rotation and gray scale transform invariant texture identification using wavelet decomposition and hidden markov model in this correspondence we have presented a rotation and gray scale transform invariant texture recognition scheme using the combination of quadrature mirror filter qmf bank and hidden markov model hmm in the first stage the qmf bank is used as the wavelet transform to decompose the texture image into subbands the gray scale transform invariant features derived from the statistics based on first order distribution of gray levels are then extracted from each subband image in the second stage the sequence of subbands is modeled as a hidden markov model hmm and one hmm is designed for each class of textures the hmm is used to exploit the dependence among these subbands and is able to capture the trend of changes caused by rotation during recognition the unknown texture is matched against all the models the best matched model identifies the texture class up to 93 33 classification accuracy is reported

2 d shape classification using hidden markov model the authors present a planar shape recognition approach based on the hidden markov model and autoregressive parameters this approach segments closed shapes to make classifications at a finer level the algorithm can tolerate a lot of shape contour perturbation and a moderate amount of occlusion an orientation scheme is described to make the overall classification insensitive to shape orientation excellent recognition results have been reported a distinct advantage of the approach is that the classifier does not have to be trained again when a new class of shapes is added

fuzzy vector spaces abstract this paper defines a basis for a fuzzy vector space and its dimension a class of fuzzy vector spaces having dimension is introduced and two standard results from crisp theory are proved for this case namely d i m e1 e2 d i m e1 d i m e2 d i m e1 e2 and rmd i m i m f d i m k e r f the product of two fuzzy vector spaces under certain conditions is also characterised

conditional probability logic lifted bayesian networks and almost sure quantifier elimination abstract we introduce a formal logical language called conditional probability logic cpl which extends first order logic and which can express probabilities conditional probabilities and which can compare conditional probabilities intuitively speaking although formal details are different cpl can express the same kind of statements as some languages which have been considered in the artificial intelligence community we also consider a way of making precise the notion of lifted bayesian network where this notion is a type of lifted probabilistic graphical model used in machine learning data mining and artificial intelligence a lifted bayesian network in the sense defined here determines in a natural way a probability distribution on the set of all structures in the sense of first order logic with a common finite domain d our main result theorem 3 14 is that for every noncritical cpl formula x there is a quantifier free formula x which is almost surely equivalent to x as the cardinality of d tends towards infinity this is relevant for the problem of making probabilistic inferences on large domains d because a the problem of evaluating by brute force the probability of x being true for some sequence d of elements from d has in general highly exponential time complexity in the cardinality of d and b the corresponding probability for the quantifier free x depends only on the lifted bayesian network and not on d some conclusions regarding the computational complexity of finding are given in remark 3 17 the main result has two corollaries one of which is a convergence law and zero one law for noncritial cpl formulas

on flags and fuzzy subspaces of vector spaces this paper deals with fuzzy subspaces of a vector space in terms of flags we define the operations sum product tensor product hom and intersection of fuzzy subspaces and in each case we characterise the corresponding flag some of these have been considered in the literature in different context the novelty of this paper is in the use of flags as primary tool to study fuzzy subspaces

_ 1 free graphs asymptotic structure and a 0 1 law etude asymptotique de la structure des graphes etiquetes sans k l 1 etablissement de la l colorabilite et de la loi 0 1

rotation invariant texture classification using lbp variance lbpv with global matching local or global rotation invariant feature extraction has been widely used in texture classification local invariant features e g local binary pattern lbp have the drawback of losing global spatial information while global features preserve little local texture information this paper proposes an alternative hybrid scheme globally rotation invariant matching with locally variant lbp texture features using lbp distribution we first estimate the principal orientations of the texture image and then use them to align lbp histograms the aligned histograms are then in turn used to measure the dissimilarity between images a new texture descriptor lbp variance lbpv is proposed to characterize the local contrast information into the one dimensional lbp histogram lbpv does not need any quantization and it is totally training free to further speed up the proposed matching scheme we propose a method to reduce feature dimensions using distance measurement the experimental results on representative databases show that the proposed lbpv operator and global matching scheme can achieve significant improvement sometimes more than 10 in terms of classification accuracy over traditional locally rotation invariant lbp method

