image annotation via graph learning image annotation has been an active research topic in recent years due to its potential impact on both image understanding and web image search in this paper we propose a graph learning framework for image annotation first the image based graph learning is performed to obtain the candidate annotations for each image in order to capture the complex distribution of image data we propose a nearest spanning chain nsc method to construct the image based graph whose edge weights are derived from the chain wise statistical information instead of the traditional pairwise similarities second the word based graph learning is developed to refine the relationships between images and words to get final annotations for each image to enrich the representation of the word based graph we design two types of word correlations based on web search results besides the word co occurrence in the training set the effectiveness of the proposed solution is demonstrated from the experiments on the corel dataset and a web image dataset

spatial reasoning and similarity retrieval of images using 2d c string knowledge representation abstract the data structure called 2d string to represent symbolic pictures was proposed by chang et al it allows a natural way to construct iconic indexes for pictures a new spatial knowledge representation of a 2d c string with accompanying cutting mechanism and a set of spatial operators are proposed 2d c string is more characteristic of spatial knowledge in images and is more efficient in representation and manipulation of images since a spatial relationship is a fuzzy concept the capability of similarity retrieval is essential in image database systems the spatial query and spatial reasoning based on a 2d c string representation are presented the similarity measure is defined and the algorithm for similarity retrieval of iconic images is also proposed

periodicity directionality and randomness wold features for image modeling and retrieval one of the fundamental challenges in pattern recognition is choosing a set of features appropriate to a class of problems in applications such as database retrieval it is important that image features used in pattern comparison provide good measures of image perceptual similarities we present an image model with a new set of features that address the challenge of perceptual similarity the model is based on the 2d wold decomposition of homogeneous random fields the three resulting mutually orthogonal subfields have perceptual properties which can be described as periodicity directionality and randomness approximating what are indicated to be the three most important dimensions of human texture perception the method presented improves upon earlier wold based models in its tolerance to a variety of local inhomogeneities which arise in natural textures and its invariance under image transformation such as rotation an image retrieval algorithm based on the new texture model is presented different types of image features are aggregated for similarity comparison by using a bayesian probabilistic approach the effectiveness of the wold model at retrieving perceptually similar natural textures is demonstrated in comparison to that of two other well known pattern recognition methods the wold model appears to offer a perceptually more satisfying measure of pattern similarity while exceeding the performance of these other methods by traditional pattern recognition criteria examples of natural scene wold texture modeling are also presented

generalizations of the quaternion algebra and lie algebras natural generalizations of the quaternion algebra called quaternionlike algebras ql algebras are considered the notion of a lie algebra induced by a ql algebra is introduced and a classification of such lie algebras is presented it is shown that local lie groups defined by lie algebras induced by ql algebras exhaust with accuracy to local isomorphisms all local lie groups endowed with some simple composition laws of their local parameters

robust rotation invariant texture classification using a model based approach in this paper a model based texture classification procedure is presented the texture is modeled as the output of a linear system driven by a binary image this latter retains the morphological characteristics of the texture and it is specified by its spatial autocorrelation function acf we show that features extracted from the acf of the binary excitation suffice to represent the texture for classification purposes specifically we employ a moment invariants based technique to classify the acf the resulting proposed classification procedure is thus inherently rotation invariant moreover it is robust with respect to additive noise experimental results show that this approach allows obtaining high correct rotation invariant classification rates while containing the size of the feature space

reduced complexity rotation invariant texture classification using a blind deconvolution approach in this paper we present a texture classification procedure that makes use of a blind deconvolution approach specifically the texture is modeled as the output of a linear system driven by a binary excitation we show that features computed from one dimensional slices extracted from the two dimensional autocorrelation function acf of the binary excitation allows representing the texture for rotation invariant classification purposes the two dimensional classification problem is thus reconduced to a more simple one dimensional one which leads to a significant reduction of the classification procedure computational complexity

