Fuzzy measures for color image retrieval

In this paper we present a scheme for fuzzy similarity based strategy to retrieve an image from a library of color images. Color features are among the most important features used in image database retrieval. Due to its compact representation and low complexity, direct histogram comparison is the most commonly used technique in measuring color similarity of images. A gamma membership function, derived from the Gamma distribution, has been proposed to find the membership values of the gray levels of the histogram. We present here an image retrieval scheme with some popular vector fuzzy distance measures using a gamma membership function for finding the membership values of the gray levels and evaluate the matching function to select the appropriate retrieval mechanism.     

基于模糊中值滤波的椒盐噪声去除方法

研究基于模糊中值滤波的椒盐噪声去除方法。通过比较图像各像素点的灰度值,定义基于图像梯度信息的各点被判别为噪声点的模糊隶属函数。利用此模糊隶属函数对中值滤波方法进行加权,得到了一种加权中值滤波器,可实现边缘处椒盐噪声的有效滤除。讨论这种模糊加权方法与其它先进滤波方法的结合途径,指出了其推广应用价值。最后利用数值实验验证本文方法的有效性,结果表明,相比于自适应中值滤波方法,本文方法得到的滤波图像在峰值信噪比及结构相似度方面均有明显提高。     

图像的多层次模糊增强与边缘提取

在单层次模糊增强算法中,某个灰度层次附近的边缘得到了增强,同时其它的一些边缘受到了抑制。为了同时增强图像中不同灰度层次的边缘信息,提出一种多层次模糊增强算法,并且给出了快速实现算法。此外,把多层次模糊增强算法应用于图像边缘提取中,取得了优于单层次模糊增强的效果。     

An edge driven wavelet frame model for image restoration

Wavelet frame systems are known to be effective in capturing singularities from noisy and degraded images. In this paper, we introduce a new edge driven wavelet frame model for image restoration by approximating images as piecewise smooth functions. With an implicit representation of image singularities sets, the proposed model inflicts different strength of regularization on smooth and singular image regions and edges. The proposed edge driven model is robust to both image approximation and singularity estimation. The implicit formulation also enables an asymptotic analysis of the proposed models and a rigorous connection between the discrete model and a general continuous variational model. Finally, numerical results on image inpainting and deblurring show that the proposed model is compared favorably against several popular image restoration models.     

New normalized nonlocal hybrid level set method for image segmentation

This article introduces a new normalized nonlocal hybrid level set method for image segmentation. Due to intensity overlapping, blurred edges with complex backgrounds, simple intensity and texture information, such kind of image segmentation is still a challenging task. The proposed method uses both the region and boundary information to achieve accurate segmentation results. The region information can help to identify rough region of interest and prevent the boundary leakage problem. It makes use of normalized nonlocal comparisons between pairs of patches in each region, and a heuristic intensity model is proposed to suppress irrelevant strong edges and constrain the segmentation. The boundary information can help to detect the precise location of the target object, it makes use of the geodesic active contour model to obtain the target boundary. The corresponding variational segmentation problem is implemented by a level set formulation. We use an internal energy term for geometric active contours to penalize the deviation of the level set function from a signed distance function. At last, experimental results on synthetic images and real images are shown in the paper with promising results.     

Fractional programming approach to fuzzy weighted average

This paper proposes a fractional programming approach to construct the membership function for fuzzy weighted average. Based on the -cut representation of fuzzy sets and the extension principle, a pair of fractional programs is formulated to find the -cut of fuzzy weighted average. Owing to the special structure of the fractional programs, in most cases, the optimal solution can be found analytically. Consequently, the exact form of the membership function can be derived by taking the inverse function of the -cut. For other cases, a discrete but exact solution to fuzzy weighted average is provided via an efficient solution method. Examples are given for illustration.     

A note on inverses in arithmetic with fuzzy numbers

Algorithms for systematical search of inverse in arithmetic operations with fuzzy numbers are discussed. The fuzzy number derived is considered either in a discrete representation of its support or described by the parameters of the corresponding membership function formula. Both algorithms are easy to be programmed for desk calculators.     

Twofold fuzzy sets and rough sets—Some issues in knowledge representation

This paper deals with the representation of sets where the membership of some elements may be ill-known rather than just a matter of degree as in a fuzzy set. The notion of a twofold fuzzy set is introduced when the relevant information for determining the membership status is incomplete. A twofold fuzzy set is made of a nested pair of fuzzy sets: the one which gathers the elements which more or less necessarily belong and the one which gathers the elements which more or less possibly belong. Twofold fuzzy sets are compared from a frontal and from a semantical point of view with other proposals and particularly with the notion of a rough set recently introduced by Pawlak. Set operations of twofold fuzzy sets are discussed and the cardinality of a twofold fuzzy set is defined. Twofold fuzzy relations are also introduced. Finally, various applications of twofold fuzzy sets in knowledge representation are briefly discussed.     

