pairwise rotation invariant co occurrence local binary pattern designing effective features is a fundamental problem in computer vision however it is usually difficult to achieve a great tradeoff between discriminative power and robustness previous works shown that spatial co occurrence can boost the discriminative power of features however the current existing co occurrence features are taking few considerations to the robustness and hence suffering from sensitivity to geometric and photometric variations in this work we study the transform invariance ti of co occurrence features concretely we formally introduce a pairwise transform invariance pti principle and then propose a novel pairwise rotation invariant co occurrence local binary pattern pricolbp feature and further extend it to incorporate multi scale multi orientation and multi channel information different from other lbp variants pricolbp can not only capture the spatial context co occurrence information effectively but also possess rotation invariance we evaluate pricolbp comprehensively on nine benchmark data sets from five different perspectives e g encoding strategy rotation invariance the number of templates speed and discriminative power compared to other lbp variants furthermore we apply pricolbp to six different but related applications texture material flower leaf food and scene classification and demonstrate that pricolbp is efficient effective and of a well balanced tradeoff between the discriminative power and robustness

aggregating local image descriptors into compact codes this paper addresses the problem of large scale image search three constraints have to be taken into account search accuracy efficiency and memory usage we first present and evaluate different ways of aggregating local image descriptors into a vector and show that the fisher kernel achieves better performance than the reference bag of visual words approach for any given vector dimension we then jointly optimize dimensionality reduction and indexing in order to obtain a precise vector comparison as well as a compact representation the evaluation shows that the image representation can be reduced to a few dozen bytes while preserving high accuracy searching a 100 million image data set takes about 250 ms on one processor core

q oscillator realizations of the quantum superalgebras slq m n andospq m 2n realizations of the quantum superalgebras corresponding to thea m n b m n c n 1 andd m n series are given in terms of the creation and annihilation operators ofq deformed bose and fermi oscillators

finite dimensional irreducible representations of the quantum superalgebra u q gl n 1 it is shown that every finite dimensional irreducible module over the general linear lie superalgebragl n 1 can be deformed to an irreducible module ofu q gl n 1 aq analogue of the universal enveloping algebra ofgl n 1 the results are extended also to all kac modules which in the atypical cases remain indecomposible within each module expressions for the transformations of the gel fand zetlin basis under the action of the algebra generators are written down an analogoue of the poincare birkhoff witt theorem is formulated

finite dimensional representations of the quantum superalgebra uq gl 3 2 in a reduced uq gl 3 2 contains implies uq gl 3 1 contains implies uq gl 3 basis for generic q we give expressions for the transformations of all essentially typical finite dimensional modules of the hopf superalgebra uq ql 3 2 the latter is a deformation of the universal enveloping algebra of the lie superalgebra gl 3 2 the basis within each module is similar to the gel fand zetlin basis for gl 5 we write down expressions for the transformations of the basis under the action of the chevalley generators

induced representations of the multiparameter hopf superalgebras uuq gl m n and uuq sl m n we construct the induced holomorphic representations of the multiparameter hopf superalgebras uuq gl m n and uuq sl m n the first superalgebra we constructed earlier as the dual of the multiparameter quantum deformation of the supergroup gl m n the second superalgebra is a hopf subalgebra of the first for a special choice of the parameters the representations are labelled by m n integer numbers respectively m n 1 complex numbers and act in the space of formal power series of m n m n 1 2 non commuting variables of which mn are odd and the rest are even these variables generate a q deformation of a flag supermanifold of the supergroup gl m n respectively sl m n

texture characterization using shape co occurrence patterns texture characterization is a key problem in image understanding and pattern recognition in this paper we present a flexible shape based texture representation using shape co occurrence patterns more precisely texture images are first represented by a tree of shapes each of which is associated with several geometrical and radiometric attributes then four typical kinds of shape co occurrence patterns based on the hierarchical relationships among the shapes in the tree are learned as codewords three different coding methods are investigated for learning the codewords which can be used to encode any given texture image into a descriptive vector in contrast with existing works the proposed approach not only inherits the shape based method s strong ability to capture geometrical aspects of textures and high robustness to variations in imaging conditions but also provides a flexible way to consider shape relationships and to compute high order statistics on the tree to the best of our knowledge this is the first time that co occurrence patterns of explicit shapes have been used as a tool for texture analysis experiments on various texture and scene data sets demonstrate the efficiency of the proposed approach