equivalence of julesz ensembles and frame models in the past thirty years research on textures has been pursued along two different lines the first line of research pioneered by julesz 1962 ire transactions of information theory it 8 84 92 seeks essential ingredients in terms of features and statistics in human texture perception this leads us to a mathematical definition of textures in terms of julesz ensembles zhu et al ieee trans on pami vol 22 no 6 2000 a julesz ensemble is a set of images that share the same value of some basic feature statistics images in the julesz ensemble are defined on a large image lattice a mathematical idealization being z2 so that exact constraint on feature statistics makes sense the second line of research studies markov random field mrf models that characterize texture patterns on finite or small image lattice in a statistical way this leads us to a general class of mrf models called frame filter random field and maximum entropy zhu et al neural computation 9 1627 1660 in this article we bridge the two lines of research by the fundamental principle of equivalence of ensembles in statistical mechanics gibbs 1902 elementary principles of statistical mechanics yale university press we show that 1 as the size of the image lattice goes to infinity a frame model concentrates its probability mass uniformly on a corresponding julesz ensemble therefore the julesz ensemble characterizes the global statistical property of the frame models 2 for a large image randomly sampled from a julesz ensemble any local patch of the image given its environment follows the conditional distribution specified by a corresponding frame model therefore the frame model describes the local statistical property of the julesz ensemble and is an inevitable texture model on finite or small lattice if texture perception is decided by feature statistics the key to derive these results is the large deviation estimate of the volume of or the number of images in the julesz ensemble which we call the entropy function studying the equivalence of ensembles provides deep insights into questions such as the origin of mrf models typical images of statistical models and error rates in various texture related vision tasks yuille and coughlan ieee trans on pami vol 2 no 2 2000 the second thrust of this paper is to study texture distance based on the texture models of both small and large lattice systems we attempt to explain the asymmetry phenomenon observed in texture pop out experiments by the asymmetry of kullback leibler divergence our results generalize the traditional signal detection theory green and swets 1988 signal detection theory and psychophysics peninsula publishing for distance measures from iid cases to random fields our theories are verified by two groups of computer simulation experiments

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

structure of spin groups associated with degenerate clifford algebras clifford algebras over finite dimensional vector spaces endowed with degenerate quadratic form contain a nontrivial two sided nilpotent ideal the jacobson radical generated by the orthogonal complement of such spaces thus they cannot be faithfully represented by matrix algebras following the theory of spin representations of classical clifford algebras the left regular spin representations of these degenerate algebras can be studied in suitably constructed left ideals first structure of the group of units of such algebras is examined for a quadratic form of arbitrary rank it is shown to be a semidirect product of a group generated by the radical and the group of units of a maximal nondegenerate clifford subalgebra next in the special case of corank 1 clifford pin and spin groups are defined an their structures are described as an example a galilei clifford algebra over the galilei space time is considered a covering theorem is then proved analogous to the one well known in the theory of

comparison of texture analysis schemes under nonideal conditions several recent advancements in the field of texture analysis prompt some fundamental questions for instance what is the true impact of these novel advancements under real world environments when do these novel advancements fail to perform which methods perform better and under what conditions in this work we investigate these and other issues under nonideal image acquisition environments specifically environments with changing conditions due to illumination variations and those caused by both affine and nonaffine transformations we study the performance of nine popular texture analysis algorithms using three different datasets with varying levels of difficulty experiments are performed on nonideal texture datasets under five different setups we find that most state of the art techniques do not perform well under these conditions to a large extent their performance under nonideal conditions depends critically on the nature of the textural surface moreover most techniques fail to perform reliably when the number of classes in the dataset is increased significantly over the regular size datasets used in previous work multiscale features performed reasonably well against variations caused by illumination and rotation but are prone to fail under changes in scale surprisingly the performance for most of the algorithms is generally stable on structured or periodic textures even with variations in illumination or affine transformations

notes on a cross product of vectors the relation between quaternionlike algebras and cross products of vectors is demonstrated a classification of all cross products of vectors is given

reduced complexity modeling and reproduction of colored textures an unsupervised color texture synthesis by analysis method is described the texture is reproduced to appear perceptually similar to a given prototype by copying its statistical properties up to the second order the synthesized texture is obtained at the output of a single input three output nonlinear system driven by a realization of a white gaussian random field significant complexity reduction is gained by exploiting the rank deficiency of the cross power spectral density matrix of the color texture samples

