cores for feller semigroups with an invariant measure abstract let a i j 1 n a i j x d i j i 1 n b i x d i be an elliptic differential operator with unbounded coefficients on r n and assume that the associated feller semigroup t t t 0 has an invariant measure then t t t 0 extends to a strongly continuous semigroup t p t t 0 on l p l p r n for every 1 p we prove that under mild conditions on the coefficients of a the space of test functions c c r n is a core for the generator a p d p of t p t t 0 in l p for 1 p

cores for parabolic operators with unbounded coefficients abstract let a i j 1 n q i j s x d i j i 1 n b i s x d i be a family of elliptic differential operators with unbounded coefficients defined in r n 1 in m kunze l lorenzi a lunardi nonautonomous kolmogorov parabolic equations with unbounded coefficients trans amer math soc in press under suitable assumptions it has been proved that the operator g a d s generates a semigroup of positive contractions t p t in l p r n 1 for every 1 p where is an infinitesimally invariant measure of t p t here under some additional conditions on the growth of the coefficients of a which cover also some growths with an exponential rate at we provide two different cores for the infinitesimal generator g p of t p t in l p r n 1 for p 1 and we also give a partial characterization of d g p finally we extend the results so far obtained to the case when the coefficients of the operator a are t periodic with respect to the variable s for some t 0

global properties of invariant measures abstract we study global regularity properties of invariant measures associated with second order differential operators in r n under suitable conditions we prove global boundedness of the density sobolev regularity a harnack inequality and pointwise upper and lower bounds

color image watermark extraction based on support vector machines abstract this work proposes a novel watermarking technique called svm based color image watermarking sciw based on support vector machines svms for the authentication of color images to protect the copyright of a color image a signature a watermark which is represented by a sequence of binary data is embedded in the color image the watermark extraction issue can be treated as a classification problem involving binary classes the sciw method constructs a set of training patterns with the use of binary labels by employing three image features which are the differences between a local image statistic and the luminance value of the center pixel in a sliding window with three distinct shapes this set of training patterns is gathered from a pair of images an original image and its corresponding watermarked image in the spatial domain a quasi optimal hyperplane a binary classifier can be realized by an svm the sciw method utilizes this set of training patterns to train the svm and then applies the trained svm to classify a set of testing patterns following the results produced by the classifier the trained svm the sciw method retrieves the hidden signature without the original image during watermark extraction experimental results have demonstrated that the sciw method is sufficiently robust against several color image manipulations and that it outperforms other proposed methods considered in this work

spectrum of ornstein uhlenbeck operators in lp spaces with respect to invariant measures abstract let a i j 1 n q ij d ij i j 1 n b ij x j d i be a possibly degenerate ornstein uhlenbeck operator in r n and assume that the associated markov semigroup has an invariant measure we compute the spectrum of a in l p for 1 p

l p uniqueness for elliptic operators with unbounded coefficients in r n let a be an elliptic operator with unbounded and sufficiently smooth coefficients and let be a sub invariant measure of the operator a in this paper we give sufficient conditions guaranteeing that the closure of the operator a cc rn generates a sub markovian strongly continuous semigroup of contractions in lp rn applications are given in the case when a is a generalized schrodinger operator

on the ornstein uhlenbeck operator in spaces of continuous functions we study the realization of the ornstein uhlenbeck operator a in the space of the uniformly continuous and bounded functions in rn we prove that it generates a semigroup which is neither strongly continuous nor analytic but enjoys nice smoothing properties such properties are used to prove a schauder type theorem for the elliptic equation u au f

nonautonomous kolmogorov parabolic equations with unbounded coefficients we study a class of elliptic operators a with unbounded coeffi cients defined in i r d for some unbounded interval ir we prove that for any s 2 i the cauchy problem u s f 2 cb r d for the parabolic equation dtu au admits a unique bounded classical solution u this allows to associate an evolution family g t s with a in a natural way we study the main properties of this evolution family and prove gradient estimates for the function g t s f under suitable assumptions we show that there exists an evolution system of measures for g t s and we study the first properties of the extension of g t s to the l p spaces with respect to such measures

spatial multi scale gradient orientation consistency for place instance and scene category recognition gradient orientation consistency goc was proposed to encode local structure of images the goc feature is more robust to illumination variances the spatial multi scale goc histogram could achieve competitive performance for both place instance and scene category recognition this paper presents a novel image feature called gradient orientation consistency goc and an image representation based on the spatial multi scale goc histogram for place instance and scene category recognition gradient orientations have proven to be a more robust descriptor of the image information than intensities in the presence of illumination variances the goc feature is obtained by imposing a local binary pattern lbp type of non parametric operator to the gradient orientation codes hence captures the local structures in an image the histogram of goc further encodes the global structure of the entire image the multi scale analysis and spatial pyramid techniques are also used to enrich the longer range structure information resulting in a comprehensive image representation we apply this representation method for place instance and scene category recognition on five different datasets and show that it outperforms the state of the art

