Wavelet packet neural networks for texture classification

Texture can be defined as a local statistical pattern of texture primitives in observer’s domain of interest. Texture classification aims to assign texture labels to unknown textures, according to training samples and classification rules. This paper describes the usage of wavelet packet neural networks (WPNN) for texture classification problem. The proposed schema composed of a wavelet packet feature extractor and a multi-layer perceptron classifier. Entropy and energy features are integrated wavelet feature extractor. The performed experimental studies show the effectiveness of the WPNN structure. The overall success rate is about 95%.     

An optimum feature extraction method for texture classification

Texture can be defined as a local statistical pattern of texture primitives in observer’s domain of interest. Texture classification aims to assign texture labels to unknown textures, according to training samples and classification rules. In this paper a novel method, which is an intelligent system for texture classification is introduced. It used a combination of genetic algorithm, discrete wavelet transform and neural network for optimum feature extraction from texture images. An algorithm called the intelligent system, which processes the pattern recognition approximation, is developed. We tested the proposed method with several texture images. The overall success rate is about 95%.     

A note on “A new method for ranking discovered rules from data mining by DEA”, and a full ranking approach

In a recent paper by Toloo et al. [Toloo, M., Sohrabi, B., & Nalchigar, S. (2009). A new method for ranking discovered rules from data mining by DEA. Expert Systems with Applications, 36, 8503–8508], they proposed a new integrated data envelopment analysis model to find most efficient association rule in data mining. Then, utilizing this model, an algorithm is developed for ranking association rules by considering multiple criteria. In this paper, we show that their model only selects one efficient association rule by chance and is totally depended on the solution method or software is used for solving the problem. In addition, it is shown that their proposed algorithm can only rank efficient rules randomly and will fail to rank inefficient DMUs. We also refer to some other drawbacks in that paper and propose another approach to set up a full ranking of the association rules. A numerical example illustrates some contents of the paper.     

Sorted random projections for robust rotation-invariant texture classification

This paper presents a simple, novel, yet very powerful approach for robust rotation-invariant texture classification based on random projection. The proposed sorted random projection maintains the strengths of random projection, in being computationally efficient and low-dimensional, with the addition of a straightforward sorting step to introduce rotation invariance. At the feature extraction stage, a small set of random measurements is extracted from sorted pixels or sorted pixel differences in local image patches. The rotation invariant random features are embedded into a bag-of-words model to perform texture classification, allowing us to achieve global rotation invariance. The proposed unconventional and novel random features are very robust, yet by leveraging the sparse nature of texture images, our approach outperforms traditional feature extraction methods which involve careful design and complex steps. We report extensive experiments comparing the proposed method to six state-of-the-art methods, RP, Patch, LBP, WMFS and the methods of Lazebnik et al. and Zhang et al., in texture classification on five databases: CUReT, Brodatz, UIUC, UMD and KTH-TIPS. Our approach leads to significant improvements in classification accuracy, producing consistently good results on each database, including what we believe to be the best reported results for Brodatz, UMD and KTH-TIPS.     

Texture classification using non-separable two-dimensional wavelets

In this paper, a new feature to the characterization of texture coarseness at multiple resolutions is proposed for texture classification. The feature is characterized by the extremum number of 2-D non-separable wavelet transforms (NSWT) estimated at the output of the corresponding filter bank. On a set of twelve Brodatz textures, the performances of texture classification based on pyramidal decomposition will be comparatively studied using the variance, entropy, extremum number and entropy of extremum as features, respectively. Experimental results show that the extremum number-based measure performs best among the features. In addition, we suggest that the wavelet coefficients of local extremum represent the original texture image instead of the entire wavelet coefficients. To explore the suitability of the NSWT for the texture characterization, the time varying, rotation invariant, and discriminatory characteristics are further investigated. It is shown that the textures have no time varying property and the NSWT is not rotation invariant to arbitrarily chosen degree of sample rotation. Finally, we show that the discriminatory characteristics of features do spread more in lower frequency subbands evaluated by a novel evaluation function based on genetic algorithms (GA).     