fuzzy normal subgroups and fuzzy cosets abstract we introduce here the notion of 1 i a fuzzy normal subgroup and 2 ii a fuzzy coset we prove that for a group g a fuzzy subgroup is fuzzy normal if and only if it is constant on the conjugate classes of g further we show that the level subgroups of a fuzzy normal subgroup are all normal we obtain several results which are analogs of some basic theorems of group theory in particular a fuzzy version of lagrange s theorem is established

fuzzy topological vector spaces over r in this paper the concepts of fuzzy vector fuzzy vector space and fuzzy topological vector space are investigated a topology called sendograph topology which is compatible with the algebraic structure is given

fuzzy linear maps the concept of the fuzzy subspace of a space of fuzzy linear maps is defined and investigated also the fuzzy basis of this subspace is determined

multiresolution feature extraction and selection for texture segmentation an approach is described for unsupervised segmentation of textured images local texture properties are extracted using local linear transforms that have been optimized for maximal texture discrimination local statistics texture energy measures are estimated at the output of an equivalent filter bank by means of a nonlinear transformation absolute value followed by an iterative gaussian smoothing algorithm this procedure generates a multiresolution sequence of feature planes with a half octave scale progression a feature reduction technique is then applied to the data and is determined by simultaneously diagonalizing scatter matrices evaluated at two different spatial resolutions this approach provides a good approximation of r a fisher s 1950 multiple linear discriminants and has the advantage of requiring no a priori knowledge this feature reduction methods appears to be an improvement on the commonly used karhunen loeve transform and allows efficient texture segmentation based on simple thresholding

fuzzy hypervector spaces based on fuzzy singletons we introduce and study fuzzy hypervector spaces based on fuzzy singletons in this regard by considering the notion of fuzzy singletons we characterize a fuzzy hypervector space fuzzily spanned by a fuzzy subset then we use these results to introduce the concept of fuzzy freeness of a fuzzy subset m of a hypervector space v and finally we characterize it in terms of linear independence in the usual sense

log polar wavelet energy signatures for rotation and scale invariant texture classification classification of texture images is important in image analysis and classification this paper proposes an effective scheme for rotation and scale invariant texture classification using log polar wavelet signatures the rotation and scale invariant feature extraction for a given image involves applying a log polar transform to eliminate the rotation and scale effects but at same time produce a row shifted log polar image which is then passed to an adaptive row shift invariant wavelet packet transform to eliminate the row shift effects so the output wavelet coefficients are rotation and scale invariant the adaptive row shift invariant wavelet packet transform is quite efficient with only o n spl middot log n complexity a feature vector of the most dominant log polar wavelet energy signatures extracted from each subband of wavelet coefficients is constructed for rotation and scale invariant texture classification in the experiments we employed a mahalanobis classifier to classify a set of 25 distinct natural textures selected from the brodatz album the experimental results based on different testing data sets for images with different orientations and scales show that the proposed classification scheme using log polar wavelet signatures outperforms two other texture classification methods its overall accuracy rate for joint rotation and scale invariance being 90 8 percent demonstrating that the extracted energy signatures are effective rotation and scale invariant features concerning its robustness to noise the classification scheme also performs better than the other methods

optimal gabor filters for texture segmentation texture segmentation involves subdividing an image into differently textured regions many texture segmentation schemes are based on a filter bank model where the filters called gabor filters are derived from gabor elementary functions the goal is to transform texture differences into detectable filter output discontinuities at texture boundaries by locating these discontinuities one can segment the image into differently textured regions distinct discontinuities occur however only if the gabor filter parameters are suitably chosen some previous analysis has shown how to design filters for discriminating simple textures designing filters for more general natural textures though has largely been done ad hoc we have devised a more rigorously based method for designing gabor filters it assumes that an image contains two different textures and that prototype samples of the textures are given a priori we argue that gabor filter outputs can be modeled as rician random variables often approximated well as gaussian rv s and develop a decision theoretic algorithm for selecting optimal filter parameters to improve segmentations for difficult texture pairs we also propose a multiple filter segmentation scheme motivated by the rician model experimental results indicate that our method is superior to previous methods in providing useful gabor filters for a wide range of texture pairs

fuzzy linear and affine spaces abstract elementary properties of fuzzy linear and affine spaces are studied the concept of a basis for a fuzzy linear space is defined and an algorithm for computing a basis when the underlying space is finite dimensional is given

