed sc fac model is able to robustly segment the lips mouth that belongs to a given mouth shape space while minimizing the energy functional the shape space is defined by a 2d modified active shape model masm whereas the active contour model is based on the chan vese functional our sc fac energy functional is able to overcome the drawback of noise while minimizing the fitting forces under the shape constraints we conducted our experiments on images captured under challenging conditions such as varying illumination low contrast facial expression low resolution blurring wearing beard moustache and cosmetic affection from the mbgc vidtimit jaffe and lfw databases the results from our studies indicate that the proposed sc fac model is reliable and accurately perform prior shape weak object segmentation the average performance of the mouth segmentation using proposed sc fac on 1918 images from the mbgc database under different illuminations expressions and complex background reaches to a precision of 91 30 a recall of 91 32 and an f measure of 90 62 highlightspropose a novel joint formulation of contour and shape for lips segmentation robustly segment lips under challenging environment and complex background the energy functional is composed of 5 terms based on the chan vese functional the shape space is defined by a 2d experiments are conducted from the mbgc vidtimit jaffe and lfw databases

indefinite core vector machine abstract the recently proposed kr in space support vector machine ksvm is an efficient classifier for indefinite learning problems but with quadratic to cubic complexity and a non sparse decision function in this paper a kr in space core vector machine icvm solver is derived a sparse model with linear runtime complexity can be obtained under a low rank assumption the obtained icvm models can be applied to indefinite kernels without additional preprocessing using icvm one can solve cvm with usually troublesome kernels having large negative eigenvalues or large numbers of negative eigenvalues experiments show that our algorithm is similar efficient as the kr in space support vector machine but with substantially lower costs such that also large scale problems can be processed

dense neighborhoods on affinity graph in this paper we study the problem of how to reliably compute neighborhoods on affinity graphs the k nearest neighbors knn is one of the most fundamental and simple methods widely used in many tasks such as classification and graph construction previous research focused on how to efficiently compute knn on vectorial data however most real world data have no vectorial representations and only have affinity graphs which may contain unreliable affinities since the knn of an object o is a set of k objects with the highest affinities to o it is easily disturbed by errors in pairwise affinities between o and other objects and also it cannot well preserve the structure underlying the data to reliably analyze the neighborhood on affinity graphs we define the k dense neighborhood kdn which considers all pairwise affinities within the neighborhood i e not only the affinities between o and its neighbors but also between the neighbors for an object o its kdn is a set kdn o of k objects which maximizes the sum of all pairwise affinities of objects in the set o kdn o we analyze the properties of kdn and propose an efficient algorithm to compute it both theoretic analysis and experimental results on shape retrieval semi supervised learning point set matching and data clustering show that kdn significantly outperforms knn on affinity graphs especially when many pairwise affinities are unreliable

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

robust symbolic representation for shape recognition and retrieval a new method for shape recognition and retrieval is proposed here the suggested algorithm is based on several steps the algorithm analyzes the contour of pairs of shapes their contours are recovered and represented by a pair of n points obtained by linear interpolation given two points p i and q j from the two shapes the cost of their matching is evaluated by using the shape context and by using dynamic programming the best matching between the point sets is obtained dynamic programming not only recovers the best matching but also identifies occlusions i e points in the two shapes which cannot be properly matched given the correspondence between the two point sets the two contours are aligned using procrustes analysis after alignment each contour is transformed into a string of symbols and a modified version of edit distance is used to compute the similarity between strings of symbols finally recognition and retrieval are obtained by a simple nearest neighbor procedure the algorithm has been tested on a large set of shape databases kimia mpeg 7 natural silhouette database gesture database marine database swedish leaf database diatom database eth 80 3d object database providing performances for both in recognition and in retrieval superior to most of previously proposed approaches

flexible syntactic matching of curves and its application to automatic hierarchical classification of silhouettes curve matching is one instance of the fundamental correspondence problem our flexible algorithm is designed to match curves under substantial deformations and arbitrary large scaling and rigid transformations a syntactic representation is constructed for both curves and an edit transformation which maps one curve to the other is found using dynamic programming we present extensive experiments where we apply the algorithm to silhouette matching in these experiments we examine partial occlusion viewpoint variation articulation and class matching where silhouettes of similar objects are matched based on the qualitative syntactic matching we define a dissimilarity measure and we compute it for every pair of images in a database of 121 images we use this experiment to objectively evaluate our algorithm first we compare our results to those reported by others second we use the dissimilarity values in order to organize the image database into shape categories the veridical hierarchical organization stands as evidence to the quality of our matching and similarity estimation

contour grouping based on contour skeleton duality in this paper we present a method for grouping relevant object contours in edge maps by taking advantage of contour skeleton duality regularizing contours and skeletons simultaneously allows us to combine both low level perceptual constraints as well as higher level model constraints in a very effective way the models are represented using paths in symmetry sets skeletons are treated as trajectories of an imaginary virtual robot in a discrete space of symmetric points obtained from pairs of edge segments boundaries are then defined as the maps obtained by grouping the associated pairs of edge segments along the trajectories casting the grouping problem in this manner makes it similar to the problem of simultaneous localization and mapping slam hence we adapt the state of the art probabilistic framework namely rao blackwellized particle filtering that has been successfully applied to slam we use the framework to maximize the joint posterior over skeletons and contours

improving skeletal shape abstraction using multiple optimal solutions shape abstraction is an important problem faced by researchers in many fields such as pattern recognition computer vision and industrial design a recently developed previous shape abstraction framework demirci et al 20 generates an abstracted shape based on the correspondences between the features of the input shapes where the correspondences are obtained using the first optimal solution of a well known transportation problem as the size of the feature space grows the possibility of having more than one optimal solution for the same problem increases considering the case where multiple optimal solutions exist for the same transportation problem we first rank all optimal solutions based on how much they preserve the local neighborhood relations in this paper instead of creating the abstracted shape using the first optimal solution as done by the previous work we create the abstracted shape using the highest ranked optimal solution with this new property more effective abstracted shapes are generated experimental evaluation of the framework demonstrates that the proposed approach compares favorably with the previous technique in a set of shape retrieval experiments for different datasets highlightsskeletal shape abstraction is reformulated as the transportation problem a distortion free graph embedding is used for a better representation all optimal solutions for the transportation problem are considered the optimal solution which most resembles the neighborhood relations is used experiments demonstrate the improved performance