A complete characterization of statistical query learning with applications to evolvability

Statistical query (SQ) learning model of Kearns is a natural restriction of the PAC learning model in which a learning algorithm is allowed to obtain estimates of statistical properties of the examples but cannot see the examples themselves (Kearns, 1998 [29]). We describe a new and simple characterization of the query complexity of learning in the SQ learning model. Unlike the previously known bounds on SQ learning (Blum, et al., 1994; Bshouty and Feldman, 2002; Yang, 2005; Balcázar, et al., 2007; Simon, 2007 [9], [11], [42], [3], [37]) our characterization preserves the accuracy and the efficiency of learning. The preservation of accuracy implies that our characterization gives the first characterization of SQ learning in the agnostic learning framework of Haussler (1992) [23] and Kearns, Schapire and Sellie (1994) [31]. The preservation of efficiency is achieved using a new boosting technique and allows us to derive a new approach to the design of evolution algorithms in Valiant?s model of evolvability (Valiant, 2009 [40]). We use this approach to demonstrate the existence of a large class of monotone evolution algorithms based on square loss performance estimation. These results differ significantly from the few known evolution algorithms and give evidence that evolvability in Valiant?s model is a more versatile phenomenon than there had been previous reason to suspect.     

Using association rules as texture features

A new type of texture feature based on association rules is proposed in this paper. Association rules have been used in applications such as market basket analysis to capture relationships present among items in large data sets. It is shown that association rules can be adapted to capture frequently occurring local structures in images. Association rules capture both structural and statistical information, and automatically identifies the structures that occur most frequently and relationships that have significant discriminative power. Methods for classification and segmentation of textured images using association rules as texture features are described. Simulation results using images consisting of man made and natural textures show that association rule features perform well compared to other widely used texture features. It is shown that association rule features can distinguish texture pairs with identical first, second, and third order statistics, and texture pairs that are not easily discriminable visually     

A new method for expert target recognition system: Genetic wavelet extreme learning machine (GAWELM)

In last year’s, the expert target recognition has been become very important topic in radar literature. In this study, a target recognition system is introduced for expert target recognition (ATR) using radar target echo signals of High Range Resolution (HRR) radars. This study includes a combination of an adaptive feature extraction and classification using optimum wavelet entropy parameter values. The features used in this study are extracted from radar target echo signals. Herein, a genetic wavelet extreme learning machine classifier model (GAWELM) is developed for expert target recognition. The GAWELM composes of three stages. These stages of GAWELM are genetic algorithm, wavelet analysis and extreme learning machine (ELM) classifier. In previous studies of radar target recognition have shown that the learning speed of feedforward networks is in general much slower than required and it has been a major disadvantage. There are two important causes. These are: (1) the slow gradient-based learning algorithms are commonly used to train neural networks, and (2) all the parameters of the networks are fixed iteratively by using such learning algorithms. In this paper, a new learning algorithm named extreme learning machine (ELM) for single-hidden layer feedforward networks (SLFNs) Ahern et al., 1989, Al-Otum and Al-Sowayan, 2011, Avci et al., 2005a, Avci et al., 2005b, Biswal et al., 2009, Frigui et al., in press, Cao et al., 2010, Guo et al., 2011, Famili et al., 1997, Han and Huang, 2006, Huang et al., 2011, Huang et al., 2006, Huang and Siew, 2005, Huang et al., 2009, Jiang et al., 2011, Kubrusly and Levan, 2009, Le et al., 2011, Lhermitte et al., in press, Martínez-Martínez et al., 2011, Matlab, 2011, Nelson et al., 2002, Nejad and Zakeri, 2011, Tabib et al., 2009, Tang et al., 2011, which randomly choose hidden nodes and analytically determines the output weights of SLFNs, to eliminate the these disadvantages of feedforward networks for expert target recognition area. Then, the genetic algorithm (GA) stage is used for obtaining the feature extraction method and finding the optimum wavelet entropy parameter values. Herein, the optimal one of four variant feature extraction methods is obtained by using a genetic algorithm (GA). The four feature extraction methods proposed GAWELM model are discrete wavelet transform (DWT), discrete wavelet transform–short-time Fourier transform (DWT–STFT), discrete wavelet transform–Born–Jordan time–frequency transform (DWT–BJTFT), and discrete wavelet transform–Choi–Williams time–frequency transform (DWT–CWTFT). The discrete wavelet transform stage is performed for optimum feature extraction in the time–frequency domain. The discrete wavelet transform stage includes discrete wavelet transform and calculating of discrete wavelet entropies. The extreme learning machine (ELM) classifier is performed for evaluating the fitness function of the genetic algorithm and classification of radar targets. The performance of the developed GAWELM expert radar target recognition system is examined by using noisy real radar target echo signals. The applications results of the developed GAWELM expert radar target recognition system show that this GAWELM system is effective in rating real radar target echo signals. The correct classification rate of this GAWELM system is about 90% for radar target types used in this study.     

