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

analysis in space time bundles iii higher spin bundles the universal cosmos m is the unique four dimensional globally causal space time manifold to which the dirac and maxwell equations among others maximally and covariantly extend a systematic treatment is presented of general fields over m of arbitrary spin considered are fields induced from all irreducible representation of the isotropy group scale extended poincare group to g the connected causal group of m restricted to any species of such fields the k invariant canonical dirac operator k maximal essentially compact subgroup of g is shown g covariant for a unique conformal weight a normalized k finite basis for such fields is constructed the basis actions thereon of the dirac operator infinitesimal generators of g discrete symmetries second order casimir and the essentially unique third order noncentral quantum number enveloping algebra element invariant under k are derived composition series under g of a class of these field spaces namely the extension to m of the relativistic fields considered by bargman and wigner or arbitrary spin and conformal weight are determined distinguishing by invariance and causality features alone the essentially conventional positive energy mass 0 subspaces and massive invariant sub quotient spaces whose unitarity under g is given a new proof the completely positive subclass cf below of representations is determined a more detailed treatment of spin one bundles vector and two form of arbitrary conformal weight is included the exterior derivative transformations are diagonalized and the conformally invariant massive spin one scalar product is identified with a mathematical version of the conventional electromagnetic field lagrangian

maximum likelihood parameter estimation of discrete homogeneous random fields with mixed spectral distributions this paper presents a maximum likelihood solution to the general problem of fitting a parametric model to observations from a single realization of a real valued 2 d homogeneous random field with mixed spectral distribution on the basis of a 2 d wold like decomposition the field is represented as a sum of mutually orthogonal components of three types purely indeterministic harmonic and evanescent the proposed algorithm provides a complete solution to the joint estimation problem of the random field components 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 provides a complete solution of the field model parameter estimation problem

analysis in space time bundles iv natural bundles deforming into and composed of the same invariant factors as the spin and form bundles abstract we study two interesting new bundles over the universal cosmos m or maximal isotropic space time which may be physically applicable the treatment is from a homogeneous vector bundle point of view and uses the notation and some of the results of the treatment in papers i iii s m paneitz and i e segal j funct anal 47 1982 78 142 49 1982 335 414 54 1983 18 22 of conventional bundles over m the spannor bundle deforms into essentially the usual spinor bundle as a conformally invariant parameter that may be interpreted as the space curvature becomes arbitrarily small from a minkowski space standpoint however the spannors involve a nontrivial action of space time translations that deforms into a trivial action in the spinor limit and also have more complex transformation properties under discrete symmetries also studied are the plyors consisting of the dual to the bundle product of the spannors with themselves composition series for the spannor and plyor section spaces are treated relative to the conformal group and irreducible subquotients are identified with certain that occur in conventional bundles in particular factors corresponding to the maxwell and massless dirac equations and which may represent certain of the observed elementary particles are determined a gauge and conformally invariant nonlinear coupling between spannors and plyors constituting essentially a generalization of that used in quantum electrodynamics is developed and an associated invariant nonlinear partial differential equation is derived covariant and causal quantization for spannors as fermions and plyors as bosons is formulated algebraically the present treatment is basically mathematical but physical motivations and possible interpretations are briefly noted

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

the derived category of an exact category there is some confusion in the literature regarding the derived category of an exact category 8 thomason gives a satisfactory treatment of the bounded derived category in ct 1 11 6 see also appendix a the result is that provided all weakly split epimorphisms in 8 are admissible the bounded derived category may be defined as usual although thomason does not say it the categories d 6 d d may also be defined in the same way the definition of the unbounded derived category is more difficult and is very poorly treated in the literature for instance in bbd this derived category is only defined provided every morphism in 6 admits a kernel see bbd 1 1 41 this is very unsatisfactory since very few exact categories satisfy the condition in this article we will show that d b may be defined whenever 6 is saturated karoubian in thomason s terminology an exact category is saturated if every idempotent splits i e 6 contains all direct summands of its objects for the purpose of comparing with thomason s result the bounded derived category is defined for more 8 s all that is required to define db is that whenever an idempotent e a a factors as a f ba a with fog lb then e is split thomason calls such idempotents weakly split and we will honor his notation we will show here that these constructions are in some sense best possible remark 1 8 for d 6 remarks 1 9 and 1 10 for d d d b db 6 there are two reasons why i wrote this note one is to correct the misconceptions in the literature but more importantly the proof of the key result lemma 1 2 depends on an important characterization of tpaisse subcategories due to rickard and this article is intended to highlight rickard s criterion a full triangulated subcategory y of a triangulated

