一种归一化图像的分形零水印算法

为了提高水印的稳定性和抗几何攻击能力,提出了一种结合图像归一化技术和分形理论的零水印算法。该算法首先利用归一化技术将原始图像映射到几何不变空间中,再以几何中心为中点提取归一化图像的重要区域;然后对该区域进行分形编码,由拼贴误差获得重要区域的边缘信息,即图像特征信息。最后用该信息与水印做相应的处理后即可得到提取水印的密钥矩阵。仿真实验结果表明,算法对常规图像处理和几何攻击具有较强的鲁棒性。     

一种基于包络控制的三角形收缩简化三维几何模型的新算法

本文算法先将原始模型上的每一点沿各自的法矢量方向偏移一定的距离，使整个原始模型收缩或扩张，生成内外两层包络．在构造包络时采用了一维搜索中的二分法来逼近最佳偏移值，以保证原始模型尽可能简化，然后依次选择原始模型上的一些三角形，将其三个顶点合并，收缩成一个三雏点．如果这样收缩简化后的模型依然位于两层包络围成的空间中．则收缩操作产生的误差被认为是可接受的．这也就保证了简化模型与原始模型外形上的相似．同时，本文还设计了一个演示系统，实现了这种算法．实验结果表明．通过这种算法简化三维几何模型后，简化模型不仅具有一定的压缩率，而且保留了原始几何模型的尖锐特征，两者在外形上十分相似。     

鲁棒的高阶双边滤波去噪算法

提出了一种统一的局部高阶双边滤波算法.与传统的双边滤波去噪算法不同,该算法通过引入鲁棒统计理论获得模型表面较为准确的几何属性;进而在曲率空间中对包含主曲率和Frenet标架的表面几何属性进行各向异性的滤波,既有利于保持模型的细节,又能保证曲面的光滑性;与此同时,优化各个顶点的法向;最后在优化后的几何属性引导下,在几何空间中进行高阶双边滤波去噪.实验结果表明,即使在大噪声的情况下,该算法仍然能够有效地保持模型细节,避免模型的收缩和顶点漂移.     

一类几何分形的表示模型

结合迭代函数系统和有限自动机,提出了几何分形的正则生成系统表示模型,并应用生成测试法和自动机归纳学习算法研究了一类几何分形的建模方法,实验结果表明,该模型是简单有效的。     

一种抗几何形变的数字水印方法的研究

基于迭代函数系统IFS的数字水印算法首先将数字水印信息转化成自相似分形集的IFS参数，然后给出由该IFS参数生成的自相似分形图对给定图像的嵌入和提取数字水印算法，最后，对该算法抗几何形变和JPEG压缩的顽健性进行了测试，结果表明基于IFS的数字水印算法具有很好的顽健性。     

利用计算机实现分形插值算法图形模拟

本文针对传统的计算几何方法对三维自然景物等较困难的现状。通过用计算机模拟实现分形几何中的分形插值算法。借助于公式和参数，能用少量的数据来刻画事物的大致轮廓或有关特征，为计算机模拟实际景物起到抛砖引玉的功能。     

基于分形几何的真实场景物体表示及应用

介绍了分形维数的概念,对利用自拟似分形和自仿射分形实现分形物体的绘制算法进行了描述。实现了场景中不规则自然景物几何形状的真实感表达。     

OpenGL在自然对象真实感图形生成中的应用

针对自然对象不规则的几何形状,介绍了分形几何在其数据建模方面的优势和基本思想,并以山脉地形为中心阐述了以fBm方法为基础的几何数据模型生成算法。探讨了OpenGL在以山脉地形为代表的自然对象真实感图形生成过程中的基本用法。对于在分形几何对象图形渲染过程中,OpenGL默认的法矢量计算函数无法正常运行的问题,引入了行之有效的求取算法。最后通过计算机模拟实验对整个过程算法过程予以验证。     

基于OpenGL的分形山三维模拟生成技术

采用OpenGL技术与VC＋＋6.0结合分形几何的方法来模拟绘制三维分形山。利用分形几何理论建立几何模型;依据分形插值理论设计相应的算法,得到模拟对象的几何数据,绘制出三维山和云的图形;利用OpenGL的图形处理及渲染功能对生成的图形进行色彩、光照、纹理等方面的处理,得到三维分形山的模拟图形。     