extraction of shift invariant wavelet features for classification of images with different sizes an effective shift invariant wavelet feature extraction method for classification of images with different sizes is proposed the feature extraction process involves a normalization followed by an adaptive shift invariant wavelet packet transform an energy signature is computed for each subband of these invariant wavelet coefficients a reduced subset of energy signatures is selected as the feature vector for classification of images with different sizes experimental results show that the proposed method can achieve high classification accuracy of 98 5 percent and outperforms the other two image classification methods

an adaptive hybrid pattern for noise robust texture analysis local binary patterns lbp achieve great success in texture analysis however they are not robust to noise the two reasons for such disadvantage of lbp schemes are 1 they encode the texture spatial structure based only on local information which is sensitive to noise and 2 they use exact values as the quantization thresholds which make the extracted features sensitive to small changes in the input image in this paper we propose a noise robust adaptive hybrid pattern ahp for noised texture analysis in our scheme two solutions from the perspective of texture description model and quantization algorithm have been developed to reduce the feature s noise sensitiveness first a hybrid texture description model is proposed in this model the global texture spatial structure which is depicted by a global description model is encoded with the primitive microfeature for texture description second we develop an adaptive quantization algorithm in which equal probability quantization is utilized to achieve the maximum partition entropy higher noise tolerance can be obtained with the minimum lost information in the quantization process the experimental results of texture classification on two texture databases with three different types of noise show that our approach leads significant improvement in noised texture analysis furthermore our scheme achieves state of the art performance in noisy face recognition highlightsa hybrid texture description model is proposed for noise robust texture modeling an adaptive quantization algorithm is designed for robust angular space quantization based on the new description model and quantization algorithm we develop the ahp experimental results demonstrate the significant improvement achieved by our scheme

on fuzzy ideals of a ring 1 abstract the aim of this paper is to study fuzzy ideals of a ring to characterise regular rings and noetherian rings by fuzzy ideals and to determine all fuzzy prime ideals of the ring z of integers

a completed modeling of local binary pattern operator for texture classification in this correspondence a completed modeling of the local binary pattern lbp operator is proposed and an associated completed lbp clbp scheme is developed for texture classification a local region is represented by its center pixel and a local difference sign magnitude transform ldsmt the center pixels represent the image gray level and they are converted into a binary code namely clbp center clbp c by global thresholding ldsmt decomposes the image local differences into two complementary components the signs and the magnitudes and two operators namely clbp sign clbp s and clbp magnitude clbp m are proposed to code them the traditional lbp is equivalent to the clbp s part of clbp and we show that clbp s preserves more information of the local structure than clbp m which explains why the simple lbp operator can extract the texture features reasonably well by combining clbp s clbp m and clbp c features into joint or hybrid distributions significant improvement can be made for rotation invariant texture classification

fuzzy cardinality and the modeling of imprecise quantification abstract the concept of cardinality of a fuzzy set has received attention from several researchers and has been defined in several apparently independent manners a systematic investigation of this notion is performed which unifies and improves previous attempts the cardinality of a fuzzy set viewed as a fuzzy integer is related to scalar cardinality indices the closely related question of the probability of a fuzzy event is dealt with lastly the usefulness of fuzzy cardinality for meaning representation of statements or queries involving fuzzy linguistic quantifiers is emphasized

classification of textures using gaussian markov random fields the problem of texture classification arises in several disciplines such as remote sensing computer vision and image analysis in this paper we present two feature extraction methods for the classification of textures using two dimensional 2 d markov random field mrf models it is assumed that the given m m texture is generated by a gaussian mrf model in the first method the least square ls estimates of model parameters are used as features in the second method using the notion of sufficient statistics it is shown that the sample correlations over a symmetric window including the origin are optimal features for classification simple minimum distance classifiers using these two feature sets yield good classification accuracies for a seven class problem

fuzzy ideals and fuzzy prime ideals of a ring abstract besides obtaining certain ring theoretic analogues some peculiarities of the fuzzy setting are also discussed in particular a study of i the conditions under which a given fuzzy ideal can or cannot be expressed as a union of two proper fuzzy ideals ii the algebraic nature of images and preimages of fuzzy prime ideals under homomorphisms and iii the ring of all the fuzzy cosets of a fuzzy prime fuzzy maximal ideal is carried out