基于三角隶属函数和模糊熵的图像增强方法及其相关应用研究

鉴于图像增强技术在生活应用中的重要性,模糊技术在图像应用中的实用性和广泛性,提出了一种基于三角隶属函数和模糊熵的新的图像增强算法(T-FE增强算法),使用三角函数作为隶属函数,重构参数型对比增强算子,运用模糊熵最大原则选取阈值,计算快速,简单.并且将T-FE算法运用于图像分割,边缘检测.通过实验仿真表明,T-FE算法在进行图像处理时有较好效果.     

The Topological Gradient Method: From Optimal Design to Image Processing

The aim of this article is to review and extend the applications of the topological gradient to major image processing problems. We briefly review the topological gradient, and then present its application to the crack localization problem, which can be solved using the Dirichlet to Neumann approach. A very natural application of this technique in image processing is the inpainting problem, which can be solved by identifying the optimal location of the missing edges. Edge detection is of extreme importance, as edges convey essential information in a picture. A second natural application is then the image reconstruction. A class of image reconstruction problems is considered that includes restoration, demosaicing, segmentation and super-resolution. These problems are studied using a unified theoretical framework which is based on the topological gradient method. This tool is able to find the localization and orientation of the edges for blurred, low sampled, partially masked, noisy images. We review existing algorithms and propose new ones. The performance of our approach is compared with conventional image reconstruction processes.     

基于内容检索中的模糊处理

基于内容的检索是多媒体信息处理中的一个重要问题，图像、视频作为多媒体中最直观、最形象的内容，对它们的检索和查询是多媒体内容处理的一个重要方面。以往对图像检索往往借助于图像理解等领域发展起来的模式识别技术，但检索在很多方面又不同于模式识别，它通常并不需要精确匹配，而且由于检索中人一机交互性起着很重要的作用，使得在检索中有必要利用模糊的方法来提出查询要求，计算机也可以通过模糊相似性匹配来给出结果。本文提出了以信任度、可能性测度、权重有隶属函数概念作为模糊相似性匹配的基础来检索图像的方法。     

Image Denoising by a Local Clustering Framework

Images often contain noise due to imperfections in various image acquisition techniques. Noise should be removed from images so that the details of image objects (e.g., blood vessels, inner foldings, or tumors in the human brain) can be clearly seen, and the subsequent image analyses are reliable. With broad usage of images in many disciplines—for example, medical science—image denoising has become an important research area. In the literature, there are many different types of image denoising techniques, most of which aim to preserve image features, such as edges and edge structures, by estimating them explicitly or implicitly. Techniques based on explicit edge detection usually require certain assumptions on the smoothness of the image intensity surface and the edge curves which are often invalid especially when the image resolution is low. Methods that are based on implicit edge detection often use multiresolution smoothing, weighted local smoothing, and so forth. For such methods, the task of determining the correct image resolution or choosing a reasonable weight function is challenging. If the edge structure of an image is complicated or the image has many details, then these methods would blur such details. This article presents a novel image denoising framework based on local clustering of image intensities and adaptive smoothing. The new denoising method can preserve complicated edge structures well even if the image resolution is low. Theoretical properties and numerical studies show that it works well in various applications.     

Optimization of Fuzzy Controller for an Uninhabited Airplane Using Genetic Algorithms

The design of a fuzzy logic based controller for an uninhabited airplane using genetic algorithms for parameter optimization is illustrated. The airvehicle mission requires that a prescribed trajectory be followed with a satisfactory accuracy. Fuzzy control modules are present in each of the four control channels. Inputs are position and velocity errors. The parameters of the fuzzy controller are: trapezoidal membership functions, five linguistic values, and height defuzzification method associated with peak value. The scaling factors of the fuzzy controller are optimized by means of a genetic algorithm such that, a performance index, based on errors from a stationary flight path, is minimized. The genetic algorithm is based on binary genetic representation, an elitist roulette wheel selection technique and two genetic operators: mutation and crossover. The performance of the resulting optimal fuzzy controller is assessed through numerical simulation.     

Analysis of maximum total return in the continuous knapsack problem with fuzzy object weights

This paper proposes a parametric programming approach to analyze the fuzzy maximum total return in the continuous knapsack problem with fuzzy objective weights, in that the membership function of the maximum total return is constructed. The idea is based on Zadeh’s extension principle, α-cut representation, and the duality theorem of linear programming. A pair of linear programs parameterized by possibility level α is formulated to calculate the lower and upper bounds of the fuzzy maximum total return at α, through which the membership function of the maximum total return is constructed. To demonstrate the validity of the proposed procedure, an example studied by the previous studies is investigated successfully. Since the fuzzy maximum total return is completely expressed by a membership function rather than by a crisp value reported in previous studies, the fuzziness of object weights is conserved completely, and more information is provided for making decisions in real-world resource allocation applications. The generalization of the proposed approach for other types of knapsack problems is also straightforward.     