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

multiple resolution segmentation of textured images a multiple resolution algorithm is presented for segmenting images into regions with differing statistical behavior in addition an algorithm is developed for determining the number of statistically distinct regions in an image and estimating the parameters of those regions both algorithms use a causal gaussian autoregressive model to describe the mean variance and spatial correlation of the image textures together the algorithms can be used to perform unsupervised texture segmentation the multiple resolution segmentation algorithm first segments images at coarse resolution and then progresses to finer resolutions until individual pixels are classified this method results in accurate segmentations and requires significantly less computation than some previously known methods the field containing the classification of each pixel in the image is modeled as a markov random field segmentation at each resolution is then performed by maximizing the a posteriori probability of this field subject to the resolution constraint at each resolution the a posteriori probability is maximized by a deterministic greedy algorithm which iteratively chooses the classification of individual pixels or pixel blocks the unsupervised parameter estimation algorithm determines both the number of textures and their parameters by minimizing a global criterion based on the aic information criterion clusters corresponding to the individual textures are formed by alternately estimating the cluster parameters and repartitioning the data into those clusters concurrently the number of distinct textures is estimated by combining clusters until a minimum of the criterion is reached

real spinor fields and the electroweak interaction the space of real spinor fields of a given massm 0 in minkowski space is the direct sum of two irreducibly invariant subspaces under the connected poincare groupp these subspaces admit uniquep invariant positive energy complex unitarizable structures in terms of which they are unitarily and canonically equivalent to the conventional left electron and right positron subspaces defined by the dirac equation space reversalpand time reversaltactp covariantly as antiunitary operators on the real fields they also extend to the complex fields in terms of whichpexchanges the two subspaces whiletacts separately on each whenm 0 the identical formalism produces a rigorous version of the conventional neutrino formalism the restriction to the real context of the conventional spinor vector interaction is equivalent to the conventionalv ainteraction together with a computationally equivalent form of quantum electrodynamics in which the right electron and left electron are redundant

auslander gorenstein algebras and precluster tilting abstract we generalize the notions of n cluster tilting subcategories and selfinjective algebras into n precluster tilting subcategories and n selfinjective algebras where we show that a subcategory naturally associated to n precluster tilting subcategories has a higher auslander reiten theory furthermore we give a bijection between n precluster tilting subcategories and n minimal auslander gorenstein algebras which is a higher dimensional analog of auslander solberg correspondence 8 as well as a gorenstein analog of n auslander correspondence 22 the auslander reiten theory associated to an n precluster tilting subcategory is used to classify the n minimal auslander gorenstein algebras into four disjoint classes our method is based on relative homological algebra due to auslander solberg

on quiver grassmannians and orbit closures for representation finite algebras we show that auslander algebras have a unique tilting and cotilting module which is generated and cogenerated by a projective injective its endomorphism ring is called the projective quotient algebra for any representation finite algebra we use the projective quotient algebra to construct desingularizations of quiver grassmannians orbit closures in representation varieties and their desingularizations this generalizes results of cerulli irelli feigin and reineke