local binary features for texture classification local binary patterns lbp have emerged as one of the most prominent and widely studied local texture descriptors truly a large number of lbp variants has been proposed to the point that it can become overwhelming to grasp their respective strengths and weaknesses and there is a need for a comprehensive study regarding the prominent lbp related strategies new types of descriptors based on multistage convolutional networks and deep learning have also emerged in different papers the performance comparison of the proposed methods to earlier approaches is mainly done with some well known texture datasets with differing classifiers and testing protocols and often not using the best sets of parameter values and multiple scales for the comparative methods very important aspects such as computational complexity and effects of poor image quality are often neglected in this paper we provide a systematic review of current lbp variants and propose a taxonomy to more clearly group the prominent alternatives merits and demerits of the various lbp features and their underlying connections are also analyzed we perform a large scale performance evaluation for texture classification empirically assessing forty texture features including thirty two recent most promising lbp variants and eight non lbp descriptors based on deep convolutional networks on thirteen widely used texture datasets the experiments are designed to measure their robustness against different classification challenges including changes in rotation scale illumination viewpoint number of classes different types of image degradation and computational complexity the best overall performance is obtained for the median robust extended local binary pattern mrelbp feature for textures with very large appearance variations fisher vector pooling of deep convolutional neural networks is clearly the best but at the cost of very high computational complexity the sensitivity to image degradations and computational complexity are among the key problems for most of the methods considered highlightsa taxonomy and comprehensive survey of lbp variants characteristics of and connections between lbp variants are provided a comprehensive experimental evaluation of 32 lbp methods comparison of 32 lbp variants with 8 deep convnets features evaluation of robustness to rotation illumination scale and noise changes comparison of computational complexity of forty variants

support vector machines with genetic fuzzy feature transformation for biomedical data classification abstract in this paper we present a genetic fuzzy feature transformation method for support vector machines svms to do more accurate data classification given data are first transformed into a high feature space by a fuzzy system and then svms are used to map data into a higher feature space and then construct the hyperplane to make a final decision genetic algorithms are used to optimize the fuzzy feature transformation so as to use the newly generated features to help svms do more accurate biomedical data classification under uncertainty the experimental results show that the new genetic fuzzy svms have better generalization abilities than the traditional svms in terms of prediction accuracy

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

local multiple patterns based multiresolution gray scale and rotation invariant texture classification the local binary pattern lbp is a robust but computationally simple approach in texture analysis however lbp does not have enough information to discriminate among multiple patterns due to its binary patterns only comprising of 0s and 1s thus a multi resolution gray scale and rotation invariant texture classification based on local multiple patterns lmp is proposed in the paper the lmp extends binary patterns to multiple patterns which can preserve more structural information and be more suitable for image analysis including the analysis of flat image areas in which case lbp code is often a random value and thus unsuitable in addition several extensions to the lmp including multi resolution analysis with the uniform lmp with rotation invariance are presented the uniform lmp can be regarded as a gray scale and rotation invariant description in various applications and its discrete occurrence histogram over a region of image is proved to be a powerful invariant texture feature experimental results of multi resolution texture classification with support vector machine show that the proposed method obtains overall better performance than other common methods in several aspects of space resolution and gray scale variation rotation and noise

binary feature from intensity quantization and weakly spatial contextual coding for image search during the past few years a number of local binary feature descriptors for images have been proposed e g brief orb brisk and freak the binary descriptors have several advantages over the well established floating vector descriptors such as sift and surf for their fast computing speed and much low memory consumption nevertheless the binary descriptor still suffer from the poor performance in computer vision applications for its low discriminative power and hamming distance metric to improve the capability of binary descriptors some works focusing on the points selection pattern algorithm in the descriptor extraction are proposed these works mostly adopt more optimal selection pattern brisk and freak to enhance the performance of binary descriptors rather than random chosen pattern in our study however the points selection algorithm does not have much contributions for the promotion on performance therefore in this paper we try to solve the problem of low discriminative power and robustness through two novel methods intensity difference quantization and weakly spatial context coding the experimental results on the public datasets show that our method can significantly boost the performance of binary features and highly enhance the retrieval accuracy of the image search system even though our proposed method increases slightly memory usage and computing efficiency compared to the original binary descriptors