unsupervised texture segmentation using gabor filters abstract this paper presents a texture segmentation algorithm inspired by the multi channel filtering theory for visual information processing in the early stages of human visual system the channels are characterized by a bank of gabor filters that nearly uniformly covers the spatial frequency domain and a systematic filter selection scheme is proposed which is based on reconstruction of the input image from the filtered images texture features are obtained by subjecting each selected filtered image to a nonlinear transformation and computing a measure of energy in a window around each pixel a square error clustering algorithm is then used to integrate the feature images and produce a segmentation a simple procedure to incorporate spatial information in the clustering process is proposed a relative index is used to estimate the true number of texture categories

on the dimension of a fuzzy subspace abstract isomorphism between two fuzzy subspaces is defined and some properties of two isomorphic fuzzy subspaces are discussed in terms of their image sets level subspaces and dimensions the dimension of a fuzzy quotient space is also studied

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

radon transform orientation estimation for rotation invariant texture analysis this paper presents a new approach to rotation invariant texture classification the proposed approach benefits from the fact that most of the texture patterns either have directionality anisotropic textures or are not with a specific direction isotropic textures the wavelet energy features of the directional textures change significantly when the image is rotated however for the isotropic images the wavelet features are not sensitive to rotation therefore for the directional textures it is essential to calculate the wavelet features along a specific direction in the proposed approach the radon transform is first employed to detect the principal direction of the texture then the texture is rotated to place its principal direction at 0 degrees a wavelet transform is applied to the rotated image to extract texture features this approach provides a features space with small intraclass variability and therefore good separation between different classes the performance of the method is evaluated using three texture sets experimental results show the superiority of the proposed approach compared with some existing methods

texture classification using dominant neighborhood structure this paper proposes a new approach to extract global image features for the purpose of texture classification the proposed texture features are obtained by generating an estimated global map representing the measured intensity similarity between any given image pixel and its surrounding neighbors within a certain window the intensity similarity map is an average representation of the texture image dominant neighborhood similarity the estimated dominant neighborhood similarity is robust to noise and referred to as image dominant neighborhood structure the global rotation invariant features are then extracted from the generated image dominant neighborhood structure features obtained from the local binary patterns lbps are then extracted in order to supply additional local texture features to the generated features from the dominant neighborhood structure both features complement each other the experimental results on representative texture databases show that the proposed method is robust to noise and can achieve significant improvement in terms of the obtained classification accuracy in comparison to the lbp method in addition the method classification accuracy is comparable to the two recent lbp extensions dominant lbp and completed lbp

on fuzzy inner product spaces and fuzzy co inner product spaces abstract the notions of fuzzy co norm and fuzzy co orthogonality are introduced by formulating the notion of a fuzzy co inner product space and their basic properties are studied

exploring space frequency co occurrences via local quantized patterns for texture representation local binary pattern lbp has shown its power in texture classification and face recognition however the lbp operator is performed in the original image space and it lacks deeper pixel interactions to capture a richer description in this paper we propose to explore space frequency co occurrences via local quantized patterns for texture representation the proposed method proceeds in two channels in each channel the multi resolution spatial maps are first obtained by specific spatial filtering and local frequency features spectral maps are subsequently extracted by applying the local fourier transform to the spatial map two types of quantization via global thresholding are employed to quantize the spatial and spectral maps into three and two levels respectively the quantized patterns are then jointly encoded to construct a space frequency co occurrence histogram finally the two channel histograms are combined to characterize the texture without resort to the texton based representation our method directly encodes the joint information in the space and frequency domains while preserving the robustness to image rotation illumination scale and viewpoint changes extensive experiments have been conducted on three well known texture databases and our method achieves the best classification results compared with state of the art approaches investigated highlightstwo channel space frequency feature spaces are designed to obtain invariant features two types of quantization via global thresholding are developed the joint space frequency coding is explored to capture a richer description our method outperforms the state of the art on three well known texture datasets