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

a subspace approach for matching 2d shapes under affine distortions this paper presents a subspace approach to matching a pair of 2d shapes and estimating the affine transformation that aligns the two 2d shapes in the proposed method by considering each shape as a 2d signal one shape is projected onto the subspace spanned by the other and the affine transformation is estimated by minimizing the projection error in the subspace the proposed method is fast easy to implement and with a clear physical interpretation furthermore it is robust to noise due to the merit of the subspace method the proposed approach has been tested for registration accuracy computation time and robustness to noise its performance on synthetic and real images is compared with the state of the art reference algorithms the experimental results show that our approach compares favorably to the reference methods in terms of registration accuracy computation speed and robustness

principal warps thin plate splines and the decomposition of deformations the decomposition of deformations by principal warps is demonstrated the method is extended to deal with curving edges between landmarks this formulation is related to other applications of splines current in computer vision how they might aid in the extraction of features for analysis comparison and diagnosis of biological and medical images in indicated

learning shape metrics with monte carlo optimization abstract quantifying and modeling shape variation within a population identifying morphological contrasts across groups and categorizing individuals or objects according to morphological similarity are central problems in numerous domains of science and applications in this paper we present an approach to optimal shape categorization through a new family of metrics for shapes presented as a finite collection of labeled landmark points we develop a technique to learn metrics that optimally differentiate and categorize shapes using monte carlo optimization methods we discuss the theory and the practice of the methods and apply them to the analysis of synthetic data and the classification of multiple species of fruit flies based on the shape of their wings

computing the inner distances of volumetric models for articulated shape description with a visibility graph a new visibility graph based algorithm is presented for computing the inner distances of a 3d shape represented by a volumetric model the inner distance is defined as the length of the shortest path between landmark points within the shape the inner distance is robust to articulation and can reflect the deformation of a shape structure well without an explicit decomposition our method is based on the visibility graph approach to check the visibility between pairwise points we propose a novel fast and robust visibility checking algorithm based on a clustering technique which operates directly on the volumetric model without any surface reconstruction procedure where an octree is used for accelerating the computation the inner distance can be used as a replacement for other distance measures to build a more accurate description for complex shapes especially for those with articulated parts the binary executable program for the windows platform is available from https engineering purdue edu precise vmid

rotation invariant kernels and their application to shape analysis shape analysis requires invariance under translation scale and rotation translation and scale invariance can be realized by normalizing shape vectors with respect to their mean and norm this maps the shape feature vectors onto the surface of a hypersphere after normalization the shape vectors can be made rotational invariant by modeling the resulting data using complex scalar rotation invariant distributions defined on the complex hypersphere e g using the complex bingham distribution however the use of these distributions is hampered by the difficulty in estimating their parameters and the nonlinear nature of their formulation in the present paper we show how a set of kernel functions that we refer to as rotation invariant kernels can be used to convert the original nonlinear problem into a linear one as their name implies these kernels are defined to provide the much needed rotation invariance property allowing one to bypass the difficulty of working with complex spherical distributions the resulting approach provides an easy fast mechanism for 2d 3d shape analysis extensive validation using a variety of shape modeling and classification problems demonstrates the accuracy of this proposed approach

anechoic blind source separation using wigner marginals blind source separation problems emerge in many applications where signals can be modeled as superpositions of multiple sources many popular applications of blind source separation are based on linear instantaneous mixture models if specific invariance properties are known about the sources for example translation or rotation invariance the simple linear model can be extended by inclusion of the corresponding transformations when the sources are invariant against translations spatial displacements or time shifts the resulting model is called an anechoic mixing model we present a new algorithmic framework for the solution of anechoic problems in arbitrary dimensions this framework is derived from stochastic time frequency analysis in general and the marginal properties of the wigner ville spectrum in particular the method reduces the general anechoic problem to a set of anechoic problems with non negativity constraints and a phase retrieval problem the first type of subproblem can be solved by existing algorithms for example by an appropriate modification of non negative matrix factorization nmf the second subproblem is solved by established phase retrieval methods we discuss and compare implementations of this new algorithmic framework for several example problems with synthetic and real world data including music streams natural 2d images human motion trajectories and two dimensional shapes

multiscale distance matrix for fast plant leaf recognition in this brief we propose a novel contour based shape descriptor called the multiscale distance matrix to capture the shape geometry while being invariant to translation rotation scaling and bilateral symmetry the descriptor is further combined with a dimensionality reduction to improve its discriminative power the proposed method avoids the time consuming pointwise matching encountered in most of the previously used shape recognition algorithms it is therefore fast and suitable for real time applications we applied the proposed method to the task of plan leaf recognition with experiments on two data sets the swedish leaf data set and the icl leaf data set the experimental results clearly demonstrate the effectiveness and efficiency of the proposed descriptor

shape clustering this paper aims to address the problem of shape clustering by discovering the common structure which captures the intrinsic structural information of shapes belonging to the same cluster it is based on a skeleton graph named common structure skeleton graph cssg which expresses possible correspondences between nodes of the individual skeletons of the cluster to construct the cssg we derive the correspondences by the optimal subsequence bijection osb to cluster the shape data we apply an agglomerative clustering scheme in each iteration the cssgs are formed from each cluster and the two closest clusters are merged into one the proposed agglomerative clustering algorithm has been evaluated on several shape data sets including three articulated shape data sets torsello s data set and a gesture data set in all experiments our method demonstrates effective performance compared to other algorithms highlights a method is proposed to discover the common structure of a cluster of shapes a cluster of shapes are represented by their cssg assigning weights to nodes and edges in cssgs to help measure their distances an agglomerative strategy is proposed for shape clustering based on cssgs