Fuzzy Relation Equations for Compression/Decompression Processes of Colour Images in the RGB and YUV Colour Spaces

We use particular fuzzy relation equations for compression/decompression of colour images in the RGB and YUV spaces, by comparing the results of the reconstructed images obtained in both cases. Our tests are made over well known images of 256×256 pixels (8 bits per pixel in each band) extracted from Corel Gallery. After the decomposition of each image in the three bands of the RGB and YUV colour spaces, the compression is performed using fuzzy relation equations of “min - →_t” type, where “t” is the Lukasiewicz t-norm and “→_t” is its residuum. Any image is subdivided in blocks and each block is compressed by optimizing a parameter inserted in the Gaussian membership functions of the fuzzy sets, used as coders in the fuzzy equations. The decompression process is realized via a fuzzy relation equation of max-t type. In both RGB and YUV spaces we evaluate and compare the root means square error (RMSE) and the consequentpeak signal to noise ratio (PSNR) on the decompressed images with respect to the original image under several compression rates.     

Evaluation of fuzzy linear regression models by comparing membership functions

Fuzzy linear regression models can provide an estimated fuzzy number that has a fuzzy membership function. If a point that has the highest membership value from the estimated fuzzy number is not within the support of the observed fuzzy membership function, a decision-maker can have high risk from the estimate. In this study a modification of fuzzy linear regression analysis based on a criterion of minimizing the difference of the fuzzy membership values between the observed and estimated fuzzy numbers is proposed. Two numerical examples are used to evaluate the fuzzy regression models.     

Image restoration with a high-order total variation minimization method

In this paper, we propose a fast and efficient way to restore blurred and noisy images with a high-order total variation minimization technique. The proposed method is based on an alternating technique for image deblurring and denoising. It starts by finding an approximate image using a Tikhonov regularization method. This corresponds to a deblurring process with possible artifacts and noise remaining. In the denoising step, a high-order total variation algorithm is used to remove noise in the deblurred image. We see that the edges in the restored image can be preserved quite well and the staircase effect is reduced effectively in the proposed algorithm. We also discuss the convergence of the proposed regularization method. Some numerical results show that the proposed method gives restored images of higher quality than some existing total variation restoration methods such as the fast TV method and the modified TV method with the lagged diffusivity fixed-point iteration.     

Multicriteria Decision-making Method Based on Risk Attitude under Interval-valued Intuitionistic Fuzzy Environment

Based on the feature of interval-valued intuitionistic fuzzy multi-attribute decision-making, in this thesis, a mentality parameter is used to reflect the decision makers’ risk attitude in determining of both a membership degree and a non-membership degree. Besides, with the mentality parameter, a new score function and accuracy function are proposed, which integrate the membership degree, the non-membership degree and the hesitancy degree into one index. Furthermore, to compare two interval-valued intuitionistic fuzzy numbers, a new ranking method is generated with the score function and accuracy function. Finally, a multi-attribute decision method under interval-valued intuitionistic fuzzy environment is developed in a linear weighted average operator. And promising numerical results show that this method is available.     

On multiresolution schemes using a stencil selection procedure: applications to ENO schemes

This paper is devoted to multiresolution schemes that use a stencil selection procedure in order to obtain adaptation to the presence of edges in the images. Since non adapted schemes, based on a centered stencil, are less affected by the presence of texture, we propose the introduction of some weight that leads to a more frequent use of the centered stencil in regions without edges. In these regions the different stencils have similar weights and therefore the selection becomes an ill-posed problem with high risk of instabilities. In particular, numerical artifacts appear in the decompressed images. Our attention is centered in ENO schemes, but similar ideas can be developed for other multiresolution schemes. A nonlinear multiresolution scheme corresponding to a nonlinear interpolatory technique is analyzed. It is based on a modification of classical ENO schemes. As the original ENO stencil selection, our algorithm chooses the stencil within a region of smoothness of the interpolated function if the jump discontinuity is sufficiently big. The scheme is tested, allowing to compare its performances with other linear and nonlinear schemes. The algorithm gives results that are at least competitive in all the analyzed cases. The problems of the original ENO interpolation with the texture of real images seem solved in our numerical experiments. Our modified ENO multiresolution will lead to a reconstructed image free of numerical artifacts or blurred regions, obtaining similar results than WENO schemes. Similar ideas can be used in multiresolution schemes based in other stencil selection algorithms.      

O型模糊数及其结构元表示方法

为研究平面或空间模糊几何问题的需要,在平面或空间模糊点的背景下,给出了O型模糊数的概念,它是一类二维实数域上的模糊集,同时给出了O型模糊数的二维模糊结构元表示方法.二维模糊数的结构元方法,可以使O型模糊数的运算变成普通实数与模糊结构元之间的运算,使得过去必须依赖扩张原理和表现定理来刻画的模糊数运算变得更加简单与直观,不仅仅为模糊分析计算的简化提供了工具,也为二维实数域上模糊分析理论与应用的研究开创了一条新的途径.