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。     

Content-based image retrieval using visually significant point features

This paper presents a new image retrieval scheme using visually significant point features. The clusters of points around significant curvature regions (high, medium, and weak type) are extracted using a fuzzy set theoretic approach. Some invariant color features are computed from these points to evaluate the similarity between images. A set of relevant and non-redundant features is selected using the mutual information based minimum redundancy-maximum relevance framework. The relative importance of each feature is evaluated using a fuzzy entropy based measure, which is computed from the sets of retrieved images marked relevant and irrelevant by the users. The performance of the system is evaluated using different sets of examples from a general purpose image database. The robustness of the system is also shown when the images undergo different transformations.     

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。     

Examples of fuzzy metrics and applications

In this paper we present new examples of fuzzy metrics in the sense of George and Veeramani. The examples have been classified attending to their construction and most of the well-known fuzzy metrics are particular cases of those given here. In particular, novel fuzzy metrics, by means of fuzzy and classical metrics and certain special types of functions, are introduced. We also give an extension theorem for two fuzzy metrics that agree in its nonempty intersection. Finally, we give an application of this type of fuzzy metrics to color image processing. We propose a fuzzy metric that simultaneously takes into account two different distance criteria between color image pixels and we use this fuzzy metric to filter noisy images, obtaining promising results. This application is also illustrative of how fuzzy metrics can be used in other engineering problems.     

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.     

Unsupervised construction of fuzzy measures through self-organizing feature maps and its application in color image segmentation

The paper presents a framework for the segmentation of multi-dimensional images, e.g., color, satellite, multi-sensory images, based on the employment of the fuzzy integral, which undertakes the classification of the input features. The framework makes use of a self-organizing feature map, whereby the coefficients of the fuzzy measure are determined. This process is unsupervised and therefore constitutes one of the main contributions of the paper.The performance of the framework is shown by successfully realizing the segmentation of color images in two different applications. First, the features of the framework and its parameterization are analyzed by segmenting different images used as benchmark in image processing. Finally, the framework is applied in the segmentation of different images taken under difficult illumination conditions. The images serve the development of an automated cashier system, where the weak segmentation constitutes the first step for the identification of different market items. The presented framework succeeds in the segmentation of all these color images.     

Multiobjective improved spatial fuzzy c-means clustering for image segmentation combining Pareto-optimal clusters

In this paper, we propose a grayscale image segmentation method based on a multiobjective optimization approach that optimizes two complementary criteria (region and edge based). The region-based fitness used is the improved spatial fuzzy c-means clustering measure that is shown performing better than the standard fuzzy c-means (FCM) measure. The edge-based fitness used is based on the contour statistics and the number of connected components in the image segmentation result. The optimization algorithm used is the multiobjective particle swarm optimization (MOPSO), which is well suited to handle continuous variables problems, the case of FCM clustering. In our case, each particle of the swarm codes the centers of clusters. The result of the multiobjective optimization technique is a set of Pareto-optimal solutions, where each solution represents a segmentation result. Instead of selecting one solution from the Pareto front, we propose a method that combines all solutions to get a better segmentation. The combination method takes place in two steps. The first step is the detection of high-confidence points by exploiting the similarity between the results and the membership degrees. The second step is the classification of the remaining points by using the high-confidence extracted points. The proposed method was evaluated on three types of images: synthetic images, simulated MRI brain images and real-world MRI brain images. This method was compared to the most widely used FCM-based algorithms of the literature. The results demonstrate the effectiveness of the proposed technique.     

Rough fuzzy set based scale space transforms and their use in image analysis

In this paper we present a multi-scale method based on the hybrid notion of rough fuzzy sets, coming from the combination of two models of uncertainty like vagueness by handling rough sets and coarseness by handling fuzzy sets. Marrying both notions lead to consider, as instance, approximation of sets by means of similarity relations or fuzzy partitions. The most important features are extracted from the scale spaces by unsupervised cluster analysis, to successfully tackle image processing tasks. Here, we report some results achieved by applying the method to multi-class image segmentation and edge detection, but it can be shown to be successfully applied to texture discrimination problem too.     

Piecewise parametric polynomial fuzzy sets

We present a scheme for tractable parametric representation of fuzzy set membership functions based on the use of a recursive monotonic hierarchy that yields different polynomial functions with different orders. Polynomials of the first order were found to be simple bivalent sets, while the second order polynomials represent the typical saw shape triangles. Higher order polynomials present more diverse membership shapes. The approach demonstrates an enhanced method to manage and fit the profile of membership functions through the access to the polynomials order, the number and the multiplicity of anchor points as wells as the uniformity and periodicity features used in the approach. These parameters provide an interesting means to assist in fitting a fuzzy controller according to system requirements. Besides, the polynomial fuzzy sets have tractable characteristics concerning the continuity and differentiability that depend on the order of the polynomials. Higher order polynomials can be differentiated as many times as the order of the polynomial less the multiplicity of the anchor points. An algorithmic optimization approach using the steepest descent method is introduced for fuzzy controller tuning. It was shown that the controller can be optimized to model a certain output within small number of iterations and very small error margins. The mathematics generated by the approach is consistent and can be simply generalized to standard applications. The recursive propagation was noticed for its clarity and ease of calculations. Further, the degree of association between the sets is not limited to the neighbors as in traditional applications; instead, it may extend beyond.Such approach can be useful in dynamic fuzzy sets for adaptive modeling in view of the fact that the shape parameters can be easily altered to get different profiles while keeping the math unchanged. Hypothetically, any shape of membership functions under the partition of unity constraint can be produced. The significance of the mentioned characteristics of such modeling can be observed in the field of combinatorial and continuous parameter optimization, automated tuning, optimal fuzzy control, fuzzy-neural control, membership function fitting, adaptive modeling, and many other fields that require customized as well as standard fuzzy membership functions. Experimental work of different scenarios with diverse fuzzy rules and polynomial sets has been conducted to verify and validate our results.     