The existence theorems of solutions for generalized vector-valued variational-like inequalities

The purpose of this paper is to introduce a new kind of variational inequality, a ‘generalized vector variational-like inequality’ which includes several classical and well-known variational inequalities as special cases. As an application of the Knaster-Kuratowski-Mazurkiewicz principle as extended by Fan in 1961 [1], we prove that there exist solutions for our generalized vector variational-like inequality under reasonable hypotheses. These results generalize corresponding results given by Chen et al. in [2], Giannessi [3], Harker and Pang [4], Hartman and Stampacchia [5], Isac [6], Lee et al. [7], Noor [8], Saigal [9], Siddiqi et al. [10], and Yang [11].     

基于SVM算法和纹理特征提取的遥感图像分类

遥感图像分类是遥感图像处理领域中的一个重要的研究方向,传统的遥感图像分类方法根据像素值进行分类,忽视了遥感影像中丰富的纹理特征信息.小波分析通过引入宽度可变的窗口,可以同时对信号的局部信息进行频率域和时间域的变换.小波分析算法可以有效地提取出图像中的纹理特征信息.支持向量机算法是20世纪90年代提出的一种新的机器学习算法,通常被用来进行模式识别和分类.结合小波纹理提取算法,利用支持向量机进行遥感图像分类.研究结果表明,结合纹理特征的支持向量机分类的效果优于直接对灰度图像进行分类.     

An Algorithmic Approach to the Identification of Rigid Domains in Proteins

Many proteins undergo conformational changes to perform their functions. A simple mechanism of conformational change in proteins is a rigid domain motion, in which two parts of a structure move rigidly with respect to each other. The identification of rigid domains is therefore useful in understanding the structure-function relationship of proteins. Many algorithms, including those in [16], [22], [13], [10], and [19], have been developed to identify rigid domains. In this paper we complement these works by proposing a mathematical definition of a rigid domain. We argue that our definition more accurately captures the intuitive notion of rigid domain in the previous work, than the quantitative definition of a rigid domain introduced by Nichols et al. [19]. Furthermore, our definition admits a practical approximation algorithm. We can prove theoretical guarantee on the quality of the output of our algorithm. We implement a randomized version of our algorithm, and demonstrate its effectiveness on several known protein complexes.     

A Unifying and Rigorous Shape from Shading Method Adapted to Realistic Data and Applications

We propose a new method for the Lambertian Shape From Shading (SFS) problem based on the notion of Crandall-Lions viscosity solution. This method has the advantage of requiring the knowledge of the solution (the surface to be reconstructed) only on some part of the boundary and/or of the singular set (the set of the points at maximal intensity). Moreover it unifies in an unique mathematical formulation the works of Rouy et al. [34, 50], Falcone et al. [21], Prados et al. [46, 48, 49], based on the notion of viscosity solutions and the work of Dupuis and Oliensis [17] dealing with classical solutions and value functions. Also, it allows to generalize their results to the “perspective SFS” problem recently simultaneously introduced in [13,46,55]. While the theoretical part has been developed in [44], in this paper we give some stability results and we describe numerical schemes for the SFS based on this method. We construct provably convergent and robust algorithms. Finally, we apply our SFS method to real images and we suggest some real-life applications.     

Advances on multivariate image analysis for product quality monitoring

An increasing number of industrial applications requires visual inspection of products. Computer vision provides consolidated tools for reliable and fully automatic characterization and classification of the product quality at relatively low costs. One of such powerful tool is multivariate image analysis (MIA). In the MIA procedure as proposed in [1] is considered, that is well suited for texture analysis. To extend the performance of the MIA procedure in [1] to the analysis of wider spatial domains and to improve the algorithm from the computational point of view, a new formulation, named iMIA, has been recently proposed in [2]. The main contribution of the present paper is a modification of the iMIA algorithm that, by exploiting fast Fourier transform filtering, allows a considerable reduction of the computational time when spatial neighborhoods larger than few pixels are considered. Secondly, a different texture characterization with respect to [2] is proposed, to further extend the algorithm range of applicability. The characterization is based on histograms of textural features [3]. The algorithm is tested on two case studies in the field of texture analysis, namely, classification of rice quality, where the different characterization of texture allows a great improvement with respect to [2], and the characterization of nanofiber assemblies.     