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

a no reference texture regularity metric based on visual saliency this paper presents a no reference perceptual metric that quantifies the degree of perceived regularity in textures the metric is based on the similarity of visual attention va of the textural primitives and the periodic spatial distribution of foveated fixation regions throughout the image a ground truth eye tracking database for textures is also generated as part of this paper and is used to evaluate the performance of the most popular va models using the saliency map generated by the best va model the proposed texture regularity metric is computed it is shown through subjective testing that the proposed metric has a strong correlation with the mean opinion score for the perceived regularity of textures the proposed texture regularity metric can be used to improve the quality and performance of many image processing applications like texture synthesis texture compression and content based image retrieval

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

maximum likelihood parameter estimation of textures using a wold decomposition based model we present a solution to the problem of modeling parameter estimation and synthesis of natural textures the texture field is assumed to be a realization of a regular homogeneous random field which can have a mixed spectral distribution on the basis of a 2 d wold like decomposition the field is represented as a sum of a purely indeterministic component a harmonic component and a countable number of evanescent fields we present a maximum likelihood solution to the joint parameter estimation problem of these components from a single observed realization of the texture field the proposed solution is a twostage algorithm in the first stage we obtain an estimate for the number of harmonic and evanescent components in the field and a suboptimal initial estiqate for the parameters of their spectral supports in the second stage we refine these initial estimates by iterative maximization of the likelihood function of the observed data by introducing appropriate parameter transformations the highly nonlinear least squares problem that results from the maximization of the likelihood function is transformed into a separable least squares problem in this new problem the solution for the unknown spectral supports of the harmonic and evanescent components reduces the problem of solving for the transformed parameters of the field to linear least squares solution of the transformation equations then provides a complete solution of the field model parameter estimation problem the wold based model and the resulting analysis and synthesis algorithms are seen applicable to a wide variety of texture types found in natural images the support or shape of the analyzed texture patch may be arbitrary our model is very efficient in terms of the number of parameters required to represent and faithfully reconstruct the original texture

texture decomposition by harmonics extraction from higher order statistics in this paper a method of harmonics extraction from higher order statistics hos is developed for texture decomposition we show that the diagonal slice of the fourth order cumulants is proportional to the autocorrelation of a related noiseless sinusoidal signal with identical frequencies we propose to use this fourth order cumulants slice to estimate a power spectrum from which the harmonic frequencies can be easily extracted hence a texture can be decomposed into deterministic components and indeterministic components as in a unified texture model through a wold like decomposition procedure the simulation and experimental results demonstrated that this method is effective for texture decomposition and it performs better than traditional lower order statistics based decomposition methods

spatial reasoning and similarity retrieval for image database systems based on rs strings in this paper we propose a rotation invariant spatial knowledge representation called rs string then we present the string generation algorithm to automatically generate rs strings for segmented pictures we also propose the spatial reasoning and similarity retrieval algorithms based on rs strings the similarity retrieval algorithm is much more flexible than all previous 2d string representations because our approach can consider every possible view of a query picture thus the system does not require the user to provide a query picture which must have the same orientation as that of a database picture finally we provide several examples to demonstrate the capabilities of spatial reasoning and similarity retrieval based on the rs string representation

using 2d c strings as spatial knowledge representation for image database systems abstract the pictorial data structure based on 2d strings provides an efficient method for iconic indexing in image database systems previous approaches ignore the sizes of and distances between objects these representations have deficiencies in picture reconstruction similarity retrieval and spatial reasoning in this paper we propose a new spatial knowledge representation scheme called 2d c strings as well as a picture reconstruction algorithm as a result our scheme offers the following major advantages 1 more accuracy in picture reconstruction 2 less ambiguity in similarity retrieval 3 reasoning about relative sizes locations and distances for a symbolic picture is possible

reasoning about pictures and similarity retrieval for image information systems based on sk set knowledge representation spatial reasoning and similarity retrieval are two important functions of any image information system good spatial knowledge representation for images is necessary to adequately support these two functions in this paper we propose a new spatial knowledge representation called the sk set based on morphological skeleton theories spatial reasoning algorithms which achieve more accurate results by directly analysing skeletons are described sk set facilitates browsing and progressive visualization we also define four new types of similarity measures and propose a similarity retrieval algorithm for performing image retrieval moreover using sk set as a spatial knowledge representation will reduce the storage space required by an image database significantly

