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

a graduated assignment algorithm for graph matching a graduated assignment algorithm for graph matching is presented which is fast and accurate even in the presence of high noise by combining graduated nonconvexity two way assignment constraints and sparsity large improvements in accuracy and speed are achieved its low order computational complexity o lm where l and m are the number of links in the two graphs and robustness in the presence of noise offer advantages over traditional combinatorial approaches the algorithm not restricted to any special class of graph is applied to subgraph isomorphism weighted graph matching and attributed relational graph matching to illustrate the performance of the algorithm attributed relational graphs derived from objects are matched then results from twenty five thousand experiments conducted on 100 mode random graphs of varying types graphs with only zero one links weighted graphs and graphs with node attributes and multiple link types are reported no comparable results have been reported by any other graph matching algorithm before in the research literature twenty five hundred control experiments are conducted using a relaxation labeling algorithm and large improvements in accuracy are demonstrated

a method for registration of 3 d shapes the authors describe a general purpose representation independent method for the accurate and computationally efficient registration of 3 d shapes including free form curves and surfaces the method handles the full six degrees of freedom and is based on the iterative closest point icp algorithm which requires only a procedure to find the closest point on a geometric entity to a given point the icp algorithm always converges monotonically to the nearest local minimum of a mean square distance metric and the rate of convergence is rapid during the first few iterations therefore given an adequate set of initial rotations and translations for a particular class of objects with a certain level of shape complexity one can globally minimize the mean square distance metric over all six degrees of freedom by testing each initial registration one important application of this method is to register sensed data from unfixtured rigid objects with an ideal geometric model prior to shape inspection experimental results show the capabilities of the registration algorithm on point sets curves and surfaces

algorithms for approximate string matching the edit distance between strings a 1 a m and b 1 b n is the minimum cost s of a sequence of editing steps insertions deletions changes that convert one string into the other a well known tabulating method computes s as well as the corresponding editing sequence in time and in space o mn in space o min m n if the editing sequence is not required starting from this method we develop an improved algorithm that works in time and in space o s min m n another improvement with time o s min m n and space o s min s m n is given for the special case where all editing steps have the same cost independently of the characters involved if the editing sequence that gives cost s is not required our algorithms can be implemented in space o min s m n since s o max m n the new methods are always asymptotically as good as the original tabulating method as a by product algorithms are obtained that given a threshold value t test in time o t min m n and in space o min t m n whether s t finally different generalized edit distances are analyzed and conditions are given under which our algorithms can be used in conjunction with extended edit operation sets including for example transposition of adjacent characters

flexible spatial configuration of local image features local image features have been designed to be informative and repeatable under rigid transformations and illumination deformations even though current state of the art local image features present a high degree of repeatability their local appearance alone usually does not bring enough discriminative power to support a reliable matching resulting in a relatively high number of mismatches in the correspondence set formed during the data association procedure as a result geometric filters commonly based on global spatial configuration have been used to reduce this number of mismatches however this approach presents a trade off between the effectiveness to reject mismatches and the robustness to nonrigid deformations in this paper we propose two geometric filters based on a semilocal spatial configuration of local features that are designed to be robust to nonrigid deformations and to rigid transformations without compromising its efficacy to reject mismatches we compare our methods to the hough transform which is an efficient and effective mismatch rejection step based on the global spatial configuration of features in these comparisons our methods are shown to be more effective in the task of rejecting mismatches for rigid transformations and nonrigid deformations at comparable time complexity figures finally we demonstrate how we can integrate these methods in a probabilistic recognition system such that the final verification step uses not only the similarity between features but also their semilocal configuration

a mixture of transformed hidden markov models for elastic motion estimation elastic motion is a nonrigid motion constrained only by some degree of smoothness and continuity consequently elastic motion estimation by explicit feature matching actually contains two correlated subproblems shape registration and motion tracking which account for spatial smoothness and temporal continuity respectively if we ignore their interrelationship solving each of them alone will be rather challenging especially when the cluttered features are involved to integrate them into a probabilistic model one straightforward approach is to draw the dependence between their hidden states with regard to their separated states there are however two different explanations of motion which are still made under the individual constraint of smoothness or continuity each one can be error prone and their coupling causes error propagation therefore it is highly desirable to design a probabilistic model in which a unified state is shared by the two subproblems this paper is intended to propose such a model i e a mixture of transformed hidden markov models mthmm where a unique explanation of motion is made simultaneously under the spatiotemporal constraints as a result the mthmm could find a coherent global interpretation of elastic motion from local cluttered edge features and experiments show its robustness under ambiguities data missing and outliers

monge properties of sequence alignment alignment is an important sequence comparison measure algorithms that compute alignments have a wide range of applications namely in bioinformatic tools alignments can be computed as maximum scoring paths in alignment dags in this paper we study the properties of matrices that contain alignment scores between a string and all the sub strings of another string we focus on the fact that these matrices have the monge property and are sparse in some sense related studies were recently presented for hsm and dist matrices leading to o nlogn procedure for multiplying those matrices where o n bounds the sizes of the strings our results strictly generalize previous solutions we measure the sparseness of the matrices with variable d and present an algorithm for matrix multiplication in o email protected log 3 email protected time which we improve to o email protected log 2 email protected within the same space we discuss applications of this algorithm namely fully incremental alignment and alignment update we study experimentally the performance of the methods we propose