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

on hidden markov models and cyclic strings for shape recognition abstract shape descriptions and the corresponding matching techniques must be robust to noise and invariant to transformations for their use in recognition tasks most transformations are relatively easy to handle when contours are represented by strings however starting point invariance is difficult to achieve one interesting possibility is the use of cyclic strings which are strings that have no starting and final points we propose new methodologies to use hidden markov models to classify contours represented by cyclic strings experimental results show that our proposals outperform other methods in the literature

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

some geometrical consequences of physical symmetries invariant submanifolds of the linear representation space c4m of the physical symmetry group su 2 2 su m and its subgroup p su m are studied in some detail it is shown that there exists only one such manifold admitting unique projection onto minkowski space the structure of this manifold is investigated by using proper local coordinate systems

hierarchical projective invariant contexts for shape recognition shape descriptors play an important role in various computer vision tasks many existing descriptors are typically derived from pair wise measures such as distances and angles which may vary with severe geometrical deformations including affine and projective transformations in this paper we propose a new shape descriptor from a newly developed projective invariant the characteristic number cn this new descriptor is invariant to projective or perspective transformations by computing cn values on a series of 5 sample points along the shape contour with the intervals varying from coarse to fine this hierarchical strategy yields a compacter descriptor so that the time complexity for both descriptor construction and shape matching are less or comparable to many existing methods we also use the derived points out of the contour and the ratio of two invariant values in order to improve the stability at finer scales and robustness to noise we demonstrate the performance of the descriptor by comparing with the state of the art on the mcd and other public shape sets with severe perspective transformations and other type variations including noise missing parts and articulated deformations graphical abstract highlightswe propose a new shape descriptor hcnc invariant to projective deformations hcnc is compact with a hierarchical strategy rendering efficient matching hcnc is robust to noise part missing and articulated deformations

in plane rotation and scale invariant clustering using dictionaries in this paper we present an approach that simultaneously clusters images and learns dictionaries from the clusters the method learns dictionaries and clusters images in the radon transform domain the main feature of the proposed approach is that it provides both in plane rotation and scale invariant clustering which is useful in numerous applications including content based image retrieval cbir we demonstrate the effectiveness of our rotation and scale invariant clustering method on a series of cbir experiments experiments are performed on the smithsonian isolated leaf kimia shape and brodatz texture datasets our method provides both good retrieval performance and greater robustness compared to standard gabor based and three state of the art shape based methods that have similar objectives

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

robust non rigid point set registration using spatially constrained gaussian fields estimating transformations from degraded point sets is necessary for many computer vision and pattern recognition applications in this paper we propose a robust non rigid point set registration method based on spatially constrained context aware gaussian fields we first construct a context aware representation e g shape context for assignment initialization then we use a graph laplacian regularized gaussian fields to estimate the underlying transformation from the likely correspondences on the one hand the intrinsic manifold is considered and used to preserve the geometrical structure and a priori knowledge of the point set is extracted on the other hand by using the deterministic annealing the presented method is extended to a projected high dimensional feature space i e reproducing kernel hilbert space through a kernel trick to solve the transformation in which the local structure is propagated by the coarse to fine scaling strategy in this way the proposed method gradually recovers much more correct correspondences and then estimates the transformation parameters accurately and robustly when facing degradations experimental results on 2d and 3d synthetic and real data point sets demonstrate that the proposed method reaches better performance than the state of the art algorithms

object detection using the statistics of parts in this paper we describe a trainable object detector and its instantiations for detecting faces and cars at any size location and pose to cope with variation in object orientation the detector uses multiple classifiers each spanning a different range of orientation each of these classifiers determines whether the object is present at a specified size within a fixed size image window to find the object at any location and size these classifiers scan the image exhaustively each classifier is based on the statistics of localized parts each part is a transform from a subset of wavelet coefficients to a discrete set of values such parts are designed to capture various combinations of locality in space frequency and orientation in building each classifier we gathered the class conditional statistics of these part values from representative samples of object and non object images we trained each classifier to minimize classification error on the training set by using adaboost with confidence weighted predictions shapire and singer 1999 in detection each classifier computes the part values within the image window and looks up their associated class conditional probabilities the classifier then makes a decision by applying a likelihood ratio test for efficiency the classifier evaluates this likelihood ratio in stages at each stage the classifier compares the partial likelihood ratio to a threshold and makes a decision about whether to cease evaluation labeling the input as non object or to continue further evaluation the detector orders these stages of evaluation from a low resolution to a high resolution search of the image our trainable object detector achieves reliable and efficient detection of human faces and passenger cars with out of plane rotation