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

noise resistant local binary pattern with an embedded error correction mechanism local binary pattern lbp is sensitive to noise local ternary pattern ltp partially solves this problem both lbp and ltp however treat the corrupted image patterns as they are in view of this we propose a noise resistant lbp nrlbp to preserve the image local structures in presence of noise the small pixel difference is vulnerable to noise thus we encode it as an uncertain state first and then determine its value based on the other bits of the lbp code it is widely accepted that most of the image local structures are represented by uniform codes and noise patterns most likely fall into the non uniform codes therefore we assign the value of an uncertain bit hence as to form possible uniform codes thus we develop an error correction mechanism to recover the distorted image patterns in addition we find that some image patterns such as lines are not captured in uniform codes those line patterns may appear less frequently than uniform codes but they represent a set of important local primitives for pattern recognition thus we propose an extended noise resistant lbp enrlbp to capture line patterns the proposed nrlbp and enrlbp are more resistant to noise compared with lbp ltp and many other variants on various applications the proposed nrlbp and enrlbp demonstrate superior performance to lbp ltp variants

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

high order local ternary patterns with locality preserving projection for smoke detection and image classification it is a challenging task to recognize smoke from visual scenes due to large variations in the color texture shapes of smoke to improve detection accuracy we propose a novel feature extraction method by encoding high order directional derivatives at each pixel we first quantize the directional derivatives into ternary values to generate local ternary patterns ltp for the sake of simplification each ltp code is usually decomposed into an upper lbp code and a lower lbp code but this leads to loss of information hence we use joint histograms to preserve the co occurrence of upper and lower lbp codes for each order ltp then we concatenate all joint histograms from different orders to propose high order local ternary patterns hltp to improve computational efficiency we apply locality preserving projection lpp to reduce the dimension of hltp to further improve performance we present a noise resistant mechanism to remove noisy derivatives and then propose hltp based on magnitudes of noise removed derivatives and values of center pixels hltpmc finally the support vector machine svm is used for training and classification experiments on large scale smoke data sets show that our method can achieve detection rates above 94 with false alarm rates below 1 33 experiments on a multi class brodatz texture data set also achieved good performance with low dimensional features so our method has powerful discriminative capabilities and compact feature representation for multi class image classification

rapid transform based rotation invariant descriptor for texture classification under non ideal conditions rapid transform based descriptor is proposed for texture classification against rotation variations illumination variations as well as noise effect the proposed descriptor is based on the local circular neighborhood and the local feature vector is obtained by means of rapid transform the local feature vector is rotation invariant because of the cyclic shift invariance property of rapid transform combining several descriptors with different n r parameters the spatial multiscale is obtained feature selection approach is designed to improve the classification accuracy and reduce the computing cost the issue of noise is discussed and more robust descriptor based on rapid transform is introduced under noise condition texture classification experiments were carried out on the brodatz and outex databases and promising results are obtained from those experiments a rotation invariant descriptor is proposed for adapting non ideal conditions the proposed descriptor is based on rapid transform which is shift invariant feature selection approach is designed to improve the performance of the descriptor more robust descriptor is proposed under noise condition

a novel extended local binary pattern operator for texture analysis the local binary pattern lbp operator has been proved to be a theoretically simple yet very effective multiresolution statistical texture descriptor in terms of the characteristics of the local structure and has been applied in many areas however the extension to the lbp operator based on uniform patterns still has some shortcomings it discards some important texture information and is sensitive to noise a novel extended lbp operator for texture analysis is proposed in this paper the new lbp operator classifies and combines the nonuniform local patterns based on analyzing their structure and occurrence probability the new operator fully uses the texture information contained in the nonuniform local patterns which is discarded by the classical lbp operators and then becomes more robust against noise three experiments on the brodatz texture database show the performance improvement of this novel extended lbp operator

on the numerical evaluation of stress intensity factors for an interface crack of a general shape a numerical algorithm is presented for the problem of a crack along the interface of an elastic inclusion embedded in an elastic plane subjected to uniform stress at infinity the algorithm is based on a fredholm integral equation of the second kind and allows for fast and accurate solutions to geometries of great complexity in an example crack opening displacement and stress intensity factors are computed for a crack in the interface of an inclusion with nineteen protruding arms

fusion of color histogram and lbp based features for texture image retrieval and classification abstract the local binary pattern lbp operator and its variants play an important role as the image feature extractor in the textural image retrieval and classification the lbp based operator extracts the textural information of an image by considering the neighboring pixel values a single or join histogram can be derived from the lbp code which can be used as an image feature descriptor in some applications however the lbp based feature is not a good candidate in capturing the color information of an image making it is less suitable for measuring the similarity of color images with rich color information this work overcomes this problem by adding an additional color feature namely color information feature cif along with the lbp based feature in the image retrieval and classification systems the cif and lbp based feature adequately represent the color and texture features as documented in the experimental result the hybrid cif and lbp based feature presents a promising result and outperforms the existing methods over several image databases thus it can be a very competitive candidate in retrieval and classification application

