an efficient color representation for image retrieval a compact color descriptor and an efficient indexing method for this descriptor are presented the target application is similarity retrieval in large image databases using color colors in a given region are clustered into a small number of representative colors the feature descriptor consists of the representative colors and their percentages in the region a similarity measure similar to the quadratic color histogram distance measure is defined for this descriptor the representative colors can be indexed in the three dimensional 3 d color space thus avoiding the high dimensional indexing problems associated with the traditional color histogram for similarity retrieval each representative color in the query image or region is used independently to find regions containing that color the matches from all of the query colors are then combined to obtain the final retrievals an efficient indexing scheme for fast retrieval is presented experimental results show that this compact descriptor is effective and compares favorably with the traditional color histogram in terms of overall computational complexity

a theory of automatic parameter selection for feature extraction with application to feature based multisensor image registration this paper generalizes the previously developed automated edge detection parameter selection algorithm of yitzhaky and peli we generalize the approach to arbitrary multidimensional continuous or discrete parameter spaces and feature spaces this generalization enables use of the parameter selection approach with more general image features for use in feature based multisensor image registration applications we investigate the problem of selecting a suitable parameter space sampling density in the automated parameter selection algorithm a real valued sensitivity measure is developed which characterizes the effect of parameter space sampling on feature set variability closed form solutions of the sensitivity measure for special feature set relationships are derived we conduct an analysis of the convergence properties of the sensitivity measure as a function of increasing parameter space sampling density for certain parameter space sampling sequence types closed form expressions for the sensitivity measure limit values are presented we discuss an approach to parameter space sampling density selection which uses the sensitivity measure convergence behavior we provide numerical results indicating the utility of the sensitivity measure for selecting suitable parameter values

extraction of perceptually important colors and similarity measurement for image matching retrieval and analysis color descriptors are among the most important features used in image analysis and retrieval due to its compact representation and low complexity direct histogram comparison is a commonly used technique for measuring the color similarity however it has many serious drawbacks including a high degree of dependency on color codebook design sensitivity to quantization boundaries and inefficiency in representing images with few dominant colors in this paper we present a new algorithm for color matching that models behavior of the human visual system in capturing color appearance of an image we first develop a new method for color codebook design in the lab space the method is well suited for creating small fixed color codebooks for image analysis matching and retrieval then we introduce a statistical technique to extract perceptually relevant colors we also propose a new color distance measure that is based on the optimal mapping between two sets of color components representing two images experiments comparing the new algorithm to some existing techniques show that these novel elements lead to better match to human perception in judging image similarity in terms of color composition

clique descriptor of affine invariant regions for robust wide baseline image matching assuming that the image distortion between corresponding regions of a stereo pair of images with wide baseline can be approximated as an affine transformation if the regions are reasonably small recent image matching algorithms have focused on affine invariant region ir detection and its description to increase the robustness in matching however the distinctiveness of an intensity based region descriptor tends to deteriorate when an image includes homogeneous texture or repetitive pattern to address this problem we investigated the geometry of a local ir cluster also called a clique and propose a new clique based image matching method in the proposed method the clique of an ir is estimated by delaunay triangulation in a local affine frame and the hausdorff distance is adopted for matching an inexact number of multiple descriptor vectors we also introduce two adaptively weighted clique distances where the neighbour distance in a clique is appropriately weighted according to characteristics of the local feature distribution experimental results show the clique based matching method produces more tentative correspondences than variants of the sift based method

comparing images using the hausdorff distance the hausdorff distance measures the extent to which each point of a model set lies near some point of an image set and vice versa thus this distance can be used to determine the degree of resemblance between two objects that are superimposed on one another efficient algorithms for computing the hausdorff distance between all possible relative positions of a binary image and a model are presented the focus is primarily on the case in which the model is only allowed to translate with respect to the image the techniques are extended to rigid motion the hausdorff distance computation differs from many other shape comparison methods in that no correspondence between the model and the image is derived the method is quite tolerant of small position errors such as those that occur with edge detectors and other feature extraction methods it is shown that the method extends naturally to the problem of comparing a portion of a model against an image