结合微分特征和Haar小波分解的鲁棒纹理表达

针对传统的局部二值模式算子缺乏像素间深层次的相关性信息，且对图像中常见的模糊及旋转变化的鲁棒性较差的问题，提出了一种结合微分特征和Haar小波分解的鲁棒纹理表达算子。在微分特征通道上，通过各向同性的微分算子提取图像中的一阶和二阶微分特征，使图像的微分特征在本质上具有旋转不变性且对图像模糊具有较强的鲁棒性；基于小波变换在时域和频域同时具有良好的局部化的特点，在小波分解特征提取通道上采用多尺度的二维Haar小波分解提取图像中的模糊鲁棒特征；最后，串联两个通道上的特征直方图来描述图像的纹理特征。在特征判别性实验中，该算子在较复杂的UMD、UIUC和KTH-TIPS纹理库上的准确率分别达到了98.86%、98.2%和99.05%，与中值稳健扩展局部二值模式（MRELBP）算子相比，准确率分别提高了0.26%、1.32%和1.12%；在对旋转变化和图像模糊的鲁棒性分析实验中，该算子在仅存在旋转变化的TC10纹理库上的分类准确率达到99.87%，在添加了不同程度高斯模糊的TC11纹理库上的分类准确率降幅仅为6%；在计算复杂度实验中，该算子的特征维度仅为324维，在TC10纹理库上的平均特征提取时间为30.9 ms。实验结果表明，结合微分特征和Haar小波分解的方法具有很强的特征判别性，对旋转和模糊的鲁棒性较强，同时具有较低的计算复杂度，在样本数据较少的场合具有很好的适用性。     

Projective texture atlas construction for 3D photography

The use of attribute maps for 3D surfaces is an important issue in geometric modeling, visualization and simulation. Attribute maps describe various properties of a surface that are necessary in applications. In the case of visual properties, such as color, they are also called texture maps. Usually, the attribute representation exploits a parametrization g:U??²→?³ of a surface in order to establish a two-dimensional domain where attributes are defined. However, it is not possible, in general, to find a global parametrization without introducing distortions into the mapping. For this reason, an atlas structure is often employed. The atlas is a set of charts defined by a piecewise parametrization of a surface, which allows local mappings with small distortion. Texture atlas generation can be naturally posed as an optimization problem where the goal is to minimize both the number of charts and the distortion of each mapping. Additionally, specific applications can impose other restrictions, such as the type of mapping. An example is 3D photography, where the texture comes from images of the object captured by a camera [4]. Consequently, the underlying parametrization is a projective mapping. In this work, we investigate the problem of building and manipulating texture atlases for 3D photography applications. We adopt a variational approach to construct an atlas structure with the desired properties. For this purpose, we have extended the method of Cohen–Steiner et al. [6] to handle the texture mapping set-up by minimizing distortion error when creating local charts. We also introduce a new metric tailored to projective maps that is suited to 3D photography.     

结合微分特征和Haar小波分解的鲁棒纹理表达

针对传统的局部二值模式算子缺乏像素间深层次的相关性信息,且对图像中常见的模糊及旋转变化的鲁棒性较差的问题,提出了一种结合微分特征和Haar小波分解的鲁棒纹理表达算子。在微分特征通道上,通过各向同性的微分算子提取图像中的一阶和二阶微分特征,使图像的微分特征在本质上具有旋转不变性且对图像模糊具有较强的鲁棒性;基于小波变换在时域和频域同时具有良好的局部化的特点,在小波分解特征提取通道上采用多尺度的二维Haar小波分解提取图像中的模糊鲁棒特征;最后,串联两个通道上的特征直方图来描述图像的纹理特征。在特征判别性实验中,该算子在较复杂的UMD、UIUC和KTH-TIPS纹理库上的准确率分别达到了98.86%、98.2%和99.05%,与中值稳健扩展局部二值模式（MRELBP）算子相比,准确率分别提高了0.26%、1.32%和1.12%;在对旋转变化和图像模糊的鲁棒性分析实验中,该算子在仅存在旋转变化的TC10纹理库上的分类准确率达到99.87%,在添加了不同程度高斯模糊的TC11纹理库上的分类准确率降幅仅为6%;在计算复杂度实验中,该算子的特征维度仅为324维,在TC10纹理库上的平均特征提取时间为30.9 ms。实验结果表明,结合微分特征和Haar小波分解的方法具有很强的特征判别性,对旋转和模糊的鲁棒性较强,同时具有较低的计算复杂度,在样本数据较少的场合具有很好的适用性。     