a feature point matching based on spatial order constraints bilateral neighbor vote feature point matching is a fundamental and challenging problem in many computer vision applications in this paper a robust feature point matching algorithm named spatial order constraints bilateral neighbor vote socbv is proposed to remove outliers for a set of matches including outliers between two images a directed k nearest neighbor knn graph of match sets is generated and the problem of feature point matching is formulated as a binary discrimination problem in the discrimination process the class labeled matrix is built via the spatial order constraints defined on the edges that connect a point to its knn then the posterior inlier class probability of each match is estimated with the knn density estimation and spatial order constraints the vote of each match is determined by averaging all posterior class probabilities that originate from its associative inliers set and is used for removing outliers the algorithm iteratively removes outliers from the directed graph and recomputes the votes until the stopping condition is satisfied compared with other popular algorithms such as ransac rsoc gtm soc and wgtm experiments under various testing data sets demonstrate strong robustness for the proposed algorithm

robust point pattern matching based on spectral context finding correspondences between two related feature point sets is a basic task in computer vision and pattern recognition in this paper we present a novel method for point pattern matching via spectral graph analysis in particular we aim to render the spectral matching algorithm more robust for positional jitter and outlier a local structural descriptor namely the spectral context is proposed to describe the attribute domain of point sets which is fundamentally different from the previous methods furthermore the approximate distance order is defined and employed as the metric for geometric consistency of neighboring points in this work by combining these two novel ingredients we formulate feature point set matching as an optimization problem with one to one constraints the correspondences are then obtained by maximizing the given objective function via the technique of probabilistic relaxation comparative experiments conducted on both synthetic and real data demonstrate the effectiveness of the proposed method especially in the presence of positional jitter and outliers a novel spectral method is proposed for the problem of point pattern matching we propose a local structural descriptor via spectral graph analysis we define a metric of geometric consistency by using the quantity of order

incremental string comparison the problem of comparing two sequences a and b to determine their longest common subsequence lcs or the edit distance between them has been much studied in this paper we consider the following incremental version of these problems given an appropriate encoding of a comparison between a and b can one incrementally compute the answer for a and bb and the answer for a and bb with equal efficiency where b is an additional symbol our main result is a theorem exposing a surprising relationship between the dynamic programming solutions for two such adjacent problems given a threshold k on the number of differences to be permitted in an alignment the theorem leads directly to an o k algorithm for incrementally computing a new solution from an old one as contrasts the o k2 time required to compute a solution from scratch we further show with a series of applications that this algorithm is indeed more powerful than its nonincremental counterpart we show this by solving the applications with greater asymptotic efficiency than heretofore possible for example we obtain o nk algorithms for the longest prefix approximate match problem the approximate overlap problem and cyclic string comparison

discriminative feature selection for on line signature verification abstract on line handwritten signatures are collected as real time dynamical signals which are written on collective devices by users since individuals have different writing habits consistent and discriminative features should be selected to distinguish genuine signatures from forged signatures in this paper two methods which are based on full factorial experiment design and optimal orthogonal experiment design are proposed for selecting discriminative features among candidates to improve the robustness consistency of feature is analyzed at first and more consistent features are selected as candidates for discriminative feature selection to reduce the influences of fluctuations caused by internal and external writing environments changes before verification signatures are effectively aligned to their reference templates based on gaussian mixture model a modified dynamic time warping with signature curve constraint is presented for verification to improve the efficiency comprehensive experiments are implemented based on the data of the open access databases mcyt and svc2004 task2 experimental results verify the effectiveness and robustness of our proposed methods

scale affine invariant interest point detectors in this paper we propose a novel approach for detecting interest points invariant to scale and affine transformations our scale and affine invariant detectors are based on the following recent results 1 interest points extracted with the harris detector can be adapted to affine transformations and give repeatable results geometrically stable 2 the characteristic scale of a local structure is indicated by a local extremum over scale of normalized derivatives the laplacian 3 the affine shape of a point neighborhood is estimated based on the second moment matrix our scale invariant detector computes a multi scale representation for the harris interest point detector and then selects points at which a local measure the laplacian is maximal over scales this provides a set of distinctive points which are invariant to scale rotation and translation as well as robust to illumination changes and limited changes of viewpoint the characteristic scale determines a scale invariant region for each point we extend the scale invariant detector to affine invariance by estimating the affine shape of a point neighborhood an iterative algorithm modifies location scale and neighborhood of each point and converges to affine invariant points this method can deal with significant affine transformations including large scale changes the characteristic scale and the affine shape of neighborhood determine an affine invariant region for each point we present a comparative evaluation of different detectors and show that our approach provides better results than existing methods the performance of our detector is also confirmed by excellent matching resultss the image is described by a set of scale affine invariant descriptors computed on the regions associated with our points

information theoretic shape matching in this paper we describe two related algorithms that provide both rigid and non rigid point set registration with different computational complexity and accuracy the first algorithm utilizes a nonlinear similarity measure known as correntropy the measure combines second and high order moments in its decision statistic showing improvements especially in the presence of impulsive noise the algorithm assumes that the correspondence between the point sets is known which is determined with the surprise metric the second algorithm mitigates the need to establish a correspondence by representing the point sets as probability density functions pdf the registration problem is then treated as a distribution alignment the method utilizes the cauchy schwarz divergence to measure the similarity distance between the point sets and recover the spatial transformation function needed to register them both algorithms utilize information theoretic descriptors however correntropy works at the realizations level whereas cauchy schwarz divergence works at the pdf level this allows correntropy to be less computationally expensive and for correct correspondence more accurate the two algorithms are robust against noise and outliers and perform well under varying levels of distortion they outperform several well known and state of the art methods for point set registration