spinor currents as vector particles abstract we study a prototype for the problem of determining the irreducible factors of the spaces spanned by currents between homogeneous vector bundles more specifically let g denote the conformal group of minkowski space time m 0 or more precisely su 2 2 it is shown that the positive energy unitary g irreducible massive factors of the one form bundle over the conformal compactification of m 0 are bundle equivalent to spaces spanned by currents of the spinor bundle this has the interpretation that the z particle may be modelled by the representation of g of lowest k type lkt 3 emsp14 1 2 1 2 where k su 1 su 2 su 2 and m j j refers to the representation in which the lowest eigenvalue of the su 1 generator is m while j and j are the spins of the left and right su 2 representations in particular this z representation is bundle equivalent to the representation of g in a space of currents between neutrinos of lkt 3 2 0 1 2 and antineutrinos of lkt 3 2 1 2 0 the w particle representation may similarly be modelled by the representation of g of lowest k type 4 0 0 the only other massive positive energy unitary factor of the one form bundle in particular the w is equivalent to a space of currents between the electron of lkt 5 2 0 1 2 and the antineutrino these results are consistent with the possibility that all quasi stable elementary particles may be modelled by similar subspaces of bundle products

parameter estimation of two dimensional moving average random fields this paper considers the problem of estimating the parameters of two dimensional 2 d moving average random ma fields we first address the problem of expressing the covariance matrix of nonsymmetrical half plane noncausal and quarter plane ma random fields in terms of the model parameters assuming the random field is gaussian we derive a closed form expression for the cramer rao lower bound crlb on the error variance in jointly estimating the model parameters a computationally efficient algorithm for estimating the parameters of the ma model is developed the algorithm initially fits a 2 d autoregressive model to the observed field and then uses the estimated parameters to compute the ma model a maximum likelihood algorithm for estimating the ma model parameters is also presented the performance of the proposed algorithms is illustrated by monte carlo simulations and is compared with the cramer rao bound

identification and restoration of noisy blurred images using the expectation maximization algorithm a maximum likelihood approach to the blur identification problem is presented the expectation maximization algorithm is proposed to optimize the nonlinear likelihood function in an efficient way in order to improve the performance of the identification algorithm low order parametric image and blur models are incorporated into the identification method the resulting iterative technique simultaneously identifies and restores noisy blurred images

classification of rotated and scaled textured images using gaussian markov random field models consideration is given to the problem of classifying a test textured image that is obtained from one of c possible parent texture classes after possibly applying unknown rotation and scale changes to the parent texture the training texture images parent classes are modeled by gaussian markov random fields gmrfs to classify a rotated and scaled test texture the rotation and scale changes are incorporated in the texture model through an appropriate transformation of the power spectral density of the gmrf for the rotated and scaled image a bona fide likelihood function that shows the explicit dependence of the likelihood function on the gmrf parameters as well as on the rotation and scale parameters is derived although in general the scaled and or rotated texture does not correspond to a finite order gmrf it is possible nonetheless to write down a likelihood function for the image data the likelihood function of the discrete fourier transform of the image data corresponds to that of a white nonstationary gaussian random field with the variance at each pixel i j being a known function of the rotation the scale the gmrf model parameters and i j the variance is an explicit function of the appropriately sampled power spectral density of the gmrf the estimation of the rotation and scale parameters is performed in the frequency domain by maximizing the likelihood function associated with the discrete fourier transform of the image data cramer rao error bounds on the scale and rotation estimates are easily computed a modified bayes decision rule is used to classify a given test image into one of c possible texture classes the classification power of the method is demonstrated through experimental results on natural textures from the brodatz album

adaptive restoration of textured images with mixed spectra we consider the adaptive restoration of inhomogeneous textured images where the individual regions are modeled using a wold like decomposition a generalized wiener filter is developed to accommodate mixed spectra and unsupervised restoration is achieved by using the expectation maximization em algorithm to estimate the degradation parameters this algorithm yields superior results when compared with supervised wiener filtering using autoregressive ar image models

desingularization of quiver grassmannians for dynkin quivers abstract a desingularization of arbitrary quiver grassmannians for representations of dynkin quivers is constructed in terms of quiver grassmannians for an algebra derived equivalent to the auslander algebra of the quiver