a representation for shape based on peaks and ridges in the difference of low pass transform this paper defines a multiple resolution representation for the two dimensional gray scale shapes in an image this representation is constructed by detecting peaks and ridges in the difference of lowpass dolp transform descriptions of shapes which are encoded in this representation may be matched efficiently despite changes in size orientation or position motivations for a multiple resolution representation are presented first followed by the definition of the dolp transform techniques are then presented for encoding a symbolic structural description of forms from the dolp transform this process involves detecting local peaks and ridges in each bandpass image and in the entire three dimensional space defined by the dolp transform linking adjacent peaks in different bandpass images gives a multiple resolution tree which describes shape peaks which are local maxima in this tree provide landmarks for aligning manipulating and matching shapes detecting and linking the ridges in each dolp bandpass image provides a graph which links peaks within a shape in a bandpass image and describes the positions of the boundaries of the shape at multiple resolutions detecting and linking the ridges in the dolp three space describes elongated forms and links the largest peaks in the tree the principles for determining the correspondence between symbols in pairs of such descriptions are then described such correspondence matching is shown to be simplified by using the correspondence at lower resolutions to constrain the possible correspondence at higher resolutions

variational regularized 2 d nonnegative matrix factorization a novel approach for adaptive regularization of 2 d nonnegative matrix factorization is presented the proposed matrix factorization is developed under the framework of maximum a posteriori probability and is adaptively fine tuned using the variational approach the method enables 1 a generalized criterion for variable sparseness to be imposed onto the solution and 2 prior information to be explicitly incorporated into the basis features the method is computationally efficient and has been demonstrated on two applications that is extracting features from image and separating single channel source mixture in addition it is shown that the basis features of an information bearing matrix can be extracted more efficiently using the proposed regularized priors experimental tests have been rigorously conducted to verify the efficacy of the proposed method

on the compatibility of lorentz metrics with linear connections on four dimensional manifolds this paper considers four dimensional manifolds upon which there is a lorentz metric h and a symmetric connection which are originally assumed unrelated it then derives sufficient conditions on h and expressed through the curvature tensor of for to be the levi civita connection of some local lorentz metric g and calculates the relationship between g and h some examples are provided which help to assess the strength of the sufficient conditions derived

bifurcations in a delayed fractional complex valued neural network complex valued neural networks cvnns with integer order have attracted much attention and which have been well discussed fractional complex valued neural networks fcvnns are more suitable to describe the dynamical properties of neural networks but have rarely been studied it is the first time that the stability and bifurcation of a class of delayed fcvnn is investigated in this paper the activation function can be expressed by separating into its real and imaginary parts by using time delay as the bifurcation parameter the dynamical behaviors that including local asymptotical stability and hopf bifurcation are discussed the conditions of emergence of bifurcation are obtained furthermore it reveals that the onset of the bifurcation point can be delayed as the order increases finally an illustrative example is provided to verify the correctness of the obtained theoretical results

the earth mover s distance as a metric for image retrieval we investigate the properties of a metric between two distributions the earth mover s distance emd for content based image retrieval the emd is based on the minimal cost that must be paid to transform one distribution into the other in a precise sense and was first proposed for certain vision problems by peleg werman and rom for image retrieval we combine this idea with a representation scheme for distributions that is based on vector quantization this combination leads to an image comparison framework that often accounts for perceptual similarity better than other previously proposed methods the emd is based on a solution to the transportation problem from linear optimization for which efficient algorithms are available and also allows naturally for partial matching it is more robust than histogram matching techniques in that it can operate on variable length representations of the distributions that avoid quantization and other binning problems typical of histograms when used to compare distributions with the same overall mass the emd is a true metric in this paper we focus on applications to color and texture and we compare the retrieval performance of the emd with that of other distances

signatures versus histograms definitions distances and algorithms the aim of this paper is to present a new method to compare histograms the main advantage is that there is an important time complexity reduction with respect to the methods presented before this reduction is statistically and analytically demonstrated in the paper the distances between histograms that we presented are defined on a structure called signature which is a lossless representation of histograms moreover the type of the elements of the sets that the histograms represent are ordinal nominal and modulo we show that the computational cost of these distances is o z for the ordinal and nominal types and o z 2 for the modulo one z being the number of non empty bins of the histograms the computational cost of the algorithms presented in the literature depends on the number of bins of the histograms in most of the applications the obtained histograms are sparse then considering only the non empty bins drastically decreases the time consumption of the comparison the distances and algorithms presented in this paper are experimentally validated on the comparison of images obtained from public databases and positioning of mobile robots through the recognition of indoor scenes captured in a learning stage