global propagation of affine invariant features for robust matching local invariant features have been successfully used in image matching to cope with viewpoint change partial occlusion and clutters however when these factors become too strong there will be a lot of mismatches due to the limited repeatability and discriminative power of features in this paper we present an efficient approach to remove the false matches and propagate the correct ones for the affine invariant features which represent the state of the art local invariance first a pair wise affine consistency measure is proposed to evaluate the consensus of the matches of affine invariant regions the measure takes into account both the keypoint location and the region shape size and orientation based on this measure a geometric filter is then presented which can efficiently remove the outliers from the initial matches and is robust to severe clutters and non rigid deformation to increase the correct matches we propose a global match refinement and propagation method that simultaneously finds a optimal group of local affine transforms to relate the features in two images the global method is capable of producing a quasi dense set of matches even for the weakly textured surfaces that suffer strong rigid transformation or non rigid deformation the strong capability of the proposed method in dealing with significant viewpoint change non rigid deformation and low texture objects is demonstrated in experiments of image matching object recognition and image based rendering

matching images with multiple descriptors an unsupervised approach for locally adaptive descriptor selection with the aim to improve the performance of feature matching we present an unsupervised approach for adaptive description selection in the space of homographies inspired by the observation that the homographies of correct feature correspondences vary smoothly along the spatial domain our approach stands on the unsupervised nature of feature matching and can choose a good descriptor locally for matching each feature point instead of using one global descriptor to this end the homography space serves as the domain for selecting various heterogeneous descriptors correspondences obtained by any descriptors are considered as points in the space and their geometric coherence and spatial continuity are measured via computing the geodesic distances in this way mutual verification across different descriptors is allowed and correct correspondences will be highlighted with a high degree of consistency short geodesic distances here it follows that one class svm can be applied to identifying these correct correspondences and achieves adaptive descriptor selection the proposed approach is comprehensively compared with the state of the art approaches and evaluated on five benchmarks of image matching the promising results manifest its effectiveness

an efficient globally optimal algorithm for asymmetric point matching although the robust point matching algorithm has been demonstrated to be effective for non rigid registration there are several issues with the adopted deterministic annealing optimization technique first it is not globally optimal and regularization on the spatial transformation is needed for good matching results second it tends to align the mass centers of two point sets to address these issues we propose a globally optimal algorithm for the robust point matching problem in the case that each model point has a counterpart in scene set by eliminating the transformation variables we show that the original matching problem is reduced to a concave quadratic assignment problem where the objective function has a low rank hessian matrix this facilitates the use of large scale global optimization techniques we propose a modified normal rectangular branch and bound algorithm to solve the resulting problem where multiple rectangles are simultaneously subdivided to increase the chance of shrinking the rectangle containing the global optimal solution in addition we present an efficient lower bounding scheme which has a linear assignment formulation and can be efficiently solved extensive experiments on synthetic and real datasets demonstrate the proposed algorithm performs favorably against the state of the art methods in terms of robustness to outliers matching accuracy and run time

progressive match expansion via coherent subspace constraint in this paper a quasi dense matching algorithm called progressive match expansion via coherent subspace pecs is proposed our algorithm starts from a set of sparse seeds and iteratively expands potential matches in the region around the seeds until no more matches could be found the main difference from previous methods is that our method computes a coherent non rigid transformation to relate the matching pixels instead of using local planar affine model to approximate the real scene surface within the expanding region the points in the expanding region are treated as a whole and all the matches satisfying the transformation are found at once first dense sift descriptors are extracted and a subspace encoding the feature similarity between two point sets is computed this embedding pulls two points closer if they have similar features and makes the non rigid transformation learning more robust second a coherent non rigid transformation in the subspace is computed to move one point set towards the other and the spatially aligned two points denote a match the proposed model is robust to scenes with non smooth surface and experiment results reveal the good performance in both 2d image matching and 3d reconstruction

automatic range image registration in the markov chain in this paper a novel entropy that can describe both long and short tailed probability distributions of constituents of a thermodynamic system out of its thermodynamic limit is first derived from the lyapunov function for a markov chain we then maximize this entropy for the estimation of the probabilities of possible correspondences established using the traditional closest point criterion between two overlapping range images when we change our viewpoint to look carefully at the minimum solution to the probability estimate of the correspondences the iterative range image registration process can also be modeled as a markov chain in which lessons from past experience in estimating those probabilities are learned to impose the two way constraint outliers are explicitly modeled due to the almost ubiquitous occurrence of occlusion appearance and disappearance of points in either image the estimated probabilities of the correspondences are finally embedded into the powerful mean field annealing scheme for global optimization leading the camera motion parameters to be estimated in the weighted least squares sense a comparative study using real images shows that the proposed algorithm usually outperforms the state of the art icp variants and the latest genetic algorithm for automatic overlapping range image registration