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

tilting modules of finite projective dimension tilting modules are well known and are useful in the representation theory of artinian algebras 2 4 6 11 the purpose of this paper is to define tilting modules of finite projective dimension and prove some fundamental results a unital left a module a t over a ring a is said to be a tilting module of projective dimension 0 is an integer if it satisfies the following three conditions 1 a t has a projective resolution

the evanescent field transform for estimating the parameters of homogeneous random fields with mixed spectral distributions parametric modeling and estimation of complex valued homogeneous random fields with mixed spectral distributions is a fundamental problem in two dimensional 2 d signal processing the parametric model under consideration results from the 2 d wold type decomposition of the random field the same model naturally arises as the physical model in problems of space time adaptive processing of airborne radar a computationally efficient algorithm for estimating the parameters of the field components is presented the algorithm is based on a nonlinear operator that uniquely maps each evanescent component to a single exponential the exponential s spatial frequency is a function of the spectral support parameters of the evanescent component hence employing this operator the problem of estimating the spectral support parameters of an evanescent field is replaced by the simpler problem of estimating the spatial frequency of a 2 d exponential the properties of the operator are analyzed the algorithm performance is illustrated and investigated using monte carlo simulations

simple parallel hierarchical and relaxation algorithms for segmenting noncausal markovian random fields the modeling and segmentation of images by mrf s markov random fields is treated these are two dimensional noncausal markovian stochastic processes two conceptually new algorithms are presented for segmenting textured images into regions in each of which the data are modeled as one of c mrf s the algorithms are designed to operate in real time when implemented on new parallel computer architectures that can be built with present technology a doubly stochastic representation is used in image modeling here a gaussian mrf is used to model textures in visible light and infrared images and an autobinary or autoternary etc mrf to model a priori information about the local geometry of textured image regions for image segmentation the true texture class regions are treated either as a priori completely unknown or as a realization of a binary or ternary etc mrf in the former case image segmentation is realized as true maximum likelihood estimation in the latter case it is realized as true maximum a posteriori likelihood segmentation in addition to providing a mathematically correct means for introducing geometric structure the autobinary or ternary etc mrf can be used in a generative mode to generate image geometries and artificial images and such simulations constitute a very powerful tool for studying the effects of these models and the appropriate choice of model parameters the first segmentation algorithm is hierarchical and uses a pyramid like structure in new ways that exploit the mutual dependencies among disjoint pieces of a textured region

texture synthesis using 2 d noncausal autoregressive models the purpose of this paper is to illustrate the usefulness of two dimensional noncausal autoregressive ncar models for the synthesis of textures these models characterize the gray level at a pixel as a linear combination of gray levels at nearby locations in all directions and an additive white noise variable we first show that the class of ncar models is capable of generating a wide variety of image patterns posessing the local replication attribute an essential ingredient of many natural textures it is also shown that the theoretical variograms of many ncar models possess an oscillatory behavior a characteristic of the variograms of many natural textures next we give experimental results of synthesis of 64 64 textures resembling several real textures in the brodatz album the synthetic textures generated by 16 parameter ncar models retain most the visual characteristics of the original textures the variograms of the original and synthetic textures are also similar

analysis in space time bundles i general considerations and the scalar bundle abstract mathematical features involved in the systematic development of elementary particle theory on an alternative cosmos space time are presented bundles representative of physical fields are studied in the unique variant of minkowski space m 0 enjoying similar properties of causality and symmetry the universal cosmos m is the universal cover of the causal compactification of m 0 the bundles studied are induced from representations of the scale extended poincare group which forms the isotropy group in m of the universal cover g s u 2 2 of the connected component of the group of all causal transformations on m discrete symmetries and higher dimensional cases are also discussed the primary focus is on the temporal evolution especially stability involving positivity of the energy wave equations implicative of finite propagation velocity and the unitarity and or composition series of associated actions of g general spin bundles on m are treated parallelized and correlated with bundles on m 0 associated covariant wave equations and the spectral resolution of fundamental quantum numbers are studied in detail in the scalar case