markov random field texture models we consider a texture to be a stochastic possibly periodic two dimensional image field a texture model is a mathematical procedure capable of producing and describing a textured image we explore the use of markov random fields as texture models the binomial model where each point in the texture has a binomial distribution with parameter controlled by its neighbors and number of tries equal to the number of gray levels was taken to be the basic model for the analysis a method of generating samples from the binomial model is given followed by a theoretical and practical analysis of the method s convergence examples show how the parameters of the markov random field control the strength and direction of the clustering in the image the power of the binomial model to produce blurry sharp line like and blob like textures is demonstrated natural texture samples were digitized and their parameters were estimated under the markov random field model a hypothesis test was used for an objective assessment of goodness of fit under the markov random field model overall microtextures fit the model well the estimated parameters of the natural textures were used as input to the generation procedure the synthetic microtextures closely resembled their real counterparts while the regular and inhomogeneous textures did not

subband coding of images subband coding has become quite popular for the source encoding of speech this paper presents a simple yet efficient extension of this concept to the source coding of images we specify the constraints for a set of two dimensional quadrature mirror filters qmf s for a particular frequency domain partition and show that these constraints are satisfied by a separable combination of one dimensional qmf s bits are then optimally allocated among the subbands to minimize the mean squared error for dpcm coding of the subbands also an adaptive technique is developed to allocate the bits within each subband by means of a local variance mask optimum quantization is employed with quantizers matched to the laplacian distribution subband coded images are presented along with their signal to noise ratios snr s the snr performance of the subband coder is compared to that of the adaptive discrete cosine transform dct vector quantization and differential vector quantization for bit rates of 0 67 1 0 and 2 0 bits per pixel for 256 256 monochrome images the adaptive subband coder has the best snr performance

rotation invariant multiresolution texture analysis using radon and wavelet transforms a new rotation invariant texture analysis technique using radon and wavelet transforms is proposed this technique utilizes the radon transform to convert the rotation to translation and then applies a translation invariant wavelet transform to the result to extract texture features a k nearest neighbors classifier is employed to classify texture patterns a method to find the optimal number of projections for the radon transform is proposed it is shown that the extracted features generate an efficient orthogonal feature space it is also shown that the proposed features extract both of the local and directional information of the texture patterns the proposed method is robust to additive white noise as a result of summing pixel values to generate projections in the radon transform step to test and evaluate the method we employed several sets of textures along with different wavelet bases experimental results show the superiority of the proposed method and its robustness to additive white noise in comparison with some recent texture analysis methods

from statistical knowledge bases to degrees of belief an intelligent agent will often be uncertain about various properties of its environment and when acting in that environment it will frequently need to quantify its uncertainty for example if the agent wishes to employ the expected utility paradigm of decision theory to guide its actions it will need to assign degrees of belief subjective probabilities to various assertions of course these degrees of belief should not be arbitrary but rather should be based on the information available to the agent this paper describes one approach for inducing degrees of belief from very rich knowledge bases that can include information about particular individuals statistical correlations physical laws and default rules we call our approach the random worlds method the method is based on the principle of indifference it treats all of the worlds the agent considers possible as being equally likely it is able to integrate qualitative default reasoning with quantitative probabilistic reasoning by providing a language in which both types of information can be easily expressed our results show that a number of desiderata that arise in direct inference reasoning from statistical information to conclusions about individuals and default reasoning follow directly from the semantics of random worlds for example random worlds captures important patterns of reasoning such as specificity inheritance indifference to irrelevant information and default assumptions of independence furthermore the expressive power of the language used and the intuitive semantics of random worlds allow the method to deal with problems that are beyond the scope of many other nondeductive reasoning systems

on fuzzy ideals and fuzzy bi ideals in semigroups abstract in this paper we give some properties of fuzzy ideals and fuzzy bi ideals of semigroups and characterize semigroups that are left duo left simple and semilattices of subsemigroups in terms of fuzzy ideals and fuzzy bi ideals

multiresolution gray scale and rotation invariant texture classification with local binary patterns presents a theoretically very simple yet efficient multiresolution approach to gray scale and rotation invariant texture classification based on local binary patterns and nonparametric discrimination of sample and prototype distributions the method is based on recognizing that certain local binary patterns termed uniform are fundamental properties of local image texture and their occurrence histogram is proven to be a very powerful texture feature we derive a generalized gray scale and rotation invariant operator presentation that allows for detecting the uniform patterns for any quantization of the angular space and for any spatial resolution and presents a method for combining multiple operators for multiresolution analysis the proposed approach is very robust in terms of gray scale variations since the operator is by definition invariant against any monotonic transformation of the gray scale another advantage is computational simplicity as the operator can be realized with a few operations in a small neighborhood and a lookup table experimental results demonstrate that good discrimination can be achieved with the occurrence statistics of simple rotation invariant local binary patterns