longest common subsequence problem for unoriented and cyclic strings given a finite set of strings x the longest common subsequence problem lcs consists in finding a subsequence common to all strings in x that is of maximal length lcs is a central problem in stringology and finds broad applications in text compression conception of error detecting codes or biological sequence comparison however in numerous contexts words represent cyclic or unoriented sequences of symbols and lcs must be generalized to consider both orientations and or all cyclic shifts of the strings involved this occurs especially in computational biology when genetic material is sequenced from circular dna or rna molecules in this work we define three variants of lcs when the input words are unoriented and or cyclic we show that these problems are np hard and w 1 hard if parameterized in the number of input strings these results still hold even if the three lcs variants are restricted to input languages over a binary alphabet we also settle the parameterized complexity of our problems for most relevant parameters moreover we study the approximability of these problems we discuss the existence of approximation bounds depending on the cardinality of the alphabet on the length of the shortest sequence and on the number of input sequences for this we prove that maximum independent set in r uniform hypergraphs is w 1 hard if parameterized in the cardinality of the sought independent set and at least as hard to approximate as maximum independent set in graphs

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

a robust technique for matching two uncalibrated images through the recovery of the unknown epipolar geometry abstract this paper proposes a robust approach to image matching by exploiting the only available geometric constraint namely the epipolar constraint the images are uncalibrated namely the motion between them and the camera parameters are not known thus the images can be taken by different cameras or a single camera at different time instants if we make an exhaustive search for the epipolar geometry the complexity is prohibitively high the idea underlying our approach is to use classical techniques correlation and relaxation methods in our particular implementation to find an initial set of matches and then use a robust technique the least median of squares lmeds to discard false matches in this set the epipolar geometry can then be accurately estimated using a meaningful image criterion more matches are eventually found as in stereo matching by using the recovered epipolar geometry a large number of experiments have been carried out and very good results have been obtained regarding the relaxation technique we define a new measure of matching support which allows a higher tolerance to deformation with respect to rigid transformations in the image plane and a smaller contribution for distant matches than for nearby ones a new strategy for updating matches is developed which only selects those matches having both high matching support and low matching ambiguity the update strategy is different from the classical winner take all which is easily stuck at a local minimum and also from loser take nothing which is usually very slow the proposed algorithm has been widely tested and works remarkably well in a scene with many repetitive patterns

longest common extensions in trees the longest common extension lce of two indices in a string is the length of the longest identical substrings starting at these two indices the lce problem asks to preprocess a string into a compact data structure that supports fast lce queries in this paper we generalize the lce problem to trees and suggest a few applications of lce in trees to tries and xml databases given a labeled and rooted tree t of size n the goal is to preprocess t into a compact data structure that support the following lce queries between subpaths and subtrees in t let v 1 v 2 w 1 and w 2 be nodes of t such that w 1 and w 2 are descendants of v 1 and v 2 respectively lce pp v 1 w 1 v 2 w 2 path path lce return the longest common prefix of the paths v 1 w 1 and v 2 w 2 lce pt v 1 w 1 v 2 path tree lce return maximal path path lce of the path v 1 w 1 and any path from v 2 to a descendant leaf lce tt v 1 v 2 tree tree lce return a maximal path path lce of any pair of paths from v 1 and v 2 to descendant leaves we present the first non trivial bounds for supporting these queries for lce pp queries we present a linear space solution with o log n query time for lce pt queries we present a linear space solution with o log log n 2 query time and complement this with a lower bound showing that any path tree lce structure of size o n polylog n must necessarily use log log n time to answer queries for lce tt queries we present a time space trade off that given any parameter 1 n leads to an o n space and o n query time solution all of these bounds hold on a standard unit cost ram model with logarithmic word size this is complemented with a reduction from the set intersection problem implying that a fast linear space solution is not likely to exist

implicit time integration of elasto viscoplastic solids subject to the mohr coulomb yield criterion for selected situations in geotechnical engineering the use of implicit time integration techniques for elasto viscoplastic analysis is advantageous or even unavoidable in this paper the necessary expressions are derived for the implicit analysis of a material governed by the mohr coulomb yield criterion in particular detailed expressions are provided for the viscoplastic strain rate derivative matrix hn in a form suitable for numerical computation use of this algorithm is illustrated by the solution of a numerical example

all highest scoring paths in weighted grid graphs and their application to finding all approximate repeats in strings weighted paths in directed grid graphs of dimension m x n can be used to model the string edit problem which consists of obtaining optimal weighted alignments between substrings of a a m and substrings of b b n we build a data structure in o mn log m time that supports o log m time queries about the weight of any of the o m2n best paths from the vertices in column 0 of the graph to all other vertices using these techniques we present a simple o n2 log n time and theta n 2 space algorithm to find all the locally optimal approximate tandem or nontandem repeats xy within a string of size n this improves by a factor of log n upon several previous algorithms for this problem and is the first algorithm to find all locally optimal repeats for edit graphs with weights in 0 1 1 a slight modification of our techniques yields an o n2 algorithm for the cyclic string comparison problem as compared to o n2 log n for the case of general weights