a general method of generating and classifying clifford algebras a general construction program is given for the generation of higher order clifford algebras of various signatures together with their faithful representations in terms of pauli type operators the analysis is based upon several isomorphism theorems that provide a simpler understanding of the standard classification scheme of these algebras and an improved signature index notation is suggested that identifies each of the five types of clifford algebras

visual information retrieval system via content based approach in this paper a content based image retrieval method that can search large image databases efficiently by color texture and shape content is proposed quantized rgb histograms and the dominant triple hue saturation and value which are extracted from quantized hsv joint histogram in the local image region are used for representing global local color information in the image entropy and maximum entry from co occurrence matrices are used for texture information and edge angle histogram is used for representing shape information relevance feedback approach which has coupled proposed features is used for obtaining better retrieval accuracy a new indexing method that supports fast retrieval in large image databases is also presented tree structures constructed by k means algorithm along with the idea of triangle inequality eliminate candidate images for similarity calculation between query image and each database image we find that the proposed method reduces calculation up to average 92 2 percent of the images from direct comparison

wavelet based texture retrieval using generalized gaussian density and kullback leibler distance we present a statistical view of the texture retrieval problem by combining the two related tasks namely feature extraction fe and similarity measurement sm into a joint modeling and classification scheme we show that using a consistent estimator of texture model parameters for the fe step followed by computing the kullback leibler distance kld between estimated models for the sm step is asymptotically optimal in term of retrieval error probability the statistical scheme leads to a new wavelet based texture retrieval method that is based on the accurate modeling of the marginal distribution of wavelet coefficients using generalized gaussian density ggd and on the existence a closed form for the kld between ggds the proposed method provides greater accuracy and flexibility in capturing texture information while its simplified form has a close resemblance with the existing methods which uses energy distribution in the frequency domain to identify textures experimental results on a database of 640 texture images indicate that the new method significantly improves retrieval rates e g from 65 to 77 compared with traditional approaches while it retains comparable levels of computational complexity

a multiresolution approach for texture synthesis using the circular harmonic functions in this paper an unsupervised model based texture reproduction technique is described in accordance with the julesz s 1962 conjecture the statistical properties of the prototype up to the second order are copied in order to generate a synthetic texture perceptually indistinguishable from the given sample however this task is accomplished using a hybrid approach which operates partially in the spatial domain and partially in a multiresolution domain the latter employed is the circular harmonic function chf domain since it has been proven to be well suited for mimicking the behavior of the human visual system hvs this approach allows for a wide range of textures typologies obtaining synthetic textures that better match the prototype with respect to the ones obtained using techniques based on the julesz s conjecture operating only in the spatial domain and to dramatically reduce the computational complexity of similar methods operating only in the multiresolution domain

a generalization of the construction of ilamed and salingaros ilamed and salingaros construct the real and complex algebras with three anticommuting elements which can arise in physics it is shown here that the algebra of color can be similarly constructed with six anticommuting elements as a consequence of this construction these algebras are all simple quadratic algebras

spectral representation and asymptotic properties of certain deterministic fields with innovation components in this paper we derive the spectral and ergodic properties of a special class of homogeneous random fields which includes an important family of evanescent random fields based on a derivation of the resolution of the identity for the operators generating the homogeneous field and using the properties of measurable transformations the spectral representation of both the field and its covariance sequence are derived a necessary and sufficient condition for the existence of such representation is introduced using an analysis approach that employs the solution to the linear diophantine equations further characterization and modeling of the spectral properties of evanescent fields are provided by considering their spectral pseudo density function defined in this paper the geometric properties of the spectral pseudo density of the evanescent field are investigated finally necessary and sufficient conditions for mean and strong ergodicity of the first and second order moments of these fields are derived the analysis initially carried out for complex valued random fields is later extended to include the case of real valued fields

algebras with three anticommuting elements i spinors and quaternions a general construction of alternative algebras with three anticommuting elements and a unit is given as an exhaustive result over the real and complex fields we obtain the clifford algebras h quaternions n1 dihedral clifford algebra which is related to real 2 spinors and s1 algebra of pauli matrices which is related to complex 2 spinors what is important is that the algebras n1 and s1 possess inverses everywhere except on a region akin to the light cone of the minkowski space while the quaternion algebra h has inverses everywhere except at the zero element we discuss the reasons why the three algebras n1 h and s1 are so difficult to distinguish in the representation space of 2 2 complex matrices