affine collineations in space time the existence of affine collineations in space time is discussed and the types of space time admitting proper affine collineations is displayed the close connection between such space times and their holonomy structure and local decomposability is established affine collineations with fixed points are also considered as is the problem of extending local affine collineations to the whole of space time

covariantly constant tensors and holonomy structure in general relativity this paper attempts to give a comprehensive discussion of space times that admit vector fields or second order symmetric or skew symmetric tensor fields which are covariantly constant or recurrent the relationship between such space times m and their holonomy group is given

purely magnetic space times purely magnetic space times in which the riemann tensor satisfies rabcdubud 0 for some unit timelike vector ua are studied the algebraic consequences for the weyl and ricci tensors are examined in detail and consideration given to the uniqueness of ua some remarks concerning the nature of the congruence associated with ua are made

bin ratio based histogram distances and their application to image classification large variations in image background may cause partial matching and normalization problems for histogram based representations i e the histograms of the same category may have bins which are significantly different and normalization may produce large changes in the differences between corresponding bins in this paper we deal with this problem by using the ratios between bin values of histograms rather than bin values differences which are used in the traditional histogram distances we propose a bin ratio based histogram distance brd which is an intra cross bin distance in contrast with previous bin to bin distances and cross bin distances the brd is robust to partial matching and histogram normalization and captures correlations between bins with only a linear computational complexity we combine the brd with the l 1 histogram distance and the chi 2 histogram distance to generate the l 1 brd and the chi 2 brd respectively these combinations exploit and benefit from the robustness of the brd under partial matching and the robustness of the l 1 and chi 2 distances to small noise we propose a method for assessing the robustness of histogram distances to partial matching the brds and logistic regression based histogram fusion are applied to image classification the experimental results on synthetic data sets show the robustness of the brds to partial matching and the experiments on seven benchmark data sets demonstrate promising results of the brds for image classification

a quadratically constrained map classifier using the mixture of gaussians models as a weight function in this paper we propose classifiers derived from quadratically constrained maximum a posteriori qcmap estimation the qcmap consists of the maximization of the expectation of a cost function which is derived from the maximum a posteriori probability and a quadratic constraint this criterion is highly general since its forms include least squares regressions and a support vector machine furthermore the criterion provides a novel classifier the gaussian qcmap the qcmap procedure still has large theoretical interest and its full extensibility has yet to be explored in this paper we propose using the mixture of gaussian distributions as the qcmap weight function the mixture of gaussian distributions has wide ranging applicability and encompasses forms such as a normal distribution model and a kernel density model we propose four types of mixture of gaussian functions for qcmap classifiers and conduct experiments to demonstrate their advantages

fast computation of separable two dimensional discrete invariant moments for image classification in this paper we present a new set of bivariate discrete orthogonal polynomials based on the product of meixner s discrete orthogonal polynomials by tchebichef s krawtchouk s and hahn s discrete orthogonal polynomials this set of bivariate discrete orthogonal polynomials is used to define three new types of discrete orthogonal moments as meixner tchebichef moments meixner krawtchouk moments and meixner hahn moments we also present an approach to accelerate the computation of these moments by using the image block representation for binary images and image slice representation for gray scale images a novel set of meixner tchebichef invariant moments meixner krawtchouk invariant moments and meixner hahn invariant moments is also derived these invariant moments are derived algebraically from the geometric invariant moments and their computation is accelerated using an image representation scheme the proposed algorithms are tested using several well known computer vision datasets including moment s invariability and pattern recognition the performance of these invariant moments used as pattern features for a pattern classification is compared with the shape descriptors of hu legendre tchebichef krawtchouk krawtchouk hahn and tchebichef hahn invariant moments the texture descriptors and the color descriptors for four different databases new set of bivariate discrete orthogonal polynomials separable two dimensional discrete invariant moments improving the performance of image classification acceleration of computational time of discrete orthogonal invariant moments