一种基于神经网络的分形几何图的产生与编码

本文提出用概率逻辑神经网产生一类自（互）相似（分形）图的方法，指出这类图能用一组压缩编码表示，给出快速寻找该编码的算法，既识别该分形几何图的算法，证明该编码是最优的，即码的长度最短，这些成果有希望在图象压缩和模式识别中得到应用。     

An integrated approach to fuzzy learning vector quantization andfuzzy c-means clustering

Derives an interpretation for a family of competitive learning algorithms and investigates their relationship to fuzzy c-means and fuzzy learning vector quantization. These algorithms map a set of feature vectors into a set of prototypes associated with a competitive network that performs unsupervised learning. Derivation of the new algorithms is accomplished by minimizing an average generalized distance between the feature vectors and prototypes using gradient descent. A close relationship between the resulting algorithms and fuzzy c-means is revealed by investigating the functionals involved. It is also shown that the fuzzy c-means and fuzzy learning vector quantization algorithms are related to the proposed algorithms if the learning rate at each iteration is selected to satisfy a certain condition     

竞争式Takagi-Sugeno模糊再励学习

针对连续空间的复杂学习任务,提出了一种竞争式Takagi-Sugeno模糊再励学习网络 (CTSFRLN),该网络结构集成了Takagi-Sugeno模糊推理系统和基于动作的评价值函数的再 励学习方法.文中相应提出了两种学习算法,即竞争式Takagi-Sugeno模糊Q-学习算法和竞争 式Takagi-Sugeno模糊优胜学习算法,其把CTSFRLN训练成为一种所谓的Takagi-Sugeno模 糊变结构控制器.以二级倒立摆控制系统为例,仿真研究表明所提出的学习算法在性能上优于 其它的再励学习算法.     

An adaptive fuzzy neural network for MIMO system modelapproximation in high-dimensional spaces

An adaptive fuzzy system implemented within the framework of neural network is proposed. The integration of the fuzzy system into a neural network enables the new fuzzy system to have learning and adaptive capabilities. The proposed fuzzy neural network can locate its rules and optimize its membership functions by competitive learning, Kalman filter algorithm and extended Kalman filter algorithms. A key feature of the new architecture is that a high dimensional fuzzy system can be implemented with fewer number of rules than the Takagi-Sugeno fuzzy systems. A number of simulations are presented to demonstrate the performance of the proposed system including modeling nonlinear function, operator's control of chemical plant, stock prices and bioreactor (multioutput dynamical system).     

Fuzzy classifications using fuzzy inference networks

In this paper, fuzzy inference models for pattern classifications have been developed and fuzzy inference networks based on these models are proposed. Most of the existing fuzzy rule-based systems have difficulties in deriving inference rules and membership functions directly from training data. Rules and membership functions are obtained from experts. Some approaches use backpropagation (BP) type learning algorithms to learn the parameters of membership functions from training data. However, BP algorithms take a long time to converge and they require an advanced setting of the number of inference rules. The work to determine the number of inference rules demands lots of experiences from the designer. In this paper, self-organizing learning algorithms are proposed for the fuzzy inference networks. In the proposed learning algorithms, the number of inference rules and the membership functions in the inference rules will be automatically determined during the training procedure. The learning speed is fast. The proposed fuzzy inference network (FIN) classifiers possess both the structure and the learning ability of neural networks, and the fuzzy classification ability of fuzzy algorithms. Simulation results on fuzzy classification of two-dimensional data are presented and compared with those of the fuzzy ARTMAP. The proposed fuzzy inference networks perform better than the fuzzy ARTMAP and need less training samples.     

使用模糊竞争Hopfield网络进行图像分割

针对传统自组织竞争学习方法的不足,将模糊竞争学习引入竞争Hopfield网络中,由此设计了一个用于图像分割的模糊竞争Hopfield网络,通过将图像空间映射到灰度特征空间,实现灰度特征集的模糊聚类,进而实现图像分割.实验结果表明:对于二值分割,与Ostu方法相比,此算法在分割效果和对噪声的自适应能力方面具有明显的优点.对于多类分割,此算法比目前的FCM(fuzzy C mean)算法的处理速度要快.     