character formulas for irreducible modules of the lie superalgebras sl m n kac distinguished between typical and atypical finite dimensional irreducible representations of the lie superalgebras sl m n and provided an explicit character formula appropriate to all the typical representations here the range of validity of some character formulas for atypical representations that have been proposed are discussed several of them are of the kac weyl type but then it is proved that all formulas of this type fail to correctly give the character of one particular atypical representation of sl 3 4 having ruled out therefore all such formulas a completely new extension of the kac weyl character formula is proposed the validity of this formula in the case of all covariant tensor irreducible representations is proved and some evidence in support of the conjecture that it covers all irreducible representations of sl m n is presented

decay bounds for the numerical quasiseparable preservation in matrix functions abstract given matrices a and b such that b f a where f z is a holomorphic function we analyze the relation between the singular values of the off diagonal submatrices of a and b we provide a family of bounds which depend on the interplay between the spectrum of the argument a and the singularities of the function in particular these bounds guarantee the numerical preservation of quasiseparable structures under mild hypotheses we extend the dunford cauchy integral formula to the case in which some poles are contained inside the contour of integration we use this tool together with the technology of hierarchical matrices h matrices for the effective computation of matrix functions with quasiseparable arguments

a statistical approach to texture classification from single images we investigate texture classification from single images obtained under unknown viewpoint and illumination a statistical approach is developed where textures are modelled by the joint probability distribution of filter responses this distribution is represented by the frequency histogram of filter response cluster centres textons recognition proceeds from single uncalibrated images and the novelty here is that rotationally invariant filters are used and the filter response space is low dimensional classification performance is compared with the filter banks and methods of leung and malik ijcv 2001 schmid cvpr 2001 and cula and dana ijcv 2004 and it is demonstrated that superior performance is achieved here classification results are presented for all 61 materials in the columbia utrecht texture database we also discuss the effects of various parameters on our classification algorithm such as the choice of filter bank and rotational invariance the size of the texton dictionary as well as the number of training images used finally we present a method of reliably measuring relative orientation co occurrence statistics in a rotationally invariant manner and discuss whether incorporating such information can enhance the classifier s performance

centre and representations of at roots of unity quantum groups at the roots of unity have the property that their centre is enlarged polynomial equations relate the standard deformed casimir operators and the new central elements these relations are important from a physical point of view since they correspond to relations between quantum expectation values of observables that have to be satisfied on all physical states in this paper we establish these relations in the case of the quantum lie superalgebra in the course of the argument we find and use a set of representations such that any relation satisfied on all the representations of the set is true in this set is a subset of the set of all the finite dimensional irreducible representations of which we classify and describe explicitly

on the composition factors of kac modules for the lie superalgebras sl m n in the classification of finite dimensional modules of lie superalgebras kac distinguished between typical and atypical modules kac introduced an induced module the so called kac module v with highest weight which was shown to be simple if is a typical highest weight if is an atypical highest weight the kac module is indecomposable and the simple module v can be identified with a quotient module of v in the present paper the problem of determining the composition factors of the kac modules for the lie superalgebra sl m n is considered an algorithm is given to determine all these composition factors and conversely an algorithm is given to determine all the kac modules containing a given simple module as a composition factor the two algorithms are presented in the form of conjectures and illustrated by means of detailed examples strong evidence in support of the conjectures is provided the combinatorial way in which the two algorithms are intertwined is both surprising and interesting and is a convincing argument in favor of the solution to the composition factor problem presented here

what are textons textons refer to fundamental micro structures in natural images and videos and are considered as the atoms of pre attentive human visual perception julesz 1981 unfortunately the word texton remains a vague concept in the literature for lack of a good mathematical model in this article we first present a three level generative image model for learning textons from texture images in this model an image is a superposition of a number of image bases selected from an over complete dictionary including various gabor and laplacian of gaussian functions at various locations scales and orientations these image bases are in turn generated by a smaller number of texton elements selected from a dictionary of textons by analogy to the waveform phoneme word hierarchy in speech the pixel base texton hierarchy presents an increasingly abstract visual description and leads to dimension reduction and variable decoupling by fitting the generative model to observed images we can learn the texton dictionary as parameters of the generative model then the paper proceeds to study the geometric dynamic and photometric structures of the texton representation by further extending the generative model to account for motion and illumination variations 1 for the geometric structures a texton consists of a number of image bases with deformable spatial configurations the geometric structures are learned from static texture images 2 for the dynamic structures the motion of a texton is characterized by a markov chain model in time which sometimes can switch geometric configurations during the movement we call the moving textons as motons the dynamic models are learned using the trajectories of the textons inferred from video sequence 3 for photometric structures a texton represents the set of images of a 3d surface element under varying illuminations and is called a lighton in this paper we adopt an illumination cone representation where a lighton is a texton triplet for a given light source a lighton image is generated as a linear sum of the three texton bases we present a sequence of experiments for learning the geometric dynamic and photometric structures from images and videos and we also present some comparison studies with k mean clustering sparse coding independent component analysis and transformed component analysis we shall discuss how general textons can be learned from generic natural images