a comparison of affine region detectors the paper gives a snapshot of the state of the art in affine covariant region detectors and compares their performance on a set of test images under varying imaging conditions six types of detectors are included detectors based on affine normalization around harris mikolajczyk and schmid 2002 schaffalitzky and zisserman 2002 and hessian points mikolajczyk and schmid 2002 a detector of maximally stable extremal regions proposed by matas et al 2002 an edge based region detector tuytelaars and van gool 1999 and a detector based on intensity extrema tuytelaars and van gool 2000 and a detector of salient regions proposed by kadir zisserman and brady 2004 the performance is measured against changes in viewpoint scale illumination defocus and image compression the objective of this paper is also to establish a reference test set of images and performance software so that future detectors can be evaluated in the same framework

convex hull indexed gaussian mixture model ch gmm for 3d point set registration to solve the problem of rigid non rigid 3d point set registration a novel convex hull indexed gaussian mixture model ch gmm is proposed in this paper the model works by computing a weighted gaussian mixture model gmm response over the convex hull of each point set three conditions proximity area conservation and projection consistency are incorporated into the model so as to improve its performance given that the convex hull is the tightest convex set of a point set the combination of gaussian mixture and convex hull can effectively preserve the topological structure of a point set furthermore computational complexity can be significantly reduced since only the gmm of the convex hull instead of the whole point set needs to be calculated rigid registration is achieved by seeking the best rigid transformation parameters yielding the most similar ch gmm responses non rigid deformation is realized by optimizing the coordinates of the control points used by the thin plate spline model for interpolating the entire point set experiments are designed to evaluate a method s robustness to rotational changes between two point sets positional noise differences in density and partial overlap the results demonstrated better robustness and registration accuracy of ch gmm based method over state of the art methods including iterative closest point coherent point drift and the gmm method besides the computation of ch gmm is efficient a novel ch gmm method is proposed for non rigid registration of point sets the ch gmm can effectively present the topological information of point set the ch gmm matching of the point sets is very fast the registration is very robust for points with large differences

new solutions for the modified generalized degasperis procesi equation in this paper using three distinct computational methods we obtain some new exact solutions for the generalized modified degasperis procesi equation mdp equation u t u x x t b 1 u 2u x bu xu x x uu x x x we show the graph of some of the new solutions obtained here with the aim to illustrate their physical relevance mathematica is used finally some conclusions are given

matching widely separated views based on affine invariant regions invariant regions are self adaptive image patches that automatically deform with changing viewpoint as to keep on covering identical physical parts of a scene such regions can be extracted directly from a single image they are then described by a set of invariant features which makes it relatively easy to match them between views even under wide baseline conditions in this contribution two methods to extract invariant regions are presented the first one starts from corners and uses the nearby edges while the second one is purely intensity based as a matter of fact the goal is to build an opportunistic system that exploits several types of invariant regions as it sees fit this yields more correspondences and a system that can deal with a wider range of images to increase the robustness of the system two semi local constraints on combinations of region correspondences are derived one geometric the other photometric they allow to test the consistency of correspondences and hence to reject falsely matched regions experiments on images of real world scenes taken from substantially different viewpoints demonstrate the feasibility of the approach

on the foundations of relaxation labeling processes a large class of problems can be formulated in terms of the assignment of labels to objects frequently processes are needed which reduce ambiguity and noise and select the best label among several possible choices relaxation labeling processes are just such a class of algorithms they are based on the parallel use of local constraints between labels this paper develops a theory to characterize the goal of relaxation labeling the theory is founded on a definition of con sistency in labelings extending the notion of constraint satisfaction in certain restricted circumstances an explicit functional exists that can be maximized to guide the search for consistent labelings this functional is used to derive a new relaxation labeling operator when the restrictions are not satisfied the theory relies on variational cal culus it is shown that the problem of finding consistent labelings is equivalent to solving a variational inequality a procedure nearly identical to the relaxation operator derived under restricted circum stances serves in the more general setting further a local convergence result is established for this operator the standard relaxation labeling formulas are shown to approximate our new operator which leads us to conjecture that successful applications of the standard methods are explainable by the theory developed here observations about con vergence and generalizations to higher order compatibility relations are described

robust l_ 2 e estimation of transformation for non rigid registration we introduce a new transformation estimation algorithm using the l 2 e estimator and apply it to non rigid registration for building robust sparse and dense correspondences in the sparse point case our method iteratively recovers the point correspondence and estimates the transformation between two point sets feature descriptors such as shape context are used to establish rough correspondence we then estimate the transformation using our robust algorithm this enables us to deal with the noise and outliers which arise in the correspondence step the transformation is specified in a functional space more specifically a reproducing kernel hilbert space in the dense point case for nonrigid image registration our approach consists of matching both sparsely and densely sampled sift features and it has particular advantages in handling significant scale changes and rotations the experimental results show that our approach greatly outperforms state of the art methods particularly when the data contains severe outliers

attributed string matching with merging for shape recognition a new structural approach to shape recognition using attributed string matching with merging is proposed after illustrating the disadvantages of conventional symbolic string matching using changes deletions and insertions attributed strings are suggested for matching each attributed string is an ordered sequence of shape boundary primitives each representing a basic boundary structural unit line segment with two types of numerical attributes length and direction a new type of primitive edit operation called merge is then introduced which can be used to combine and then match any number of consecutive boundary primitives in one shape with those in another the resulting attributed string matching with merging approach is shown useful for recognizing distorted shapes experimental results prove the feasibility of the proposed approach for general shape recognition some possible extensions of the approach are also included