blobworld image segmentation using expectation maximization and its application to image querying retrieving images from large and varied collections using image content as a key is a challenging and important problem we present a new image representation that provides a transformation from the raw pixel data to a small set of image regions that are coherent in color and texture this blobworld representation is created by clustering pixels in a joint color texture position feature space the segmentation algorithm is fully automatic and has been run on a collection of 10 000 natural images we describe a system that uses the blobworld representation to retrieve images from this collection an important aspect of the system is that the user is allowed to view the internal representation of the submitted image and the query results similar systems do not offer the user this view into the workings of the system consequently query results from these systems can be inexplicable despite the availability of knobs for adjusting the similarity metrics by finding image regions that roughly correspond to objects we allow querying at the level of objects rather than global image properties we present results indicating that querying for images using blobworld produces higher precision than does querying using color and texture histograms of the entire image in cases where the image contains distinctive objects

histograms analysis for image retrieval abstract this paper analyzes the use of histograms of low level image features such as color and luminance as descriptors for image retrieval purposes a novel definition of histogram capacity curve taking into account the density distribution of histograms in the corresponding spaces is proposed and used to quantify the effectiveness of image descriptors and histogram dissimilarities in image retrieval applications the results permit the design of scalable image retrieval systems which make optimal use of computational and storage resources

toward improved ranking metrics in many computer vision algorithms a metric or similarity measure is used to determine the distance between two features the euclidean or ssd sum of the squared differences metric is prevalent and justified from a maximum likelihood perspective when the additive noise distribution is gaussian based on real noise distributions measured from international test sets we have found that the gaussian noise distribution assumption is often invalid this implies that other metrics which have distributions closer to the real noise distribution should be used in this paper we consider three different applications content based retrieval in image databases stereo matching and motion tracking in each of them we experiment with different modeling functions for the noise distribution and compute the accuracy of the methods using the corresponding distance measures in our experiments we compared the ssd metric the sad sum of the absolute differences metric the cauchy metric and the kullback relative information for several algorithms from the research literature which used the ssd or sad we showed that greater accuracy could be obtained by using the cauchy metric instead

the holonomy lie algebras of neutral metrics in dimension four the lie algebra isomorphism between su 1 1 su 1 1 and o 2 2 is used to obtain a list of subalgebras of the latter the resulting list of 32 subalgebras is then examined on a case by case basis to see if each can be the lie algebra of the holonomy group of a neutral metric in four dimensions the conclusions taken in conjunction with previously known results furnish a classification of such lie subalgebras of o 2 2 with only one case remaining unresolved

an efficiently computable metric for comparing polygonal shapes a method for comparing polygons that is a metric invariant under translation rotation and change of scale reasonably easy to compute and intuitive is presented the method is based on the l sub 2 distance between the turning functions of the two polygons it works for both convex and nonconvex polygons and runs in time o mn log mn where m is the number of vertices in one polygon and n is the number of vertices in the other some examples showing that the method produces answers that are intuitively reasonable are presented

the hausdorff fuzzy quasi metric removing the condition of symmetry in the notion of a fuzzy pseudo metric in kramosil and michalek s sense one has the notion of a fuzzy quasi pseudo metric then for each fuzzy quasi pseudo metric on a set x we construct a fuzzy quasi pseudo metric on the collection of all nonempty subsets of x called the hausdorff fuzzy quasi pseudo metric we investigate several properties of this structure and present several illustrative examples as well as an application to the domain of words the notion of hausdorff fuzzy quasi pseudo metric when quasi pseudo metric fuzziness is considered in the sense of george and veeramani is also discussed

an efficient earth mover s distance algorithm for robust histogram comparison we propose emd l1 a fast and exact algorithm for computing the earth mover s distance emd between a pair of histograms the efficiency of the new algorithm enables its application to problems that were previously prohibitive due to high time complexities the proposed emd l1 significantly simplifies the original linear programming formulation of emd exploiting the l1 metric structure the number of unknown variables in emd l1 is reduced to o n from o n2 of the original emd for a histogram with n bins in addition the number of constraints is reduced by half and the objective function of the linear program is simplified formally without any approximation we prove that the emd l1 formulation is equivalent to the original emd with a l1 ground distance to perform the emd l1 computation we propose an efficient tree based algorithm tree emd tree emd exploits the fact that a basic feasible solution of the simplex algorithm based solver forms a spanning tree when we interpret emd l1 as a network flow optimization problem we empirically show that this new algorithm has an average time complexity of o n2 which significantly improves the best reported supercubic complexity of the original emd the accuracy of the proposed methods is evaluated by experiments for two computation intensive problems shape recognition and interest point matching using multidimensional histogram based local features for shape recognition emd l1 is applied to compare shape contexts on the widely tested mpeg7 shape data set as well as an articulated shape data set for interest point matching sift shape context and spin image are tested on both synthetic and real image pairs with large geometrical deformation illumination change and heavy intensity noise the results demonstrate that our emd l1 based solutions outperform previously reported state of the art features and distance measures in solving the two tasks