a robust approach for object matching and classification using partial dominant orientation descriptor this paper introduces a novel approach to measure the correspondence between objects and exploit it for object and image classification tasks using the proposed partial dominant orientation descriptor pdod in particular the object is represented by a set of stable and informative key locations sampled using difference of gaussian the proposed pdod at each extracted key location takes into account the position and partially computes the dominant orientation of other key locations relative to it thus offering a global distinctive and discriminative characterization this allows us to learn features that are largely invariant to common image transformations including changes in object colors and textures the correspondence in between two objects is performed by finding for each key location in one object the key location in the other object that has the most similar descriptor object classification proceeds by assigning the most relevant category that has maximally similar stored prototype objects to the query object using k nearest neighbors algorithm with adaptive object distance for efficiency we further investigate pdod for image classification by developing powerful image representations based on the popular bag of words model the extensive experiments demonstrate that the proposed approach greatly improves the matching and classification results while achieving the state of the art performances on several challenging benchmark datasets the obtained results suggest also broader applicability to other classification modalities we propose a novel descriptor for complex object matching and classification the proposed descriptor combines both local and global properties of interest points the proposed descriptor is highly distinctive and insensitive to common image transformations adaptive object distance is proposed to measure the similarity between objects we compare our approach with many existing methods and we achieve the state of the art performances on several benchmarks

fast detection of dense subgraphs with iterative shrinking and expansion in this paper we propose an efficient algorithm to detect dense subgraphs of a weighted graph the proposed algorithm called the shrinking and expansion algorithm sea iterates between two phases namely the expansion phase and the shrink phase until convergence for a current subgraph the expansion phase adds the most related vertices based on the average affinity between each vertex and the subgraph the shrink phase considers all pairwise relations in the current subgraph and filters out vertices whose average affinities to other vertices are smaller than the average affinity of the result subgraph in both phases sea operates on small subgraphs thus it is very efficient significant dense subgraphs are robustly enumerated by running sea from each vertex of the graph we evaluate sea on two different applications solving correspondence problems and cluster analysis both theoretic analysis and experimental results show that sea is very efficient and robust especially when there exists a large amount of noise in edge weights

plant identification using leaf shapes a pattern counting approach plant identification is required by all walks of life from professionals to the general public nevertheless it is not an easy job but requires specialized knowledge in this paper we propose a new method for plant identification using shapes of their leaves different from existing studies which target at simple leaves the proposed method can accurately recognize both simple and compound leaves in specifics we propose a novel feature that captures global and local shape information independently so that they can be examined individually during classification furthermore we advocate that when comparing two leaf individuals it is better to count the number of certain shape patterns rather than to match the extracted shape features in a point wise manner the proposed counting based shape descriptor is not only discriminative for classification but also computationally fast and storage cheap experiments conducted on five leaf image datasets demonstrate that our algorithm significantly outperforms the state of the art methods in terms of recognition accuracy efficiency and storage requirement doing statistics over learned shape patterns rather than matching contour points the proposed method can classify both simple leaves and compound leaves the learned shape patterns measure leaf shapes from different aspects we do not require any pre processing of the leaf contours i e petioles removal experiments on public datasets show the effectiveness of the proposed method

support vector shape a classifier based shape representation we introduce a novel implicit representation for 2d and 3d shapes based on support vector machine svm theory each shape is represented by an analytic decision function obtained by training svm with a radial basis function rbf kernel so that the interior shape points are given higher values this empowers support vector shape svs with multifold advantages first the representation uses a sparse subset of feature points determined by the support vectors which significantly improves the discriminative power against noise fragmentation and other artifacts that often come with the data second the use of the rbf kernel provides scale rotation and translation invariant features and allows any shape to be represented accurately regardless of its complexity finally the decision function can be used to select reliable feature points these features are described using gradients computed from highly consistent decision functions instead from conventional edges our experiments demonstrate promising results

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

hand shape recognition based on coherent distance shape contexts in this paper we propose a novel hand shape recognition method named as coherent distance shape contexts cdsc which is based on two classical shape representations i e shape contexts sc and inner distance shape contexts idsc cdsc has good ability to capture discriminative features from hand shape and can well deal with the inexact correspondence problem of hand landmark points particularly it can extract features mainly from the contour of fingers thus it is very robust to different hand poses or elastic deformations of finger valleys in order to verify the effectiveness of cdsc we create a new hand image database containing 4000 grayscale left hand images of 200 subjects on which cdsc has achieved the accurate identification rate of 99 60 for identification and the equal error rate of 0 9 for verification which are comparable with the state of the art hand shape recognition methods

shape description and matching using integral invariants on eccentricity transformed images matching occluded and noisy shapes is a problem frequently encountered in medical image analysis and more generally in computer vision to keep track of changes inside the breast for example it is important for a computer aided detection system to establish correspondences between regions of interest shape transformations computed both with integral invariants ii and with geodesic distance yield signatures that are invariant to isometric deformations such as bending and articulations integral invariants describe the boundaries of planar shapes however they provide no information about where a particular feature lies on the boundary with regard to the overall shape structure conversely eccentricity transforms ecc can match shapes by signatures of geodesic distance histograms based on information from inside the shape but they ignore the boundary information we describe a method that combines the boundary signature of a shape obtained from ii and structural information from the ecc to yield results that improve on them separately

shape based object detection via boundary structure segmentation we address the problem of object detection and segmentation using global holistic properties of object shape global shape representations are highly susceptible to clutter inevitably present in realistic images and thus can be applied robustly only using a precise segmentation of the object to this end we propose a figure ground segmentation method for extraction of image regions that resemble the global properties of a model boundary structure and are perceptually salient our shape representation called the chordiogram is based on geometric relationships of object boundary edges while the perceptual saliency cues we use favor coherent regions distinct from the background we formulate the segmentation problem as an integer quadratic program and use a semidefinite programming relaxation to solve it the obtained solutions provide a segmentation of the object as well as a detection score used for object recognition our single step approach achieves state of the art performance on several object detection and segmentation benchmarks