median robust extended local binary pattern for texture classification local binary patterns lbp are considered among the most computationally efficient high performance texture features however the lbp method is very sensitive to image noise and is unable to capture macrostructure information to best address these disadvantages in this paper we introduce a novel descriptor for texture classification the median robust extended lbp mrelbp different from the traditional lbp and many lbp variants mrelbp compares regional image medians rather than raw image intensities a multiscale lbp type descriptor is computed by efficiently comparing image medians over a novel sampling scheme which can capture both microstructure and macrostructure texture information a comprehensive evaluation on benchmark data sets reveals mrelbp s high performance robust to gray scale variations rotation changes and noise but at a low computational cost mrelbp produces the best classification scores of 99 82 99 38 and 99 77 on three popular outex test suites more importantly mrelbp is shown to be highly robust to image noise including gaussian noise gaussian blur salt and pepper noise and random pixel corruption

associating visual textures with human perceptions using genetic algorithms this paper deals with an approach allowing to associate visual textures with given human perceptions hereby based on a forward model associating human perceptions for given visual textures the deduction of an reverse process is presented which is able to associate and characterize visual textures for given human perceptions for doing so we propose a constraint based genetic algorithm approach which is able to minimize a specific optimization problem containing constraints in form of band widths for valid individuals low level features extracted from textures in a population the constraints are determined by relationships between low level features characterizing textures in form of high dimensional approximation models additionally in each iteration step checking for valid individuals is carried out with a texture non texture classifier or by using a convex hull over a set of valid textures the whole approach is evaluated based on a real world texture set used as a start population in the genetic algorithm and by defining various kinds of human perceptions for which textures are sought represented by adjective vectors in the aesthetic space the generated individuals low level feature vectors have a high level of fitness they are quite close to the pre defined adjective vectors and a small distance to the initial population the textures synthesized based on the generated individuals are visualized and compared with textures synthesized by a time intensive direct texture mixing and re combination method based on a real world texture data base

a simple method for improving local binary patterns by considering non uniform patterns the basic idea behind lbp is that an image is composed of micropatterns a histogram of these micropatterns contains information about the local features in an image these micropatterns can be divided into two types uniform and non uniform in standard applications using lbp only the uniform patterns are used the non uniform patterns are considered in only a single bin of the histogram that is used to extract features in the classification stage non uniform patterns have undesirable characteristics they are of a high dimension partially correlated and introduce unwanted noise to offset these disadvantages we explore using random subspace well known to work well with noise and correlated features to train features based also on non uniform patterns we find that a stand alone support vector machine performs best with the uniform patterns and random subspace with histograms of 50 bins performs best with the non uniform patterns superior results are obtained when the two are combined based on extensive experiments conducted in several domains using several benchmark databases it is our conclusion that non uniform patterns improve classifier performance

shape based image retrieval using support vector machines fourier descriptors and self organizing maps image retrieval based on image content has become an important topic in the fields of image processing and computer vision in this paper we present a new method of shape based image retrieval using support vector machines svm fourier descriptors and self organizing maps a list of predicted classes for an input shape is obtained using the svm ranked according to their estimated likelihood the best match of the image to the top ranked class is then chosen by the minimum mean square error the nearest neighbors can be retrieved from the self organizing map of the class we employ three databases of 99 216 and 1045 shapes for our experiment and obtain prediction accuracy of 90 96 7 and 84 2 respectively our method outperforms some existing shape based methods in terms of speed and accuracy

pattern classification of dermoscopy images a perceptually uniform model pattern classification of dermoscopy images is a challenging task of differentiating between benign melanocytic lesions and melanomas in this paper a novel pattern classification method based on color symmetry and multiscale texture analysis is developed to assist dermatologists diagnosis our method aims to classify various tumor patterns using color texture properties extracted in a perceptually uniform color space in order to design an optimal classifier and to address the problem of multicomponent patterns an adaptive boosting multi label learning algorithm adaboost mc is developed finally the class label set of the test pattern is determined by fusing the results produced by boosting based on the maximum a posteriori map and robust ranking principles the proposed discrimination model for multi label learning algorithm is fully automatic and obtains higher accuracy compared to existing multi label classification methods our classification model obtains a sensitivity se of 89 28 specificity sp of 93 75 and an area under the curve auc of 0 986 the results demonstrate that our pattern classifier based on color texture features agrees with dermatologists perception

unsupervised segmentation of ultrasonic liver images by multiresolution fractal feature vector the feasibility of selecting fractal feature vector based on multiresolution analysis to segment suspicious abnormal regions of ultrasonic liver images is described in this paper the proposed feature extraction algorithm is based on the spatial frequency decomposition and fractal geometry segmentation of various liver diseases reveals that the fractal feature vector based on multiresolution analysis is trustworthy a quantitative characterization based on the proposed unsupervised segmentation algorithm can be utilized to establish an automatic computer aided diagnostic system as well to increase the visual interpretation capability of ultrasonic liver image for junior physicians off line learning software is developed to investigate the visual criteria