applications of second order cone programming in a second order cone program socp a linear function is minimized over the intersection of an affine set and the product of second order quadratic cones socps are nonlinear convex problems that include linear and convex quadratic programs as special cases but are less general than semidefinite programs sdps several efficient primaldual interior point methods for socp have been developed in the last few years after reviewing the basic theory of socps we describe general families of problems that tan be recast as socps these include robust linear programming and robust leastsquares problems problems involving sums or maxima of norms or with convex hyperbolic constraints we discuss a variety of engineering applications such as filter design antenna array weight design truss design and grasping forte optimization in robotics we describe an efficient primaldual interior point method for solving socps which shares many of the features of primaldual interior point methods for linear program

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

retrieval of images of man made structures based on projective invariance in this paper we propose a geometry based image retrieval scheme that makes use of projectively invariant features cross ratio cr is an invariant feature under projective transformations for collinear points we compute the crs of point sets in quadruplets and the cr histogram is used as the feature for retrieval purposes being a geometric feature it allows us to retrieve similar images irrespective of view point and illumination changes we can retrieve the same building even if the facade has undergone a fresh coat of paints color and textural features can also be included if desired experimental results show a favorably very good retrieval accuracy when tested on an image database of size 4000 the method is very effective in retrieving images having man made objects rich in polygonal structures like buildings rail tracks etc

color image segmentation an innovative approach in this paper we describe a color image segmentation system that performs color clustering in a color space and then color region segmentation in the image domain for color segmentation we developed a fuzzy clustering algorithm that iteratively generates color clusters using a uniquely defined fuzzy membership function and an objective function for clustering optimization the fuzzy membership function represents belief value of a color belonging to a color cluster and the mutual interference of neighboring clusters the region segmentation algorithm merges clusters in the image domain based on color similarity and spatial adjacency we developed three different methods for merging regions in the image domain unlike many existing clustering algorithms the image segmentation system does not require the knowledge about the number of the color clusters to be generated at each stage and the resolution of the color regions can be controlled by one single parameter the radius of a cluster the color image segmentation system has been implemented and tested on a variety of color images including satellite images car and face images the experiment results are presented and the performance of each algorithm in the segmentation system is analyzed the system has shown to be both effective and efficient

fuzzy colour category map for the measurement of colour similarity and dissimilarity a new colour space for representing colour based upon psychophysical research into human perception is presented it provides both the ability to measure similarity and determine dissimilarity using the combination of fuzzy logic and psychologically based set theoretic similarity measurement these abilities are shown to enable it to be equal or superior to conventional colour spaces in measuring the similarity and dissimilarity of colours in addition to being able to saliently label colours for accurate chromatic linguistic description

holonomy groups in general relativity the infinitesimal holonomy group structure of space time is discussed and related to the petrov type of the weyl tensor and the algebraic segre type of the energy momentum tensor the number of covariant derivatives of the curvature tensor required to determine the infinitesimal holonomy group is determined in each case and the complete classification scheme is tabulated some special cases of physical interest are investigated in more detail a geometrical approach is followed throughout

curvature structure in general relativity this paper investigates the extent to which the curvature structure of space time determines the metric stucture it continues the work of earlier papers by prescribing the curvature structure and the curvature covariant derivatives up to certain orders it is shown that with the exception of the so called generalized pp waves the curvature and its first and second covariant derivatives essentially determine the metric up to coordinate transformations