two dimensional object recognition through two stage string matching a two stage string matching method for the recognition of two dimensional 2 d objects is proposed in this work the first stage is a global cyclic string matching the second stage is a local matching with local dissimilarity measure computing the dissimilarity measure function of the input shape and the reference shape are obtained by combining the global matching cost and the local dissimilarity measure the proposed method has the advantage that there is no need to set any parameter in the recognition process experimental results indicate that the hostage string matching approach significantly improves the recognition rates compared to the one stage string matching method

contrast invariant interest point detection by zero norm log filter the laplacian of gaussian log filter is widely used in interest point detection however low contrast image structures though stable and significant are often submerged by the high contrast ones in the response image of the log filter and hence are difficult to be detected to solve this problem we derive a generalized log filter and propose a zero norm log filter the response of the zero norm log filter is proportional to the weighted number of bright dark pixels in a local region which makes this filter be invariant to the image contrast based on the zero norm log filter we develop an interest point detector to extract local structures from images compared with the contrast dependent detectors such as the popular scale invariant feature transform detector the proposed detector is robust to illumination changes and abrupt variations of images experiments on benchmark databases demonstrate the superior performance of the proposed zero norm log detector in terms of the repeatability and matching score of the detected points as well as the image recognition rate under different conditions

non rigid point set registration by preserving global and local structures in previous work on point registration the input point sets are often represented using gaussian mixture models and the registration is then addressed through a probabilistic approach which aims to exploit global relationships on the point sets for non rigid shapes however the local structures among neighboring points are also strong and stable and thus helpful in recovering the point correspondence in this paper we formulate point registration as the estimation of a mixture of densities where local features such as shape context are used to assign the membership probabilities of the mixture model this enables us to preserve both global and local structures during matching the transformation between the two point sets is specified in a reproducing kernel hilbert space and a sparse approximation is adopted to achieve a fast implementation extensive experiments on both synthesized and real data show the robustness of our approach under various types of distortions such as deformation noise outliers rotation and occlusion it greatly outperforms the state of the art methods especially when the data is badly degraded

robust weighted graph transformation matching for rigid and nonrigid image registration this paper presents an automatic point matching algorithm for establishing accurate match correspondences in two or more images the proposed algorithm utilizes a group of feature points to explore their geometrical relationship in a graph arrangement the algorithm starts with a set of matches including outliers between the two images a set of nondirectional graphs is then generated for each feature and its k nearest matches chosen from the initial set using the angular distances between edges that connect a feature point to its k nearest neighbors in the graph the algorithm finds a graph in the second image that is similar to the first graph in the case of a graph including outliers the algorithm removes such outliers one by one according to their strength from the graph and re evaluates the angles until the two graphs are matched or discarded this is a simple intuitive and robust algorithm that is inspired by a previous work experimental results demonstrate the superior performance of this algorithm under various conditions such as rigid and nonrigid transformations ambiguity due to partial occlusions or match correspondence multiplicity scale and larger view variation

stress evaluation algorithms for rate constitutive equations in finite deformation analysis the stress integration algorithm for hypoelastic constitutive equations proposed by pinsky et al 3 is extended for the treatment of finite deformation elastoplastic constitutive relations another approach based on the polar decomposition of the deformation gradient tensor f r u is also introduced numerical examples and a discussion on these two approaches are given

a quasi dense approach to surface reconstruction from uncalibrated images this paper proposes a quasi dense approach to 3d surface model acquisition from uncalibrated images first correspondence information and geometry are computed based on new quasi dense point features that are resampled subpixel points from a disparity map the quasi dense approach gives more robust and accurate geometry estimations than the standard sparse approach the robustness is measured as the success rate of full automatic geometry estimation with all involved parameters fixed the accuracy is measured by a fast gauge free uncertainty estimation algorithm the quasi dense approach also works for more largely separated images than the sparse approach therefore it requires fewer images for modeling more importantly the quasi dense approach delivers a high density of reconstructed 3d points on which a surface representation can be reconstructed this fills the gap of insufficiency of the sparse approach for surface reconstruction essential for modeling and visualization applications second surface reconstruction methods from the given quasi dense geometry are also developed the algorithm optimizes new unified functionals integrating both 3d quasi dense points and 2d image information including silhouettes combining both 3d data and 2d images is more robust than the existing methods using only 2d information or only 3d data an efficient bounded regularization method is proposed to implement the surface evolution by level set methods its properties are discussed and proven for some cases as a whole a complete automatic and practical system of 3d modeling from raw images captured by hand held cameras to surface representation is proposed extensive experiments demonstrate the superior performance of the quasi dense approach with respect to the standard sparse approach in robustness accuracy and applicability

efficient all path score computations on grid graphs we study the integer weighted grid all paths scores igaps problem which is given a grid graph to compute the maximum weights of paths between every pair of a vertex on the first row of the graph and a vertex on the last row of the graph we also consider a variant of this problem periodic igaps where the input grid graph is periodic and infinite for these problems we consider both the general dense and the sparse cases for the sparse periodic igaps problem with 0 1 weights we give an o rlog 3 n 2 r time algorithm where r is the number of diagonal edges of weight 1 our result improves upon the previous o nr result by krusche and tiskin for this problem for the periodic igaps problem we give an o cn 2 time algorithm where c is the maximum weight of an edge this improves upon the previous o c 2n 2 algorithm of tiskin we also show a reduction from periodic igaps to igaps this reduction yields o n 2 algorithms for this problem

approximate periods of strings the study of approximately periodic strings is relevant to diverse applications such as molecular biology data compression and computer assisted music analysis here we study different forms of approximate periodicity under a variety of distance functions we consider three related problems for two of which we derive polynomial time algorithms we then show that the third problem is np complete