closed subbifunctors of the extension functor abstract given a subbifunctor f of ext 1 one can ask if one can generalize the construction of the derived category to obtain a relative derived category where one localizes with respect to f acyclic sequences we show that this is possible if and only if f is closed we also show that for artin algebras the closed subbifunctors correspond to serre subcategories of a category of finitely presented functors that vanish on projectives and we use this to find new examples of closed subbifunctors using relatively derived categories we give a relative version of happel s result on derived equivalences induced by tilting and we show in an example how this can be used to find ordinary derived equivalences

analysis in space time bundles ii the spinor and form bundles abstract the structures of the spin and form bundles over the universal cosmos m and their relations with corresponding bundles over the minkowski space m 0 canonically imbedded in m are treated wave equations covariant with respect to the causal group g of m are studied their solution manifolds and other stable essentially positive energy invariant subspaces of the section spaces of the bundles are determined and the indecomposability of relevant invariant subspace chains is shown explicit parallelizations of the bundles are applied to the dirac and maxwell equations on m a basis for spinor fields that diagonalizes a complete set of k covariant quantum numbers k maximal essentially compact subgroup of g is developed local multilinear invariants of bundles over m are treated and specialized to convergent mathematical versions of the fermi and yukawa interaction lagrangians that are g invariant for the appropriate conformal weights

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

n representation finite algebras and n apr tilting we introduce the notion of n representation finiteness generalizing representationfinite hereditary algebras we establish the procedure of n apr tilting and show that it preserves n representation finiteness we give some combinatorial description of this procedure and use this to completely describe a class of n representation finite algebras called type a

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

on faithfully balanced modules f cotilting and f auslander algebras abstract the aim of this paper is to give a unification of the theory of co tilting modules and higher auslander correspondence by using faithfully balanced modules i e faithful modules with the double centralizer property in the language of relative homological algebra following auslander solberg a relative version of faithfully balancedness is given which will be called 1 f faithful the relative versions of higher auslander correspondence and brenner butler theorem are also developed

unsupervised texture segmentation using markov random field models the problem of unsupervised segmentation of textured images is considered the only explicit assumption made is that the intensity data can be modeled by a gauss markov random field gmrf the image is divided into a number of nonoverlapping regions and the gmrf parameters are computed from each of these regions a simple clustering method is used to merge these regions the parameters of the model estimated from the clustered segments are then used in two different schemes one being all approximation to the maximum a posterior estimate of the labels and the other minimizing the percentage misclassification error the proposed approach is contrasted with the algorithm of s lakshamanan and h derin 1989 which uses a simultaneous parameter estimation and segmentation scheme the results of the adaptive segmentation algorithm of lakshamanan and derin are compared with a simple nearest neighbor classification scheme to show that if enough information is available simple techniques could be used as alternatives to computationally expensive schemes

three dimensional textured image blocks model based on wold decomposition in this paper we present a new parametric modeling of three dimensional homogeneous volumes of textured images 3d texture based on 3d wold decomposition for discrete processes this decomposition additively separates any 3d discrete homogeneous process into three mutually orthogonal components a purely indeterministic a remote past type deterministic and an evanescent component the evanescent component can be further decomposed into two orthogonal components called type 1 evanescent and type 2 evanescent assuming that the 3d image volume is a finite realization of a discrete homogeneous stochastic process the 3d texture field can be uniquely represented as a sum of four mutually orthogonal components with different spectral properties the aim of this paper is to present new parametric models able to describe both the spectral support and spatial characteristics of each component a spectral decomposition algorithm to separate a 3d texture into structured and unstructured parts is also proposed