unsupervised learning of categorical data with competing models this paper considers the unsupervised learning of high dimensional binary feature vectors representing categorical information a cognitively inspired framework referred to as modeling fields theory mft is utilized as the basic methodology a new mft based algorithm referred to as accelerated maximum a posteriori map is proposed accelerated map allows simultaneous learning and selection of the number of models the key feature of accelerated map is a steady increase of the regularization penalty resulting in competition among models the differences between this approach and other mixture learning and model selection methodologies are described the operation of this algorithm and its parameter selection are discussed numerical experiments aimed at finding performance limits are conducted the performance with real world data is tested by applying the algorithm to a text categorization problem and to the clustering congressional voting data

the submatrices character count problem an efficient solution using separable values the subsequence character count problem has as its input an array s s 1 s n of symbols over alphabet and a natural number m its output is for every i i 1 n m 1 the number of different alphabet symbols occurring in the subsequence s i s i 1 s i m 1 the subsequence character count problem is a natural problem that has many uses it can be solved in linear time for finite alphabets and in time o n log m for infinite alphabets when the character count problem is generalized to two dimensions it becomes the submatrix character count problem its input is an n n matrix t over alphabet and a natural number m its output is for every i j i j 1 n m 1 the number of different alphabet symbols occurring in the submatrix t i k j l k 0 m 1 l 0 m 1 the straightforward one dimensional solution slides a window along the text adding an element and deleting an element at every step the problem with two dimensions is that at every move of the window there are m elements added and m deleted in this paper we present an alternate one dimensional solution that generalizes to two dimensions we achieve a o n2 time solution to the submatrix character count problem over a finite alphabet and a o n2 log m solution over an infinite alphabet

recognition without correspondence using multidimensionalreceptive field histograms the appearance of an object is composed of local structure this local structure can be described and characterized by a vector of local features measured by local operators such as gaussian derivatives or gabor filters this article presents a technique where appearances of objects are represented by the joint statistics of such local neighborhood operators as such this represents a new class of appearance based techniques for computer vision based on joint statistics the paper develops techniques for the identification of multiple objects at arbitrary positions and orientations in a cluttered scene experiments show that these techniques can identify over 100 objects in the presence of major occlusions most remarkably the techniques have low complexity and therefore run in real time

properties of embedding methods for similarity searching in metric spaces complex data types such as images documents dna sequences etc are becoming increasingly important in modern database applications a typical query in many of these applications seeks to find objects that are similar to some target object where dis similarity is defined by some distance function often the cost of evaluating the distance between two objects is very high thus the number of distance evaluations should be kept at a minimum while ideally maintaining the quality of the result one way to approach this goal is to embed the data objects in a vector space so that the distances of the embedded objects approximates the actual distances thus queries can be performed for the most part on the embedded objects we are especially interested in examining the issue of whether or not the embedding methods will ensure that no relevant objects are left out particular attention is paid to the sparsemap fastmap and metricmap embedding methods sparsemap is a variant of lipschitz embeddings while fastmap and metricmap are inspired by dimension reduction methods for euclidean spaces we show that in general none of these embedding methods guarantee that queries on the embedded objects have no false dismissals while also demonstrating the limited cases in which the guarantee does hold moreover we describe a variant of sparsemap that allows queries with no false dismissals in addition we show that with fastmap and metricmap the distances of the embedded objects can be much greater than the actual distances this makes it impossible or at least impractical to modify fastmap and metricmap to guarantee no false dismissals

on the efficient evaluation of probabilistic similarity functions for image retrieval probabilistic approaches are a promising solution to the image retrieval problem that when compared to standard retrieval methods can lead to a significant gain in retrieval accuracy however this occurs at the cost of a significant increase in computational complexity in fact closed form solutions for probabilistic retrieval are currently available only for simple probabilistic models such as the gaussian or the histogram we analyze the case of mixture densities and exploit the asymptotic equivalence between likelihood and kullback leibler kl divergence to derive solutions for these models in particular 1 we show that the divergence can be computed exactly for vector quantizers vqs and 2 has an approximate solution for gauss mixtures gms that in high dimensional feature spaces introduces no significant degradation of the resulting similarity judgments in both cases the new solutions have closed form and computational complexity equivalent to that of standard retrieval approaches