on the direct product of fuzzy subgroups abstract anthony and sherwood 1979 1980 redefined the fuzzy subgroup the idea introduced by rosenfeld 1971 foster 1979 introduced the concept of product fuzzy subgroups using rosenfeld s definition in this paper the product fuzzy subgroups will be redefined according to anthony and sherwood s definition

multiresolution statistical analysis of high resolution digital mammograms a multiresolution statistical method for identifying clinically normal tissue in digitized mammograms is used to construct an algorithm for separating normal regions from potentially abnormal regions that is small regions that may contain isolated calcifications this is the initial phase of the development of a general method for the automatic recognition of normal mammograms the first step is to decompose the image with a wavelet expansion that yields a sum of independent images each containing different levels of image detail when calcifications are present there is strong empirical evidence that only some of the image components are necessary for the purpose of detecting a deviation from normal the underlying statistic for each of the selected expansion components can be modeled with a simple parametric probability distribution function this function serves as an instrument for the development of a statistical test that allows for the recognition of normal tissue regions the distribution function depends on only one parameter and this parameter itself has an underlying statistical distribution the values of this parameter define a summary statistic that can be used to set detection error rates once the summary statistic is determined spatial filters that are matched to resolution are applied independently to each selected expansion image regions of the image that correlate with the normal statistical model are discarded and regions in disagreement suspicious areas are flagged these results are combined to produce a detection output image consisting only of suspicious areas this type of detection output is amenable to further processing that may ultimately lead to a fully automated algorithm for the identification of normal mammograms

level subgroups and union of fuzzy subgroups abstract in this paper we investigate the conditions under which a given fuzzy subgroup of a given group can or can not be realized as a union of two proper fuzzy subgroups moreover we formulate the notion of fuzzy subgroup generated by a given fuzzy subset by level subgroups we also give characterizations of fuzzy conjugate subgroups and fuzzy characteristic subgroups by their level subgroups also we discuss the relationship between level subgroups of a given fuzzy subgroup and the level subgroups of its homomorphic image

fuzzy topological vector spaces ii abstract some of the properties of fuzzy topological vector spaces are investigated also there are given necessary and sufficient conditions for a family of fuzzy sets in a vector space e to be the family of all neighborhoods of zero for a fuzzy linear topology

fuzzy finitely generated modules abstract we introduce the category of fuzzy modules and discuss the construction of fuzzy finitely generated modules characterizations of a sort of fuzzy modules in which the fuzzy value distribution is finite are partly obtained

fuzzy prime ideals of rings abstract the notions of fuzzy ideal and fuzzy prime ideal of a ring with truth values in a complete lattice satisfying the infinite meet distributive law are introduced which generalize the existing notions with truth values in the unit interval of real numbers a procedure to construct any fuzzy ideal from a family of ideals with certain conditions is established all fuzzy prime maximal ideals of a given ring are determined by establishing a one to one correspondence between fuzzy prime maximal ideals and the pairs p where p is a prime maximal ideal of the ring and is a prime element dual atom in the complete lattice

learning completed discriminative local features for texture classification we propose a novel feature representation method namely completed discriminative local features cdlf for texture classification the cdlf learn transformation matrices for texture images that maximize the mutual information between the local features and their category labels we propose an adaptive histogram accumulation aha algorithm which leverages the local contrast characteristic in the process of histogram accumulation the cdlf achieves higher accuracy than state of the art methods on three databases local binary patterns lbp and its variants have shown great potentials in texture classification tasks lbp like texture classification methods usually follow a two step feature extraction process in the first pattern encoding step the local structure information around each pixel is encoded into a binary string in the second histogram accumulation step the binary strings are accumulated into a histogram as the feature vector of a texture image the performances of these classification methods are closely related to the distinctiveness of the feature vectors in this paper we propose a novel feature representation method namely completed discriminative local features cdlf for texture classification the proposed cdlf improves the distinctiveness of lbp like feature vectors in two aspects in the pattern encoding stage we learn a transformation matrix using labeled data which significantly increases the discrimination power of the encoded binary strings in the histogram accumulation step we use an adaptive weight strategy to consider the contributions of pixels in different regions the experimental results on three challenging texture databases demonstrate that the proposed cdlf achieves significantly better results than previous lbp like feature representation methods for texture classification tasks