shape decomposition and classification by searching optimal part pruning sequence representing shapes in terms of meaningful parts is a fundamental problem in shape analysis and part based object representation decomposition methods typically utilize handcrafted geometric rules in a nondata driven manner however these rules are insufficient to mimic human decomposition behavior which limits the applications of decomposition in vision tasks in this paper we propose a novel shape analysis framework that integrates shape decomposition with shape classification in fundamental level we first train probabilistic models for contours and part cuts involved in decomposition process next we construct a data structure called decomposition graph whose nodes represent intermediate contours and whose edges represent part cut selections the decomposition and classification results are obtained by efficiently searching the optimal path on decomposition graph with minimum energy experimental results show that such integrated framework improves the decomposition performance under various shape deformations and achieves competitive classification performance highlightsintegrating decomposition with classification will benefit both of them part based descriptor is robust to shape deformation and intra class variation class and geometric information are complementary in guiding decomposition learning from human decomposition result improves the decomposition performance the decomposition by optimal pruning sequence is solved in polynomial complexity

learning context sensitive similarity by shortest path propagation in this paper we introduce a novel shape object retrieval algorithm shortest path propagation ssp given a query object q and a target database object p we explicitly find the shortest path between them in the distance manifold of the database objects then a new distance measure between q and p is learned based on the database objects on the shortest path to replace the original distance measure the promising results on both mepg 7 shape dataset and a protein dataset demonstrate that our method can significantly improve the ranking of the object retrieval

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

deformation and contraction in clifford algebras spin ideals of clifford algebras over quadratic spaces of any rank are constructed through contractive limits of suitably deformed classical spin ideals of nondegenerate clifford algebras the deformation of the algebraic structures including the standard witt basis for the quadratic space results only from a deformation of the underlying quadratic form it is shown that a contractive limit of deformed twistor spaces considered as spin ideals of the dirac clifford algebra provides a decomposable representation space for the galilei clifford algebra the limit spin ideals of degenerate clifford algebras are then decomposed into indecomposable clifford modules

a performance evaluation of local descriptors in this paper we compare the performance of descriptors computed for local interest regions as for example extracted by the harris affine detector mikolajczyk k and schmid c 2004 many different descriptors have been proposed in the literature it is unclear which descriptors are more appropriate and how their performance depends on the interest region detector the descriptors should be distinctive and at the same time robust to changes in viewing conditions as well as to errors of the detector our evaluation uses as criterion recall with respect to precision and is carried out for different image transformations we compare shape context belongie s et al april 2002 steerable filters freeman w and adelson e setp 1991 pca sift ke y and sukthankar r 2004 differential invariants koenderink j and van doorn a 1987 spin images lazebnik s et al 2003 sift lowe d g 1999 complex filters schaffalitzky f and zisserman a 2002 moment invariants van gool l et al 1996 and cross correlation for different types of interest regions we also propose an extension of the sift descriptor and show that it outperforms the original method furthermore we observe that the ranking of the descriptors is mostly independent of the interest region detector and that the sift based descriptors perform best moments and steerable filters show the best performance among the low dimensional descriptors

lagrangian relaxation graph matching abstract graph matching is a fundamental problem in computer vision area graph matching problem that incorporates pair wise constraints can be formulated as an integer quadratic programming iqp problem with affine mapping constraint since it is known to be np hard approximate relaxation methods are usually required to find approximate solutions in this paper we present a new effective graph matching relaxation method called lagrangian relaxation graph matching lrgm which aims to generate a relaxation model by incorporating the affine mapping constraint into the matching objective optimization there are three main benefits of the proposed lrgm method 1 the nonnegative affine mapping constraint encoding one to one mapping is naturally incorporated in lrgm relaxation via lagrangian regularization 2 by further adding a l 1 norm constraint lrgm can generate a sparse solution empirically and thus returns a desired discrete solution for original iqp matching problem 3 an effective update algorithm is derived to solve the proposed lrgm model theoretically the converged solution can be proven to be karush kuhn tucker kkt optimal experimental results on both synthetic data and real world image datasets show the effectiveness and benefits of the proposed lrgm 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

layered graph matching with composite cluster sampling this paper presents a framework of layered graph matching for integrating graph partition and matching the objective is to find an unknown number of corresponding graph structures in two images we extract discriminative local primitives from both images and construct a candidacy graph whose vertices are matching candidates i e a pair of primitives and whose edges are either negative for mutual exclusion or positive for mutual consistence then we pose layered graph matching as a multicoloring problem on the candidacy graph and solve it using a composite cluster sampling algorithm this algorithm assigns some vertices into a number of colors each being a matched layer and turns off all the remaining candidates the algorithm iterates two steps 1 sampling the positive and negative edges probabilistically to form a composite cluster which consists of a few mutually conflicting connected components ccps in different colors and 2 assigning new colors to these ccps with consistence and exclusion relations maintained and the assignments are accepted by the markov chain monte carlo mcmc mechanism to preserve detailed balance this framework demonstrates state of the art performance on several applications such as multi object matching with large motion shape matching and retrieval and object localization in cluttered background

full and partial symmetries of non rigid shapes symmetry and self similarity are the cornerstone of nature exhibiting themselves through the shapes of natural creations and ubiquitous laws of physics since many natural objects are symmetric the absence of symmetry can often be an indication of some anomaly or abnormal behavior therefore detection of asymmetries is important in numerous practical applications including crystallography medical imaging and face recognition to mention a few conversely the assumption of underlying shape symmetry can facilitate solutions to many problems in shape reconstruction and analysis traditionally symmetries are described as extrinsic geometric properties of the shape while being adequate for rigid shapes such a description is inappropriate for non rigid ones extrinsic symmetry can be broken as a result of shape deformations while its intrinsic symmetry is preserved in this paper we present a generalization of symmetries for non rigid shapes and a numerical framework for their analysis addressing the problems of full and partial exact and approximate symmetry detection and classification