a parametric texture model based on joint statistics of complex wavelet coefficients we present a universal statistical model for texture images in the context of an overcomplete complex wavelet transform the model is parameterized by a set of statistics computed on pairs of coefficients corresponding to basis functions at adjacent spatial locations orientations and scales we develop an efficient algorithm for synthesizing random images subject to these constraints by iteratively projecting onto the set of images satisfying each constraint and we use this to test the perceptual validity of the model in particular we demonstrate the necessity of subgroups of the parameter set by showing examples of texture synthesis that fail when those parameters are removed from the set we also demonstrate the power of our model by successfully synthesizing examples drawn from a diverse collection of artificial and natural textures

rotation invariant texture classification using feature distributions abstract a distribution based classification approach and a set of recently developed texture measures are applied to rotation invariant texture classification the performance is compared to that obtained with the well known circular symmetric autoregressive random field csar model approach a difficult classification problem of 15 different brodatz textures and seven rotation angles is used in experiments the results show much better performance for our approach than for the csar features a detailed analysis of the confusion matrices and the rotation angles of misclassified samples produces several interesting observations about the classification problem and the features used in this study

wavelet domain multifractal analysis for static and dynamic texture classification in this paper we propose a new texture descriptor for both static and dynamic textures the new descriptor is built on the wavelet based spatial frequency analysis of two complementary wavelet pyramids standard multiscale and wavelet leader these wavelet pyramids essentially capture the local texture responses in multiple high pass channels in a multiscale and multiorientation fashion in which there exists a strong power law relationship for natural images such a power law relationship is characterized by the so called multifractal analysis in addition two more techniques scale normalization and multiorientation image averaging are introduced to further improve the robustness of the proposed descriptor combining these techniques the proposed descriptor enjoys both high discriminative power and robustness against many environmental changes we apply the descriptor for classifying both static and dynamic textures our method has demonstrated excellent performance in comparison with the state of the art approaches in several public benchmark datasets

irreducible finite dimensional representations of the lie superalgebra gl n 1 in a gel fand zetlin basis all finite dimensional irreducible representations of the general linear lie superalgebra gl n 1 are studied for each representation a concept of a gel fand zetlin basis is defined expressions for the transformation of the basis under the action of the generators are written down

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

modeling the shape of the scene a holistic representation of the spatial envelope in this paper we propose a computational model of the recognition of real world scenes that bypasses the segmentation and the processing of individual objects or regions the procedure is based on a very low dimensional representation of the scene that we term the spatial envelope we propose a set of perceptual dimensions naturalness openness roughness expansion ruggedness that represent the dominant spatial structure of a scene then we show that these dimensions may be reliably estimated using spectral and coarsely localized information the model generates a multidimensional space in which scenes sharing membership in semantic categories e g streets highways coasts are projected closed together the performance of the spatial envelope model shows that specific information about object shape or identity is not a requirement for scene categorization and that modeling a holistic representation of the scene informs about its probable semantic category

finite dimensional irreducible representations of the quantum supergroup uq gl m n finite dimensional irreducible representations of the quantum supergroup uq gl m n at both generic q and q being a root of unity are investigated systematically within the framework of the induced module construction the representation theory is rather similar to that of gl m n at generic q but drastically different when q is a root of unity in the latter case atypicality conditions of highest weight irreducible representations irreps are substantially altered and such finite dimensional irreps arise that do not have highest weight and or lowest weight vectors as concrete examples the irreps of uq gl 2 1 are classified

finite dimensional representations of the quantum superalgebra u q gl n m and related q identities explicit expressions for the generators of the quantum superalgebrau q gl n m acting on a class of irreducible representations are given the class under consideration consists of all essentially typical representations for these a gel fand zetlin basis is known the verification of the quantum superalgebra relations to be satisfied is shown to reduce to a set ofq number identities

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