On global stabilization of Burgers’ equation by boundary control

Although often referred to as a one-dimensional “cartoon” of Navier–Stokes equation because it does not exhibit turbulence, the Burgers equation is a natural first step towards developing methods for control of flows. Recent references include Burns and Kang [Nonlinear Dynamics 2 (1991) 235–262], Choi et al. [J. Fluid Mech. 253 (1993) 509–543], Ito and Kang [SIAM J. Control Optim. 32 (1994) 831–854], Ito and Yan [J. Math. Anal. Appl. 227 (1998) 271–299], Byrnes et al. [J. Dynam. Control Systems 4 (1998) 457–519] and Van Ly et al. [Numer. Funct. Anal. Optim. 18 (1997) 143–188]. While these papers have achieved tremendous progress in local stabilization and global analysis of attractors, the problem of global asymptotic stabilization has remained open. This problem is non-trivial because for large initial conditions the quadratic (convective) term – which is negligible in a linear/local analysis – dominates the dynamics. We derive nonlinear boundary control laws that achieve global asymptotic stability. We consider both the viscous and the inviscid Burgers’ equation, using both Neumann and Dirichlet boundary control. We also study the case where the viscosity parameter is uncertain, as well as the case of stochastic Burgers’ equation. For some of the control laws that would require the measurement in the interior of the domain, we develop the observer-based versions.     

Document segmentation using polynomial spline wavelets

Wavelet transforms have been widely used as effective tools in texture segmentation in the past decade. Segmentation of document images, which usually contain three types of texture information: text, picture and background, can be regarded as a special case of texture segmentation. B-spline wavelets possess some desirable properties such as being well localized in time and frequency, and being compactly supported, which make them an effective tool for texture analysis. Based on the observation that text textures provide fast-changed and relatively regular distributed edges in the wavelet transform domain, an efficient document segmentation algorithm is designed via cubic B-spline wavelets. Three-means or two-means classification is applied for classifying pixels with similar characteristics after feature estimation at the outputs of high frequency bands of spline wavelet transforms. We examine and evaluate the contributions of different factors to the segmentation results from the viewpoints of decomposition levels, frequency bands and wavelet functions. Further performance analysis reveals the advantages of the proposed method.     

Analysis of wavelet packet and statistical textures for object-oriented classification of forest-agriculture ecotones using SPOT 5 imagery

Textural features of high-resolution remote sensing imagery are a powerful data source for improving classification accuracy because using only spectral information is not sufficient for the classification of objects with within-field spectral variability. This study presents the methods of using an object-oriented texture analysis algorithm for improving high-resolution remote sensing imagery classification, including wavelet packet transform texture analysis, the grey-level co-occurrence matrix (GLCM) and local spatial statistics. Wavelet packet transform texture analysis, with the method of optimization and selection of wavelet texture for feature extraction, is a good candidate for object-oriented classification. Feature optimization is used to reduce the data dimensions in combinations of textural sub-bands and spectral bands. The result of the classification accuracy assessment indicates the improvement of texture analysis for object-oriented classification in this study. Compared with the traditional method that uses only spectral bands, the combination of GLCM homogeneity and spectral bands increases the overall accuracy from 0.7431 to 0.9192. Furthermore, wavelet packet transform texture analysis is the optimal method, increasing the overall accuracy to 0.9216 using a smaller data dimension. Local spatial statistical measures also increase the classification total accuracy, but only from 0.7431 to 0.8088. This study demonstrates that wavelet packet and statistical textures can be used to improve object-oriented classification; specifically, the texture analysis based on the multiscale wavelet packet transform is optimal for increasing the classification accuracy using a smaller data dimension.