viewpoint invariant texture description using fractal analysis image texture provides a rich visual description of the surfaces in the scene many texture signatures based on various statistical descriptions and various local measurements have been developed existing signatures in general are not invariant to 3d geometric transformations which is a serious limitation for many applications in this paper we introduce a new texture signature called the multifractal spectrum mfs the mfs is invariant under the bi lipschitz map which includes view point changes and non rigid deformations of the texture surface as well as local affine illumination changes it provides an efficient framework combining global spatial invariance and local robust measurements intuitively the mfs could be viewed as a better histogram with greater robustness to various environmental changes and the advantage of capturing some geometrical distribution information encoded in the texture experiments demonstrate that the mfs codes the essential structure of textures with very low dimension and thus represents an useful tool for texture classification

a construction relating clifford algebras and cayley dickson algebras a review of the applications of the octonions in physics is given a construction is presented both the cayley dickson algebras and the clifford algebras arise naturally under this construction from the quaternion algebras the mathematical properties of the algebras constructed are discussed

a prime number based matrix strategy for efficient iconic indexing of symbolic pictures in the previous approaches to represent pictorial data as the complexity of the representation strategy is increased the more spatial relationships can be represented which also results in a more complex strategy for query processing and a limited types of queries that can be answered in this paper we propose an efficient iconic indexing scheme called prime number based matrix pn matrix for symbolic pictures which combines the advantages of the 2d c string and the 9dlt matrix basically the proposed strategy can represent those complex relationships which are represented in 2d c strings in a matrix and an efficient module based operation can be used to support pictorial query spatial reasoning and similarity retrieval in the proposed scheme we classify 169 spatial relationships between two objects in 2d space into five spatial categories and define a category rule for each of those five spatial categories those category rules are module operation based therefore they are efficient enough as compared to the previous approaches following those category rules we propose algorithms to efficiently support spatial reasoning picture queries and similarity retrieval based on a data structure of a prime number based matrix pn matrix

extraction of major object features using vq clustering for content based image retrieval an image representation method using vector quantization vq on color and texture is proposed in this paper the proposed method is also used to retrieve similar images from database systems the basic idea is a transformation from the raw pixel data to a small set of image regions which are coherent in color and texture space a scheme is provided for object based image retrieval features for image retrieval are the three color features hue saturation and value from the hsv color model and five textural features asm contrast correlation variance and entropy from the gray level co occurrence matrices once the features are extracted from an image eight dimensional feature vectors represent each pixel in the image the vq algorithm is used to rapidly cluster those feature vectors into groups a representative feature table based on the dominant groups is obtained and used to retrieve similar images according to the object within the image this method can retrieve similar images even in cases where objects are translated scaled and rotated

rotation invariant texture retrieval with gaussianized steerable pyramids this paper presents a novel rotation invariant image retrieval scheme based on a transformation of the texture information via a steerable pyramid first we fit the distribution of the subband coefficients using a joint alpha stable sub gaussian model to capture their non gaussian behavior then we apply a normalization process in order to gaussianize the coefficients as a result the feature extraction step consists of estimating the covariances between the normalized pyramid coefficients the similarity between two distinct texture images is measured by minimizing a rotation invariant version of the kullback leibler divergence between their corresponding multivariate gaussian distributions where the minimization is performed over a set of rotation angles

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

theoremes de connexite pour les produits d espaces projectifs et les grassmanniennes we give a numerical condition on the images of two morphisms to a grassmannian or a product of projective spaces that ensures that their fibered product is connected thereby extending connectedness results of fulton and hansen this result is valid over any algebraically closed field it yields a condition on the class of an irreducible subvariety of a grassmannian that implies that it is simply connected this applies in particular to fano varieties of certain hypersurfaces in a projective space

waveguide a joint wavelet based image representation and description system data representation and content description are two basic components required by the management of any image database a wavelet based system called the waveguide which integrates these two components in a unified framework is proposed in this work in the waveguide system images are compressed with the state of the art wavelet coding technique and indexed with color texture and object shape descriptors generated in the wavelet domain during the encoding process all the content descriptors are extracted by machines automatically with a low computational complexity and stored with a low memory space extensive experiments are performed to demonstrate the performance of the new approach