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

an improved algorithm for approximate string matching given a text string a pattern string and an integer k a new algorithm for finding all occurrences of the pattern string in the text string with at most k differences is presented both its theoretical and practical variants improve upon the known algorithms

the cole hopf transformation and improved tanh coth method applied to new integrable system kdv6 abstract in this paper we study a new coupled system kdv6 from the point of view of constructing exact solutions for it by using the cole hopf transformation and one improved tanh coth method traveling wave solution which includes periodic and soliton solutions are formally derived

factorized graph matching graph matching gm is a fundamental problem in computer science and it plays a central role to solve correspondence problems in computer vision gm problems that incorporate pairwise constraints can be formulated as a quadratic assignment problem qap although widely used solving the correspondence problem through gm has two main limitations 1 the qap is np hard and difficult to approximate 2 gm algorithms do not incorporate geometric constraints between nodes that are natural in computer vision problems to address aforementioned problems this paper proposes factorized graph matching fgm fgm factorizes the large pairwise affinity matrix into smaller matrices that encode the local structure of each graph and the pairwise affinity between edges four are the benefits that follow from this factorization 1 there is no need to compute the costly in space and time pairwise affinity matrix 2 the factorization allows the use of a path following optimization algorithm that leads to improved optimization strategies and matching performance 3 given the factorization it becomes straight forward to incorporate geometric transformations rigid and non rigid to the gm problem 4 using a matrix formulation for the gm problem and the factorization it is easy to reveal commonalities and differences between different gm methods the factorization also provides a clean connection with other matching algorithms such as iterative closest point experimental results on synthetic and real databases illustrate how fgm outperforms state of the art algorithms for gm the code is available at http humansensing cs cmu edu fgm

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

gaussian field consensus a robust nonparametric matching method for outlier rejection abstract in this paper we propose a robust method called gaussian field consensus gfc for outlier rejection from given putative point set matching correspondences finding correct correspondences inliers is a key component in many computer vision and pattern recognition tasks and the goal of outlier mismatch rejection is to fit the transformation function that maps one feature point set to another our gfc starts by inputting a putative correspondence set which is contaminated by many outliers and the main task of our gfc is to identify the underlying true correspondences from outliers then we formulate this challenging problem by gaussian field nonparametric matching model which bases on the exponential distance loss and kernel method in a reproducing kernel hilbert space next we introduce a local linear constraint based on the regularization theory to preserve the topological structure of the feature points moreover the sparse approximation is used to reduce the search space in this way we can handle a large number of points easily finally we test the gfc method on several real image datasets in the presence of outliers where the experimental results show that our proposed method outperforms current state of the art methods in most test scenarios

the development and comparison of robust methodsfor estimating the fundamental matrix this paper has two goals the first is to develop a variety of robust methods for the computation of the fundamental matrix the calibration free representation of camera motion the methods are drawn from the principal categories of robust estimators viz case deletion diagnostics m estimators and random sampling and the paper develops the theory required to apply them to non linear orthogonal regression problems although a considerable amount of interest has focussed on the application of robust estimation in computer vision the relative merits of the many individual methods are unknown leaving the potential practitioner to guess at their value the second goal is therefore to compare and judge the methods comparative tests are carried out using correspondences generated both synthetically in a statistically controlled fashion and from feature matching in real imagery in contrast with previously reported methods the goodness of fit to the synthetic observations is judged not in terms of the fit to the observations per se but in terms of fit to the ground truth a variety of error measures are examined the experiments allow a statistically satisfying and quasi optimal method to be synthesized which is shown to be stable with up to 50 percent outlier contamination and may still be used if there are more than 50 percent outliers performance bounds are established for the method and a variety of robust methods to estimate the standard deviation of the error and covariance matrix of the parameters are examined the results of the comparison have broad applicability to vision algorithms where the input data are corrupted not only by noise but also by gross outliers

fast algorithms for finding nearest common ancestors we consider the following problem given a collection of rooted trees answer on line queries of the form what is the nearest common ancester of vertices x and y we show that any pointer machine that solves this problem requires omega log log n time per query in the worst case where n is the total number of vertices in the trees on the other hand we present an algorithm for a random access machine with uniform cost measure and a bound of omega log n on the number of bits per word that requires o 1 time per query and o n preprocessing time assuming that the collection of trees is static for a version of the problem in which the trees can change between queries we obtain an almost linear time and linear space algorithm