fuzzy invariant subgroups and fuzzy ideals abstract the purpose of this paper is to introduce some basic concepts of fuzzy algebra as fuzzy invariant subgroups fuzzy ideals and to prove some fundamental properties in particular it will give a characteristic of a field by a fuzzy ideal

fuzzy semiprime ideals in semigroups abstract in this paper we shall introduce the notion of fuzzy semiprimality in a semigroup which is an extension of semiprimality in it and characterize a semigroup that is a semilattice of simple semigroups in terms of fuzzy semiprimality

fuzzy cosets and some fuzzy radicals abstract an attempt is made to formulate fuzzy versions of jacobson and prime radicals of a ring certain basic results pertaining to the notions of jacobson and prime radicals of a ring are extended to the fuzzy setting in particular the following is obtained the jacobson radical prime radical of the ring of fuzzy cosets of in r is zero where r is a commutative ring with identity and is the fuzzy jacobson radical fuzzy prime radical of r

wavelet based level set evolution for classification of textured images we present a supervised classification model based on a variational approach this model is specifically devoted to textured images we want to get a partition of an image composed of texture regions separated by regular interfaces each kind of texture defines a class we use a wavelet packet transform to analyze the textures characterized by their energy distribution in each sub band in order to have an image segmentation according to the classes we model the regions and their interfaces by level set functions we define a functional on these level sets whose minimizers define the optimal classification according to texture a system of coupled pdes is deduced from the functional by solving this system each region evolves according to its wavelet coefficients and interacts with the neighbor regions in order to obtain a partition with regular contours experiments are shown on synthetic and real images

the dual of a fuzzy subspace abstract the concept of the dual of a fuzzy subspace is defined double dual fuzzy subspaces and linear maps of fuzzy subspaces are also studied

shape based invariant texture indexing this paper introduces a new texture analysis scheme which is invariant to local geometric and radiometric changes the proposed methodology relies on the topographic map of images obtained from the connected components of level sets this morphological tool providing a multi scale and contrast invariant representation of images is shown to be well suited to texture analysis we first make use of invariant moments to extract geometrical information from the topographic map this yields features that are invariant to local similarities or local affine transformations these features are invariant to any local contrast change we then relax this invariance by computing additional features that are invariant to local affine contrast changes and investigate the resulting analysis scheme by performing classification and retrieval experiments on three texture databases the obtained experimental results outperform the current state of the art in locally invariant texture analysis

frame representations for texture segmentation we introduce a novel method of feature extraction for texture segmentation that relies on multichannel wavelet frames and 2 d envelope detection we describe and compare two algorithms for envelope detection based on 1 the hilbert transform and 2 zero crossings we present criteria for filter selection and discuss quantitatively their effect on feature extraction the performance of our method is demonstrated experimentally on samples of both natural and synthetic textures

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

prime l fuzzy ideals and primary l fuzzy ideals abstract in this paper the concepts of a primary l fuzzy ideal and a prime l fuzzy ideal and p primary are introduced and some fundamental propositions proved in particular a structural theorem for a primary l fuzzy ideal belonging to a prime l fuzzy ideal is given

multiaspect target identification with wave based matched pursuits and continuous hidden markov models multiaspect target identification is effected by fusing the features extracted from multiple scattered waveforms these waveforms are characteristic of viewing the target from a sequence of distinct orientations classification is performed in the maximum likelihood sense which we show under reasonable assumptions can be implemented via a hidden markov model hmm we utilize a continuous hmm paradigm and compare its performance to its discrete counterpart the feature parsing is performed via wave based matched pursuits algorithm performance is assessed by considering measured acoustic scattering data from five similar submerged elastic targets

fuzzy vector spaces abstract let v denote a vector space over a field f and let a denote a fuzzy subspace of v over a fuzzy subfield k of f let x be a fuzzy subset of v such that x a and let x denote the intersection of all fuzzy subspaces of v over k that contain x and are contained in a we characterize the fuzzy subspace x of a over k we use this result to introduce the concept of fuzzy freeness of a fuzzy subset x of v and characterize it in terms of linear independence in the usual sense