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

statistical texture characterization from discrete wavelet representations we conjecture that texture can be characterized by the statistics of the wavelet detail coefficients and therefore introduce two feature sets 1 the wavelet histogram signatures which capture all first order statistics using a model based approach and 2 the wavelet co occurrence signatures which reflect the coefficients second order statistics the introduced feature sets outperform the traditionally used energy best performance is achieved by combining histogram and co occurrence signatures

generalized quaternions and spacetime symmetries the construction of a class of associative composition algebras qn on r4 generalizing the well known quaternions q provides an explicit representation of the universal enveloping algebra of the real three dimensional lie algebras having tracefree adjoint representations class a bianchi type lie algebras the identity components of the four dimensional lie groups gl qn 1 qn general linear group in one generalized quaternion dimension which are generated by the lie algebra of this class of quaternion algebras are diffeomorphic to the manifolds of spacetime homogeneous and spatially homogeneous spacetimes having simply transitive homogeneity isometry groups with tracefree lie algebra adjoint representations in almost all cases the complete group of isometries of such a spacetime is isomorphic to a subgroup of the group of left and right translations and automorphisms of the appropriate generalized quaternion algebra similar results hold for the single class b lie algebra of bianchi type v characteri

quadratic alternative algebras quadratic alternative algebras are completely classified up to isomorphism by means of the associated set of vectors they include the quaternion and octonion algebras but also many other nonassociative algebras used in physics

similarity retrieval of iconic image database abstract the perception of spatial relationships among objects in a picture is one of the important selection criteria to discriminate and retrieve the images in an iconic image database system the data structure called 2d string proposed by chang et al is adopted to represent symbolic pictures the 2d string preserves the objects spatial knowledge embedded in images since spatial relationship is a fuzzy concept the capability of similarity retrieval for the retrieval by subpicture is essential in this paper similarity measure based on 2d string longest common subsequence is defined the algorithm for similarity retrieval is also proposed similarity retrieval provides the iconic image database with the distinguishing function different from a conventional database

brief review of invariant texture analysis methods this paper considers invariant texture analysis texture analysis approaches whose performances are not affected by translation rotation affine and perspective transform are addressed existing invariant texture analysis algorithms are carefully studied and classified into three categories statistical methods model based methods and structural methods the importance of invariant texture analysis is presented first each approach is reviewed according to its classification and its merits and drawbacks are outlined the focus of possible future work is also suggested

algebras with anticommuting basal elements space time symmetries and quantum theory a collection a of algebras with anticommuting basal elements is investigated it is shown that the collection a includes the quaternions the octonions the algebra of color as well as other algebras familiar to the physicist each algebra a is a quadratic jordan admissible algebra and possesses a norm that is a generalization of the minkowski metric using a cayley dickson like process each such algebra a in a can be embedded into a larger algebra a that is also in the collection a these algebras should provide candidates for models to describe observables color and other phenomena encountered in particle physics

a unified texture model based on a 2 d wold like decomposition a unified texture model that is applicable to a wide variety of texture types found in natural images is presented this model leads to the derivation of texture analysis and synthesis algorithms designed to estimate the texture parameters and to reconstruct the original texture field from these parameters the texture field is assumed to be a realization of a regular homogeneous random field which is characterized in general by a mixed spectral distribution the texture field is orthogonally decomposed into a purely indeterministic component and a deterministic component the deterministic component is further orthogonally decomposed into a harmonic component and a generalized evanescent component both analytical and experimental results show that the deterministic components should be parameterized separately from the purely indeterministic component the model is very efficient in terms of the number of parameters required to faithfully represent textures reconstructed textures are practically indistinguishable from the originals

multiscale directional filter bank with applications to structured and random texture retrieval in this paper multiscale directional filter bank mdfb is investigated for texture characterization and retrieval first the problem of aliasing in decimated bandpass images on directional decomposition is addressed mdfb is then designed to suppress the aliasing effect as well as to minimize the reduction in frequency resolution second an entropy based measure on energy signatures is proposed to classify structured and random textures with the use of this measure for texture pre classification an optimized retrieval performance can be achieved by selecting the mdfb based method for retrieving structured textures and a statistical or model based method for retrieving random textures in addition a feature reduction scheme and a rotation invariant conversion method are developed the former is developed so as to find the most representative features while the latter is developed to provide a set of rotation invariant features for texture characterization experimental works confirm that they are effective for texture retrieval