exploiting pairwise recommendation and clustering strategies for image re ranking in content based image retrieval cbir systems accurately ranking collection images is of great relevance users are interested in the returned images placed at the first positions which usually are the most relevant ones commonly image content descriptors are used to compute ranked lists in cbir systems in general these systems perform only pairwise image analysis that is compute similarity measures considering only pairs of images ignoring the rich information encoded in the relations among several images this paper presents a novel re ranking approach used to improve the effectiveness of cbir tasks by exploring relations among images in our approach a recommendation based strategy is combined with a clustering method both exploit contextual information encoded in ranked lists computed by cbir systems we conduct several experiments to evaluate the proposed method our experiments consider shape color and texture descriptors and comparisons with other post processing methods experimental results demonstrate the effectiveness of our method

on the projections of representation spaces of the symmetry group on the minkowski space in this paper we generalize the projection of the representation space of the symmetry group su 2 2 u 2 on the minkowski space to arbitrary internal symmetries u m the procedure involves certain restrictions on the coordinates of the representation space representations of the symmetry group in the restricted space and in the corresponding restricted hilbert space are constructed

sparse contextual activation for efficient visual re ranking in this paper we propose an extremely efficient algorithm for visual re ranking by considering the original pairwise distance in the contextual space we develop a feature vector called sparse contextual activation sca that encodes the local distribution of an image hence re ranking task can be simply accomplished by vector comparison under the generalized jaccard metric which has its theoretical meaning in the fuzzy set theory in order to improve the time efficiency of re ranking procedure inverted index is successfully introduced to speed up the computation of generalized jaccard metric as a result the average time cost of re ranking for a certain query can be controlled within 1 ms furthermore inspired by query expansion we also develop an additional method called local consistency enhancement on the proposed sca to improve the retrieval performance in an unsupervised manner on the other hand the retrieval performance using a single feature may not be satisfactory enough which inspires us to fuse multiple complementary features for accurate retrieval based on sca a robust feature fusion algorithm is exploited that also preserves the characteristic of high time efficiency we assess our proposed method in various visual re ranking tasks experimental results on princeton shape benchmark 3d object wm srhec07 3d competition yael data set b face mpeg 7 data set shape and ukbench data set image manifest the effectiveness and efficiency of sca

shape representation and classification using the poisson equation we present a novel approach that allows us to reliably compute many useful properties of a silhouette our approach assigns for every internal point of the silhouette a value reflecting the mean time required for a random walk beginning at the point to hit the boundaries this function can be computed by solving poisson s equation with the silhouette contours providing boundary conditions we show how this function can be used to reliably extract various shape properties including part structure and rough skeleton local orientation and aspect ratio of different parts and convex and concave sections of the boundaries in addition to this we discuss properties of the solution and show how to efficiently compute this solution using multigrid algorithms we demonstrate the utility of the extracted properties by using them for shape classification and retrieval

shape of elastic strings in euclidean space we construct a 1 parameter family of geodesic shape metrics on a space of closed parametric curves in euclidean space of any dimension the curves are modeled on homogeneous elastic strings whose elasticity properties are described in terms of their tension and rigidity coefficients as we change the elasticity properties we obtain the various elastic models the metrics are invariant under reparametrizations of the curves and induce metrics on shape space analysis of the geometry of the space of elastic strings and path spaces of elastic curves enables us to develop a computational model and algorithms for the estimation of geodesics and geodesic distances based on energy minimization we also investigate a curve registration procedure that is employed in the estimation of shape distances and can be used as a general method for matching the geometric features of a family of curves several examples of geodesics are given and experiments are carried out to demonstrate the discriminative quality of the elastic metrics

similarity based leaf image retrieval using multiscale r angle description leaf image identification is a significant and challenging application of computer vision and image processing a central issue associated with this task is how to effectively and efficiently describe the leaf images and measure their similarities in this paper a novel shape descriptor termed r angle is proposed r angle describes the curvature of the contour by measuring the angle between the intersections of the shape contour with a circle of radius r centered at points sampled around the contour it is intrinsically invariant to group transforms including scaling rotation and translation varying the parameter r of the proposed r angle naturally introduces the notation of scale which we leverage to provide a coarse to fine description of the local curvature a local scale arrangement is proposed by taking the distance between each contour point and the center of the shape to be the maximum scale for a given contour point two matching schemes including l1 norm matching and dynamic programming based matching are applied to measure the similarities of the leaf shapes the retrieval experiments conducted on two challenging leaf image datasets indicate that the proposed method significantly outperforms the state of the art methods for leaf identification an additional experiment on an animal dataset also indicates its potential for general shape recognition

shapes shocks and deformations i the components of two dimensional shape and the reaction diffusion space we undertake to develop a general theory of two dimensional shape by elucidating several principles which any such theory should meet the principles are organized around two basic intuitions first if a boundary were changed only slightly then in general its shape would change only slightly this leads us to propose an operational theory of shape based on incremental contour deformations the second intuition is that not all contours are shapes but rather only those that can enclose physical material a theory of contour deformation is derived from these principles based on abstract conservation principles and hamilton jacobi theory these principles are based on the work of sethian 1985a c the osher sethian 1988 level set formulation the classical shock theory of lax 1971 1973 as well as curve evolution theory for a curve evolving as a function of the curvature and the relation to geometric smoothing of gage hamilton grayson 1986 1989 the result is a characterization of the computational elements of shape deformations parts bends and seeds which show where to place the components of a shape the theory unifies many of the diverse aspects of shapes and leads to a space of shapes the reaction diffusion space which places shapes within a neighborhood of similar ones such similarity relationships underlie descriptions suitable for recognition