invariant feature extraction for 3d model retrieval an adaptive approach using euclidean and topological metrics with the fast development of 3d model construction and widespread popularity of 3d graphic engines more applications employ 3d geometric models to provide an interactive environment as the number of 3d models increases some 3d model retrieval systems have been proposed for indexing and matching these models an important issue in a retrieval system is feature extraction an efficient and invariant feature is a global shape distribution that collects some geometric properties of a model the d2 shape descriptor by osada et al is a one dimensional histogram of euclidean distances between two random points although the d2 is effective for some cases it changes when the model deforms we propose two shape descriptors in this paper gd which is the topological metric and asf which combines both euclidean and topological metrics the topological metric is an invariant deformation factor the two features are also robust against common geometric processing including scaling rotation resampling compression and remeshing in experiments we implement these methods and confirm their feasibility

fuzzy clustering and aggregation of relational data with instance level constraints in this paper we introduce a semisupervised approach for clustering and aggregating relational data ss card we assume that data is available in a relational form where information only about the degrees to which pairs of objects in the dataset are related is available moreover we assume that the relational information is represented by multiple dissimilarity matrices these matrices could have been generated using different features different mappings or even different sensors ss card is designed to aggregate pairwise distances from multiple relational matrices partition the data into clusters and learn a relevance weight for each matrix in each cluster simultaneously these weights have two main advantages first they help in partitioning the data into more meaningful clusters second they can be used as part of a more complex learning system to enhance its learning behavior ss card uses partial supervision information that consists of a small set of constraints on which instances should link or should not link reside in the same cluster this additional information can guide the algorithm in learning the optimal relevance weights and in generating a better partition the performance of the proposed algorithm is illustrated by using it in two different applications the first one consists of categorizing the discrete nominal valued mushroom data the second application consists of categorizing a collection of images where each image is represented by several continuous features for both applications we represent the pairwise image dissimilarities by multiple relational matrices extracted from different feature sets the results are compared with those obtained by three traditional relational clustering methods we show that the partial supervision information and the learned aggregation weights can improve the results significantly

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

focal colors across languages are representative members of color categories focal colors or best examples of color terms have traditionally been viewed as either the underlying source of cross language color naming universals or derived from category boundaries that vary widely across languages existing data partially support and partially challenge each of these views here we advance a position that synthesizes aspects of these two traditionally opposed positions and accounts for existing data we do so by linking this debate to more general principles we show that best examples of named color categories across 112 languages are well predicted from category extensions by a statistical model of how representative a sample is of a distribution independently shown to account for patterns of human inference this model accounts for both universal tendencies and variation in focal colors across languages we conclude that categorization in the contested semantic domain of color may be governed by principles that apply more broadly in cognition and that these principles clarify the interplay of universal and language specific forces in color naming

curvature collineations in general relativity ii this paper is the second of a set of two papers on curvature collineations in general relativity the first paper presented the mathematical basis of curvature collineations and a possible approach to their study this paper continues from the first one by investigating in detail many of the cases where curvature collineations can occur in space time it is based on a classification of the curvature tensor which is discussed in the first paper and reviewed briefly here this together with the geometrical approach favored in this paper leads to a rather general discussion of the problem which it is hoped does not obscure those physical aspects of the situation that are important in einstein s theory

geometric algorithms to large margin classifier based on affine hulls the geometric framework for binary data classification problems provides an intuitive foundation for the comprehension and application of geometric optimization algorithms leading to practical solutions of real world classification problems in this paper some theoretical results on the candidate extreme points of the notion of reduced affine hull rah are introduced these results allow the existing nearest point algorithms to be directly applied to solve both separable and inseparable classification problems based on rahs successfully and efficiently as the practical applications of the new theoretical results the popular gilbert schlesinger kozinec and mitchell dem yanov malozemov algorithms are presented to solve binary classification problems in the context of the rah framework the theoretical analysis and some experiments show that the proposed methods successfully achieve significant performance

an introduction to kernel based learning algorithms this paper provides an introduction to support vector machines kernel fisher discriminant analysis and kernel principal component analysis as examples for successful kernel based learning methods we first give a short background about vapnik chervonenkis theory and kernel feature spaces and then proceed to kernel based learning in supervised and unsupervised scenarios including practical and algorithmic considerations we illustrate the usefulness of kernel algorithms by discussing applications such as optical character recognition and dna analysis