A survey of fuzzy clustering algorithms for pattern recognition. II

For pt.I see ibid., p.775-85. In part I an equivalence between the concepts of fuzzy clustering and soft competitive learning in clustering algorithms is proposed on the basis of the existing literature. Moreover, a set of functional attributes is selected for use as dictionary entries in the comparison of clustering algorithms. In this paper, five clustering algorithms taken from the literature are reviewed, assessed and compared on the basis of the selected properties of interest. These clustering models are (1) self-organizing map (SOM); (2) fuzzy learning vector quantization (FLVQ); (3) fuzzy adaptive resonance theory (fuzzy ART); (4) growing neural gas (GNG); (5) fully self-organizing simplified adaptive resonance theory (FOSART). Although our theoretical comparison is fairly simple, it yields observations that may appear parodoxical. First, only FLVQ, fuzzy ART, and FOSART exploit concepts derived from fuzzy set theory (e.g., relative and/or absolute fuzzy membership functions). Secondly, only SOM, FLVQ, GNG, and FOSART employ soft competitive learning mechanisms, which are affected by asymptotic misbehaviors in the case of FLVQ, i.e., only SOM, GNG, and FOSART are considered effective fuzzy clustering algorithms.     

基于局部搜索的反向学习竞争粒子群优化算法

为提升粒子群优化算法在复杂优化问题,特别是高维优化问题上的优化性能,提出一种基于Solis&Wets局部搜索的反向学习竞争粒子群优化算法(solis and wets-opposition based learning competitive particle swarm optimizer with local se...     

A Family of Fuzzy Learning Algorithms for Robust Principal Component Analysis Neural Networks

In this paper, we analyze Xu and Yuille’s robust principal component analysis (RPCA) learning algorithms by means of the distance measurement in space. Based on the analysis, a family of fuzzy RPCA learning algorithms is proposed, which is robust against outliers. These algorithms can explicitly be understood from the viewpoint of fuzzy set theory, though Xu and Yuille’s algorithms were proposed based on a statistical physics approach. In the proposed algorithms, an adaptive learning procedure overcomes the difficulty of selection of learning parameters in Xu and Yuille’s algorithms. Furthermore, the robustness of proposed algorithms is investigated by using the theory of influence functions. Simulations are carried out to illustrate the robustness of these algorithms.      

Fuzzy algorithms for learning vector quantization

This paper presents the development of fuzzy algorithms for learning vector quantization (FALVQ). These algorithms are derived by minimizing the weighted sum of the squared Euclidean distances between an input vector, which represents a feature vector, and the weight vectors of a competitive learning vector quantization (LVQ) network, which represent the prototypes. This formulation leads to competitive algorithms, which allow each input vector to attract all prototypes. The strength of attraction between each input and the prototypes is determined by a set of membership functions, which can be selected on the basis of specific criteria. A gradient-descent-based learning rule is derived for a general class of admissible membership functions which satisfy certain properties. The FALVQ 1, FALVQ 2, and FALVQ 3 families of algorithms are developed by selecting admissible membership functions with different properties. The proposed algorithms are tested and evaluated using the IRIS data set. The efficiency of the proposed algorithms is also illustrated by their use in codebook design required for image compression based on vector quantization.     

On tree types of competitive learning algorithms with their comparisons and applications to MRI segmentation

This paper considers competitive learning networks using three types of hard, soft, and fuzzy learning schemes. The hard competitive learning algorithm is with the winner‐take‐all. The soft competition learning algorithm is with a stochastic relaxation technique using the Gibbs distribution as a dynamic neighborhood function. The fuzzy competition learning algorithm is with a fuzzy relaxation technique using fuzzy membership functions as kernel type neighborhood interaction functions. Some numerical examples are made for these three types of competitive learning schemes. The numerical results show that the fuzzy learning has better performance than hard and soft learning under the normal mixture data. We then present an application to magnetic resonance image segmentation. A real case of ophthalmology recommended by a neurologist with MR image data is examined in this paper. These competitive learning algorithms are used in segmenting the ophthalmological MRI data for reducing medical image noise effects with a learning mechanism. Based on the segmentation results, the fuzzy learning gives better performance than hard and soft learning so that the fuzzy competitive learning algorithm is recommended for use in MRI segmentation as an aid for support diagnoses. © 2010 Wiley Periodicals, Inc.