bases of fuzzy vector spaces abstract let v be a vector space over a field f let a be a fuzzy subspace of v over f we give sufficient conditions for a to have a basis over a fuzzy subfield k of f we also show that if a has the sup property then a has a fully free basis over f but not necessarily a fully free basis over k

fuzzy vector spaces and fuzzy cosets abstract a fuzzy subspace is characterized by its level subspaces the algebraic nature of fuzzy subspaces under homomorphisms is studied certain conditions are obtained under which a given fuzzy subspace can or cannot be realized as a union of two fuzzy subspaces such that none is contained in the other the construction of a fuzzy subspace generated by a given fuzzy subset of a vector space is given the set of all the fuzzy cosets of a fuzzy subspace is shown to be a vector space and the dimension of the same is obtained a fuzzy quotient space is defined and an analogue of a consequence of the fundamental theorem of homomorphisms is obtained

correction to rotation and gray scale transform invariant texture classification using spiral resampling subband decomposition and hidden markov model this paper proposes a new texture classification algorithm that is invariant to rotation and gray scale transformation first we convert two dimensional 2 d texture images to one dimensional 1 d signals by spiral resampling then we use a quadrature mirror filter qmf bank to decompose sampled signals into subbands in each band we take high order autocorrelation functions as features features in different bands which form a vector sequence are then modeled as a hidden markov model bmm during classification the unknown texture is matched against all the models and the best match is taken as the classification result simulations showed that the highest correct classification rate for 16 kinds of texture was 95 14

on fuzzy bases of vector spaces abstract in this paper the concept of fuzzy basis of fuzzy vector space is studied the criterion for existence of fuzzy basis is proved any countable dimensional space has a fuzzy basis there are spaces without fuzzy basis

fuzzy hv submodules abstract in this paper we define the concept of fuzzy h v submodule of an h v module and study a few results in this respect we also consider the fundamental relation e defined on an h v module m and prove a fundamental theorem concerning the module m e

on pseudo fuzzy linear mappings in this paper we study a more general class of linear maps on fuzzy subsets of vector spaces than those on fuzzy subspaces we obtain a version of the fundamental theorem of homomorphisms which applies to these pseudo fuzzy linear maps in the case of fuzzy subspaces the results become those for fuzzy linear maps we introduce the notion of magnification of pseudo fuzzy linear mappings it is shown that this notion behaves well with respect to the fundamental theorem and with respect to the composition of mapping we note that the class of distribution functions of random variables naturally produces pseudo fuzzy linear mappings which are not fuzzy linear mappings we observe that pseudo fuzzy linear mappings are examples of gain relations we consider general properties of these relations as well as many other examples from these results additional properties of pseudo fuzzy linear mappings are obtained

zero one laws for sparse random graphs for random graph theorists see e g bollobas 1 for general reference p any constant is not the only not even the most interesting case rather they consider p p n a function approaching zero in their seminal paper erd6s and renyi 5 showed that for many interesting a there is a function p n which they called a threshold function so that if r n p n then f n r n a 0 while if p n r n then f n r n a 1 notation p r means lim p r 0 all limits are as n approaches infinity let us say p p n satisfies the zero one law if for all a in gra limf n p a 0 or 1 we shall partially characterize those p p n which satisfy the zero one law

fuzzy vector spaces under triangular norms abstract the object of this paper is to redefine fuzzy subspaces using the notion of a t norm and to obtain several results some of which are generalisations of the results of katsaras and liu 3

a theory for multiresolution signal decomposition the wavelet representation multiresolution representations are effective for analyzing the information content of images the properties of the operator which approximates a signal at a given resolution were studied it is shown that the difference of information between the approximation of a signal at the resolutions 2 sup j 1 and 2 sup j where j is an integer can be extracted by decomposing this signal on a wavelet orthonormal basis of l sup 2 r sup n the vector space of measurable square integrable n dimensional functions in l sup 2 r a wavelet orthonormal basis is a family of functions which is built by dilating and translating a unique function psi x this decomposition defines an orthogonal multiresolution representation called a wavelet representation it is computed with a pyramidal algorithm based on convolutions with quadrature mirror filters wavelet representation lies between the spatial and fourier domains for images the wavelet representation differentiates several spatial orientations the application of this representation to data compression in image coding texture discrimination and fractal analysis is discussed