模糊择近原则在多目标容差设计中的应用

利用模糊数学中的择近原则,以容差-成本模型为基础,通过引入模糊数学中的隶属度函数和贴近度原则,结合实验并设计方法提出了一种模糊容差稳健优化设计方法,较好地解决了多目标容差设计的全局最优问题.最后通过一个实例验证了该方法的合理、有效性.     

毕达哥拉斯模糊软集的相似性测度及其应用

直觉模糊软集不能处理隶属度与非隶属度之和大于1的情况,且现有的直觉模糊软集的相似性测度只考虑了隶属度与非隶属度,忽视了犹豫度。针对以上问题,本文提出了一种基于隶属度、非隶属度以及犹豫度三个参数的毕达哥拉斯模糊软集的相似性测度和加权相似性测度。在为加权相似性测度的权重取值时,本文基于现有文献中直觉模糊熵存在的缺陷建立一种改进的直觉模糊熵,利用熵权法计算权重。分别讨论两相似性测度公式的性质,最后将两相似性侧度公式应用在建筑材料的模式识别问题中。     

Geometric Encoding of Color Images

Formal analysis and computer recognition of 2D color images is an important branch of modern computer geometry. However, the present methods, in spite of their longstanding high development, are not quite satisfactory and seem to be much worse than (unknown) algorithms used by our brain to analyze visual information. Almost all existing algorithms omit colors and deal with gray scale transformations only. However, in many cases color information is important and has to be proceeded. In this paper a fundamentally new method of encoding and analyzing color digital images is proposed. The main idea of this method is that a full-color digital image is encoded by a special two-dimensional surface in the three-dimensional space. After that the surface is analyzed by methods of differential geometry rather than traditional gradient-based or Hessian-based methods (like SIFT, GLOH, SURF, Canny operator, and many other well-known algorithms).     

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.     

A variational approach for restoring images corrupted by noisy blur kernels and additive noise

In this paper, we study a deblurring algorithm for distorted images by random impulse response. We propose and develop a convex optimization model to recover the underlying image and the blurring function simultaneously. The objective function is composed of 3 terms: the data‐fitting term between the observed image and the product of the estimated blurring function and the estimated image, the squared difference between the estimated blurring function and its mean, and the total variation regularization term for the estimated image. We theoretically show that under some mild conditions, the resulting objective function can be convex in which the global minimum value is unique. The numerical results confirm that the peak‐to‐signal‐noise‐ratio and structural similarity of the restored images by the proposed algorithm are the best when the proposed objective function is convex. We also present a proximal alternating minimization scheme to solve the resulting minimization problem. Numerical examples are presented to demonstrate the effectiveness of the proposed model and the efficiency of the numerical scheme.     

Confidence levels based Pythagorean fuzzy aggregation operators and its application to decision-making process

Pythagorean fuzzy set, an extension of the intuitionistic fuzzy set which relax the condition of sum of their membership function to square sum of its membership functions is less than one. Under these environment and by incorporating the idea of the confidence levels of each Pythagorean fuzzy number, the present study investigated a new averaging and geometric operators namely confidence Pythagorean fuzzy weighted and ordered weighted operators along with their some desired properties. Based on its, a multi criteria decision-making method has been proposed and illustrated with an example for showing the validity and effectiveness of it. A computed results are compared with the aid of existing results.     

Fuzzy goal programming approach to multilevel programming problems

The purpose of this paper is to propose a procedure for solving multilevel programming problems in a large hierarchical decentralized organization through linear fuzzy goal programming approach. Here, the tolerance membership functions for the fuzzily described objectives of all levels as well as the control vectors of the higher level decision makers are defined by determining individual optimal solution of each of the level decision makers. Since the objectives are potentially conflicting in nature, a possible relaxation of the higher level decision is considered for avoiding decision deadlock. Then fuzzy goal programming approach is used for achieving highest degree of each of the membership goals by minimizing negative deviational variables. Sensitivity analysis with variation of tolerance values on decision vectors is performed to present how the solution is sensitive to the change of tolerance values. The efficiency of our concept is ascertained by comparing results with other fuzzy programming approaches.     

基于Vague集的水电工程方案模糊综合评价

水利工程建设方案决策是多目标综合评价问题,系统指标信息具有复杂、多变,模糊、不确定等特点,采用Vague集相似度量评价模型构建水利工程建设方案综合决策模型,建立基于Vlague集的指标隶属度计算方法,构造基于Vague集相似度的多目标方案评价.针对建设方案决策评价指标的不确定性,通过肯定、踌躇、否定的Vague集相似度量概念延伸了传统模糊集的评价、分析方式.将方法应用于水利工程建设方案决策实例,取得较为满意的结果,表明了方法的合理可行性,为水利工程的建设方案评价提供了科学决策的新途径.     

区间灰数直觉模糊集及其G-TOPSIS模糊多属性决策方法

提出以区间灰数为隶属度、非隶属度和犹豫度的区间灰数直觉模糊集概念,定义了两个区间灰数直觉模糊集之间的距离.对于以灰直觉模糊数为属性值的模糊多属性决策,依据经典TOPSIS准则,提出了基于区间灰数直觉模糊集的模糊多属性决策方法G-TOPSIS.其包含两种方法:一是将区间灰数白化后,按直觉模糊集的TOPSIS方法进行;一是基于区间灰数直觉模糊距离的TOPSIS方法.示例分析表明了两种方法的有效性与一致性.