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

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

robust point matching for nonrigid shapes by preserving local neighborhood structures in previous work on point matching a set of points is often treated as an instance of a joint distribution to exploit global relationships in the point set for nonrigid shapes however the local relationship among neighboring points is stronger and more stable than the global one in this paper we introduce the notion of a neighborhood structure for the general point matching problem we formulate point matching as an optimization problem to preserve local neighborhood structures during matching our approach has a simple graph matching interpretation where each point is a node in the graph and two nodes are connected by an edge if they are neighbors the optimal match between two graphs is the one that maximizes the number of matched edges existing techniques are leveraged to search for an optimal solution with the shape context distance used to initialize the graph matching followed by relaxation labeling updates for refinement extensive experiments show the robustness of our approach under deformation noise in point locations outliers occlusion and rotation it outperforms the shape context and tps rpm algorithms on most scenarios

computing exact solutions to a generalized lax seventh order forced kdv equation kdv7 abstract in this paper the cole hopf transform is used to construct exact solutions to a generalization of both the seventh order lax kdv equation lax kdv7 and the seventh order sawada kotera ito kdv equation sawada kotera ito kdv7 with forcing term

speeding up the detection of tandem repeats over the edit distance a tandem repeat in a string is a sequence of two or more contiguous approximate copies of a pattern finding an efficient deterministic algorithm to perform an exhaustive search for tandem repeats in a string is an important and practical problem due to the relevance of tandem repeats in several areas including human identity testing disease diagnosis sequence homology and population studies in this paper we present an o nklog 2k occ algorithm to find all approximate tandem repeats within a sequence of length n allowing at most k insertions deletions and mismatches in each repeat our algorithm utilizes the lempel ziv factorization which was previously used in algorithms that locate exact tandem repeats and algorithms that locate tandem repeats with only mismatches the lz framework is combined with speedups for calculating the edit distance achieving a new and efficient exhaustive search for finding tandem repeats in a string

local grayvalue invariants for image retrieval this paper addresses the problem of retrieving images from large image databases the method is based on local grayvalue invariants which are computed at automatically detected interest points a voting algorithm and semilocal constraints make retrieval possible indexing allows for efficient retrieval from a database of more than 1 000 images experimental results show correct retrieval in the case of partial visibility similarity transformations extraneous features and small perspective deformations

new exact solutions to sinh cosh gordon equation by using techniques based on projective riccati equations in this paper we present some methods for solving nonlinear partial differential equations which are based on the idea of the projective riccati equations we show how to derive well known methods such as conte s projective riccati equation method tanh coth method he s exp function method and a new method we called sn ns method we illustrate the effectiveness of the sn ns method for the problem of finding new exact solutions to the combined sinh cosh gordon equation with the aid of maple 14 and mathematica 7

a robust global and local mixture distance based non rigid point set registration we present a robust global and local mixture distance glmd based non rigid point set registration method which consists of an alternating two step process correspondence estimation and transformation updating we first define two distance features for measuring global and local structural differences between two point sets respectively the two distances are then combined to form a glmd based cost matrix which provides a flexible way to estimate correspondences by minimizing global or local structural differences using a linear assignment solution to improve the correspondence estimation and enhance the interaction between the two steps an annealing scheme is designed to gradually change the cost minimization from local to global and the thin plate spline transformation from rigid to non rigid during registration we test the performance of our method in contour registration sequence images and real images and compare with six state of the art methods where our method shows the best alignments in most scenarios highlightswe develop a multi feature based non rigid point set registration algorithm we define two distance based features a multi feature based cost matrix is designed for correspondence estimation we solve issues in the current iterative non rigid point set registration methods the performance of our method outperforms state of the art methods in this area

approximate string matching using a bidirectional index we study strategies of approximate pattern matching that exploit bidirectional text indexes extending and generalizing ideas of 9 we introduce a formalism called search schemes to specify search strategies of this type then develop a probabilistic measure for the efficiency of a search scheme prove several combinatorial results on efficient search schemes and finally provide experimental computations supporting the superiority of our strategies

lucas kanade 20 years on a unifying framework since the lucas kanade algorithm was proposed in 1981 image alignment has become one of the most widely used techniques in computer vision applications range from optical flow and tracking to layered motion mosaic construction and face coding numerous algorithms have been proposed and a wide variety of extensions have been made to the original formulation we present an overview of image alignment describing most of the algorithms and their extensions in a consistent framework we concentrate on the inverse compositional algorithm an efficient algorithm that we recently proposed we examine which of the extensions to lucas kanade can be used with the inverse compositional algorithm without any significant loss of efficiency and which cannot in this paper part 1 in a series of papers we cover the quantity approximated the warp update rule and the gradient descent approximation in future papers we will cover the choice of the error function how to allow linear appearance variation and how to impose priors on the parameters

approximating edit distance within constant factor in truly sub quadratic time edit distance is a measure of similarity of two strings based on the minimum number of character insertions deletions and substitutions required to transform one string into the other the edit d

polygonal shape recognition using string matching techniques in this paper we study several aspects of the use of string matching techniques as an approach to the problem of recognizing and classifying polygons several authors have already proposed methods for polygon recognition that are based on string matching in many cases however linear strings are used to represent polygons which makes it difficult to handle different orientations of an object efficiently we can however easily extend the linear string matching techniques to cyclic strings at some small computational cost we will propose a method to represent polygons as cyclic strings and we will show how cyclic string matching techniques can be used for rotation translation and scale independent polygonal shape recognition we will however also point out the limitations of such an approach

discrete particle swarm optimization for high order graph matching high order graph matching aims at establishing correspondences between two sets of feature points using high order constraints it is usually formulated as an np hard problem of maximizing an objective function this paper introduces a discrete particle swarm optimization algorithm for resolving high order graph matching problems which incorporates several re defined operations a problem specific initialization method based on heuristic information and a problem specific local search procedure the proposed algorithm is evaluated on both synthetic and real world datasets its outstanding performance is validated in comparison with three state of the art approaches