affinity learning with diffusion on tensor product graph in many applications we are given a finite set of data points sampled from a data manifold and represented as a graph with edge weights determined by pairwise similarities of the samples often the pairwise similarities which are also called affinities are unreliable due to noise or due to intrinsic difficulties in estimating similarity values of the samples as observed in several recent approaches more reliable similarities can be obtained if the original similarities are diffused in the context of other data points where the context of each point is a set of points most similar to it compared to the existing methods our approach differs in two main aspects first instead of diffusing the similarity information on the original graph we propose to utilize the tensor product graph tpg obtained by the tensor product of the original graph with itself since tpg takes into account higher order information it is not a surprise that we obtain more reliable similarities however it comes at the price of higher order computational complexity and storage requirement the key contribution of the proposed approach is that the information propagation on tpg can be computed with the same computational complexity and the same amount of storage as the propagation on the original graph we prove that a graph diffusion process on tpg is equivalent to a novel iterative algorithm on the original graph which is guaranteed to converge after its convergence we obtain new edge weights that can be interpreted as new learned affinities we stress that the affinities are learned in an unsupervised setting we illustrate the benefits of the proposed approach for data manifolds composed of shapes images and image patches on two very different tasks of image retrieval and image segmentation with learned affinities we achieve the bull s eye retrieval score of 99 99 percent on the mpeg 7 shape dataset which is much higher than the state of the art algorithms when the data points are image patches the ncut with the learned affinities not only significantly outperforms the ncut with the original affinities but it also outperforms state of the art image segmentation methods

feature adaptive co segmentation by complexity awareness in this paper we propose a novel feature adaptive co segmentation method that can learn adaptive features of different image groups for accurate common objects segmentation we also propose image complexity awareness for adaptive feature learning in the proposed method the original images are first ranked according to the image complexities that are measured by superpixel changing cue and object detection cue then the unsupervised segments of the simple images are used to learn the adaptive features which are achieved using an expectation minimization algorithm combining l 1 regularized least squares optimization with the consideration of the confidence of the simple image segmentation accuracies and the fitness of the learned model the error rate of the final co segmentation is tested by the experiments on different image groups and verified to be lower than the existing state of the art co segmentation methods

shape classification via image based multiscale description we introduce a new multiscale fourier based object description in 2 d space using a low pass gaussian filter lpgf and a high pass gaussian filter hpgf separately using the lpgf at different scales standard deviation represents the inner and central part of an object more than the boundary on the other hand using the hpgf at different scales represents the boundary and exterior parts of an object more than the central part our algorithms are also organized to achieve size translation and rotation invariance evaluation indicates that representing the boundary and exterior parts more than the central part using the hpgf performs better than the lpgf based multiscale representation and in comparison to zernike moments and elliptic fourier descriptors with respect to increasing noise multiscale description using hpgf in 2 d also outperforms wavelet transform based multiscale contour fourier descriptors and performs similar to the perimeter descriptors without any noise

optimality conditions for nonconvex multistate control problems in the coefficients the purpose of this paper is to attain some optimality conditions for the identification of a diffusion matrix material under several restrictions assuming that the set of such diffusion matrices is closed for the h convergence we give a method to obtain admissible directions which applies to a not necessarily convex control set our results permit obtaining the diffusion matrix from the state functions

new mathematical and algorithmic schemes for pattern classification with application to the identification of writers of important ancient documents abstract in this paper a novel approach is introduced for classifying curves into proper families according to their similarity first a mathematical quantity we call plane curvature is introduced and a number of propositions are stated and proved proper similarity measures of two curves are introduced and a subsequent statistical analysis is applied first the efficiency of the curve fitting process has been tested on 2 shapes datasets of reference next the methodology has been applied to the very important problem of classifying 23 byzantine codices and 46 ancient inscriptions to their writers thus achieving correct dating of their content the inscriptions have been attributed to ten individual hands and the byzantine codices to four writers

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

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

landmarks inside the shape in the last few decades significant advances in image matching are provided by rich local descriptors that are defined through physical measurements such as reflectance as such measurements are not naturally available for silhouettes existing arsenal of image matching tools cannot be utilized in shape matching we propose that the recently presented spem representation can be used analogous to image intensities to detect local keypoints using invariant image salient point detectors we devise a shape similarity measure based on the number of matching internal regions the performance of the similarity measure in planar shape retrieval indicates that the landmarks inside the shape silhouettes provide a strong representation of the regional characteristics of 2d planar shapes graphical abstractdisplay omitted highlightsan internal landmark based planar shape matching scheme is proposed the shape landmarks are obtained using the recently proposed spem representation properties of spem that allow the use of image descriptors inside shapes are discussed statistical evidence indicates that the number of matches can be used as a similarity measure

confidence sets for fine grained categorization and plant species identification we present a new hierarchical strategy for fine grained categorization standard fully automated systems report a single estimate of the category or perhaps a ranked list but have non neglible error rates for most realistic scenarios which limits their utility instead we propose a semi automated system which outputs a it confidence set cs a variable length list of categories which contains the true one with high probability e g a 99 cs performance is then measured by the expected size of the cs reflecting the effort required for final identification by the user the implementation is based on a hierarchical clustering of the full set of categories this tree of subsets provides a graded family of candidate cs s containing visually similar categories there is also a learned discriminant score for deciding between each subset and all others combined selection of the cs is based on the joint score likelihood under a bayesian network model we apply this method to determining the species of a plant from an image of a leaf against either a uniform or natural background extensive experiments are reported we obtain superior results relative to existing methods for point estimates for scanned leaves and report the first useful results for natural images at the expense of asking the user to initialize the process by identifying specific landmarks

shape classification using line segment statistics in this study we use straight line segment statistics for shape analysis for each contour point we consider a continuous portion with length equal to a pre defined percentage of the contour size then we compute the length of the straight line segment between its extreme points for the set of straight line segments we compute statistical moments average and stardard deviation contour shape description is an important field in computer vision this is due to the fact that shape is an important low level image feature in light of this many approaches have been proposed in order to analyze it therefore this paper introduces a very simple yet efficient shape descriptor based on straight line segment statistics for each contour point we consider a continuous portion of the contour with length equal to a pre defined percentage of the contour size then we compute the length of the straight line segment between its extreme points for the set of straight line segments we compute statistical moments average and standard deviation lastly we perform this calculation for different lengths of contour portions the proposed shape descriptor is a powerful tool for shape discrimination it is robust it can characterize a huge set of different classes of shapes and is tolerant to variations in the shapes scale and orientation classification results of the proposed method overcome traditional methods found in literature proving that it is an efficient tool for shape analysis