2d c string a new spatial knowledge representation for image database systems abstract the data structure called 2d string to represent symbolic pictures was proposed by chang et al it allows a natural way to construct iconic indexes for pictures jungert has extended 2d strings to represent more types of spatial relationships between picture objects but the operators and the derived knowledge cannot be stored in a unified structure in this paper a new spatial knowledge representation 2d c string with accompanied cutting mechanism and a set of spatial operators are proposed 2d c string is more characteristic of spatial knowledge in images and is more efficient in representation and manipulation of images the cutting and reconstruction algorithms for 2d c string representation of symbolic pictures are also developed

estimation and choice of neighbors in spatial interaction models of images some aspects of statistical inference for a class of spatial interaction models for finite images are presented primarily the simultaneous autoregressive sar models and conditional markov cm models each of these models is characterized by a set of neighbors a set of coefficients and a noise sequence of specified characteristics we are concerned with two problems the estimation of the unknown parameters in both sar and cm models and the choice of an appropriate model from a class of such competing models assuming gaussian distributed variables we discuss maximum likelihood ml estimation methods in general the ml scheme leads to nonlinear optimization problems to avoid excessive computation an iterative scheme is given for sar models which gives approximate ml estimates in the gaussian case and reasonably good estimates in some non gaussian situations as well likewise for cm models an easily computable consistent estimate is given the asymptotic mean squared error mse of this estimate for a four neighbor cm model is shown tn be substantially less than the mse of the popular coding estimate asymptotically consistent decision rules are given for choosing an appropriate sar or cm model the usefulness of the estimation scheme and the decision rule for the choice of neighbors is illustrated by using synthetic patterns synthetic patterns obeying known sar and cm models are generated and the models corresponding to true and several competing neighbor sets are fitted the estimation scheme yields estimates close to the parameters of the true models and the decision rule for the choice of neighbors picks up the true model from the class of competing models

fingerprint classification using fast fourier transform and nonlinear discriminant analysis in this paper we present a new approach for fingerprint classification based on discrete fourier transform dft and nonlinear discriminant analysis utilizing the dft and directional filters a reliable and efficient directional image is constructed from each fingerprint image and then nonlinear discriminant analysis is applied to the constructed directional images reducing the dimension dramatically and extracting the discriminant features the proposed method explores the capability of dft and directional filtering in dealing with low quality images and the effectiveness of nonlinear feature extraction method in fingerprint classification experimental results demonstrates competitive performance compared with other published results

the metric of a space and quadratic algebras a collection of algebras with product that preserves the metric of the underlying vector space is investigated it is shown that this collection includes the generalized quaternions the composition algebras and the algebra of color all the algebras in this collection that are either commutative or alternative are determined the ramifications of nondegenerate metrics are detailed if the algebra is alternative and not of dimension 1 2 4 or 8 over the base field the metric must be degenerate

rotation invariant texture retrieval via signature alignment based on steerable sub gaussian modeling this paper addresses the construction of a novel efficient rotation invariant texture retrieval method that is based on the alignment in angle of signatures obtained via a steerable sub gaussian model in our proposed scheme we first construct a steerable multivariate sub gaussian model where the fractional lower order moments of a given image are associated with those of its rotated versions the feature extraction step consists of estimating the so called covariations between the orientation subbands of the corresponding steerable pyramid at the same or at adjacent decomposition levels and building an appropriate signature that can be rotated directly without the need of rotating the image and recalculating the signature the similarity measurement between two images is performed using a matrix based norm that includes a signature alignment in angle between the images being compared achieving in this way the desired rotation invariance property our experimental results show how this retrieval scheme achieves a lower average retrieval error as compared to previously proposed methods having a similar computational complexity while at the same time being competitive with the best currently known state of the art retrieval system in conclusion our retrieval method provides the best compromise between complexity and average retrieval performance