robust shape tracking with multiple models in ultrasound images this paper addresses object tracking in ultrasound images using a robust multiple model tracker the proposed tracker has the following features 1 it uses multiple dynamic models to track the evolution of the object boundary and 2 it models invalid observations outliers reducing their influence on the shape estimates the problem considered in this paper is the tracking of the left ventricle which is known to be a challenging problem the heart motion presents two phases diastole and systole with different dynamics the multiple models used in this tracker try to solve this difficulty in addition ultrasound images are corrupted by strong multiplicative noise which prevents the use of standard deformable models robust estimation techniques are used to address this difficulty the multiple model data association mmda tracker proposed in this paper is based on a bank of nonlinear filters organized in a tree structure the algorithm determines which model is active at each instant of time and updates its state by propagating the probability distribution using robust estimation techniques

clustering and aggregation of relational data with applications to image database categorization in this paper we introduce a new algorithm for clustering and aggregating relational data card we assume that data is available in a relational form where we only have information about the degrees to which pairs of objects in the data set are related moreover we assume that the relational information is represented by multiple dissimilarity matrices these matrices could have been generated using different sensors features or mappings card is designed to aggregate pairwise distances from multiple relational matrices partition the data into clusters and learn a relevance weight for each matrix in each cluster simultaneously the cluster dependent relevance weights offer two advantages first they guide the clustering process to partition the data set into more meaningful clusters second they can be used in subsequent steps of a learning system to improve its learning behavior the performance of the proposed algorithm is illustrated by using it to categorize a collection of 500 color images we represent the pairwise image dissimilarities by six different relational matrices that encode color texture and structure information

fuzzy color histogram and its use in color image retrieval a conventional color histogram cch considers neither the color similarity across different bins nor the color dissimilarity in the same bin therefore it is sensitive to noisy interference such as illumination changes and quantization errors furthermore cchs large dimension or histogram bins requires large computation on histogram comparison to address these concerns this paper presents a new color histogram representation called fuzzy color histogram fch by considering the color similarity of each pixel s color associated to all the histogram bins through fuzzy set membership function a novel and fast approach for computing the membership values based on fuzzy c means algorithm is introduced the proposed fch is further exploited in the application of image indexing and retrieval experimental results clearly show that fch yields better retrieval results than cch such computing methodology is fairly desirable for image retrieval over large image databases

mean shift trackers with cross bin metrics cross bin metrics have been shown to be more suitable than bin by bin metrics for measuring the distance between histograms in various applications in particular a visual tracker that minimizes the earth mover s distance emd between the candidate and reference feature histograms has recently been proposed this tracker was shown to be more robust than the mean shift tracker which employs a bin by bin metric in each frame the former tracker iteratively shifts the candidate location by one pixel in the direction opposite to the emd s gradient until no improvement is made this optimization process involves the clustering of the candidate feature density in feature space as well as the computation of the emd between the candidate and reference feature histograms after each shift of the candidate location in this paper alternative trackers that employ cross bin metrics as well but that are based on mean shift ms iterations are derived the proposed trackers are simpler and faster due to 1 the use of ms based optimization which is not restricted to single pixel shifts 2 abstention from any clustering of feature densities and 3 abstention from emd computations in multidimensional spaces

focused color intersection with efficient searching for object extraction we propose focused color intersection with efficient searching for identifying and extracting the objects in a complex scene based on color similarity the method matches the models against different parts of a scene called focus regions using normalized color histogram intersection the best matching focus region is determined by an efficient search strategy employing upper bound pruning this search strategy called active search concentrates its effort on parts of the scene having high similarity with the object consequently it achieves a large reduction in computational effort without sacrificing accuracy an efficient algorithm for evaluating the color histogram intersection between a model and a focus region is also given experiments conducted demonstrate that multiple known objects in complex scenes can be extracted by this process the method is stable against scale changes two dimensional rotation moderate changes in shape and partial occlusion

efficient color histogram indexing for quadratic form distance functions in image retrieval based on color the weighted distance between color histograms of two images represented as a quadratic form may be defined as a match measure however this distance measure is computationally expensive and it operates on high dimensional features o n we propose the use of low dimensional simple to compute distance measures between the color distributions and show that these are lower bounds on the histogram distance measure results on color histogram matching in large image databases show that prefiltering with the simpler distance measures leads to significantly less time complexity because the quadratic histogram distance is now computed on a smaller set of images the low dimensional distance measure can also be used for indexing into the database