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

shape classification using invariant features and contextual information in the bag of words model in this paper we describe a classification framework for binary shapes that have scale rotation and strong viewpoint variations to this end we develop several novel techniques first we employ the spectral magnitude of log polar transform as a local feature in the bag of words model second we incorporate contextual information in the bag of words model using a novel method to extract bi grams from the spatial co occurrence matrix third a novel metric termed weighted gain ratio is proposed to select a suitable codebook size in the bag of words model the proposed metric is generic and hence it can be used for any clustering quality evaluation task fourth a joint learning framework is proposed to learn features in a data driven manner and thus avoid manual fine tuning of the model parameters we test our shape classification system on the animal shapes dataset and significantly outperform state of the art methods in the literature highlightsa shape classifier tolerant to scale rotation and viewpoint changes is proposed the inclusion of the histogram of bi grams improves the bag of words model codebook selection and feature learning improve the classification accuracy we report best results on the animal shapes dataset using the proposed method

dirac general covariance and tetrads i clifford and lie bundles and torsion the isomorphic map of clifford and lie bundles to arbitrary coordinate atlases using a global orthonormal tetrad field on a parallelizable space time is used to construct a fully covariant dirac spinor theory the klein gordon equation exhibits a natural spin torsion coupling of the einstein cartan form the torsion coming from the tetrad field the tetrad connection coefficients are explicitly derived in addition to their relationship to the usual levi civita coefficients various topological conditions for vanishing torsion are given the dirac and adjoint dirac equations are obtained from a simple lagrangian and the structure of the adjoint equation is discussed

improving shape retrieval by spectral matching and meta similarity we propose two computational approaches for improving the retrieval of planar shapes first we suggest a geometrically motivated quadratic similarity measure that is optimized by way of spectral relaxation of a quadratic assignment by utilizing state of the art shape descriptors and a pairwise serialization constraint we derive a formulation that is resilient to boundary noise articulations and nonrigid deformations this allows both shape matching and retrieval we also introduce a shape meta similarity measure that agglomerates pairwise shape similarities and improves the retrieval accuracy when applied to the mpeg 7 shape dataset in conjunction with the proposed geometric matching scheme we obtained a retrieval rate of 92 5

shape representation and recognition through morphological curvature scale spaces a multiscale morphological method for the purpose of shape based object recognition is presented a connected operator similar to the morphological hat transform is defined and two scale space representations are built using the curvature function as the underlying one dimensional signal each peak and valley of the curvature is extracted and described by its maximum and average heights and by its extent and represents an entry in the top or bottom hat transform scale spaces we demonstrate object recognition based on hat transform scale spaces for three large data sets a set of diatom contours the set of silhouettes from the mpeg 7 database and the set of two dimensional views of three dimensional objects from the coil 20 database our approach outperforms other methods for which comparative results exist

on bending invariant signatures for surfaces isometric surfaces share the same geometric structure also known as the first fundamental form for example all possible bendings of a given surface that includes all length preserving deformations without tearing or stretching the surface are considered to be isometric we present a method to construct a bending invariant signature for such surfaces this invariant representation is an embedding of the geometric structure of the surface in a small dimensional euclidean space in which geodesic distances are approximated by euclidean ones the bending invariant representation is constructed by first measuring the intergeodesic distances between uniformly distributed points on the surface next a multidimensional scaling technique is applied to extract coordinates in a finite dimensional euclidean space in which geodesic distances are replaced by euclidean ones applying this transform to various surfaces with similar geodesic structures first fundamental form maps them into similar signature surfaces we thereby translate the problem of matching nonrigid objects in various postures into a simpler problem of matching rigid objects as an example we show a simple surface classification method that uses our bending invariant signatures

using the particle filter approach to building partial correspondences between shapes constructing correspondences between points characterizing one shape with those characterizing another is crucial to understanding what the two shapes have in common these correspondences are the basis for most alignment processes and shape similarity measures in this paper we use particle filters to establish perceptually correct correspondences between point sets characterizing shapes local shape feature descriptors are used to establish the probability that a point on one shape corresponds to a point on the other shape global correspondence structures are calculated using additional constraints on domain knowledge domain knowledge is characterized by prior distributions which serve to characterize hypotheses about the global relationships between shapes these hypotheses are formulated online this means global constraints are learnt during the particle filtering process which makes the approach especially interesting for applications where global constraints are hard to define a priori as an example for such a case experiments demonstrate the performance of our approach on partial shape matching

label propagation based supervised locality projection analysis for plant leaf classification the label propagation has the benefits of nearly linear running time and easy implementation in this paper we make use of the label propagation to propose a new weight measure and present a supervised locality projection analysis slpa method for plant leaf classification firstly we apply warshall algorithm to label propagation and get the label matrix then incorporate it into the weight which has a clear physical meaning secondly multi class data points in high dimensional space are to be pulled or pushed by discriminant neighbors to form an optimum projecting to low dimensionality finally the experimental results on two plant leaf databases show that the proposed method is quite effective and feasible