离散分形布朗增量随机场模型在煤微结构定量分析中的应用

本文采用离散分形布朗增量随机场（ＤＦＢＩＲ）模型对煤样微观结构的显微图像做了分形定量研究，由于分表的表面必然会产生分形的灰度图像值，故通过提取图像各像点的灰度值，计算（ＤＦＢＩＲ）场模型的分形维数，得出了不同类型煤样微结构图像的分形维数，从而为扫描电镜用于定量研究煤结构的探索了新的途径。     

Texture features for classification of ultrasonic liver images

The classification of ultrasonic liver images is studied, making use of the spatial gray-level dependence matrices, the Fourier power spectrum, the gray-level difference statistics, and the Laws texture energy measures. Features of these types are used to classify three sets of ultrasonic liver images-normal liver, hepatoma, and cirrhosis (30 samples each). The Bayes classifier and the Hotelling trace criterion are employed to evaluate the performance of these features. From the viewpoint of speed and accuracy of classification, it is found that these features do not perform well enough. Hence, a new texture feature set (multiresolution fractal features) based on multiple resolution imagery and the fractional Brownian motion model is proposed to detect diffuse liver diseases quickly and accurately. Fractal dimensions estimated at various resolutions of the image are gathered to form the feature vector. Texture information contained in the proposed feature vector is discussed. A real-time implementation of the algorithm produces about 90% correct classification for the three sets of ultrasonic liver images.     

Exploiting the synergy between fractal dimension and lacunarity for improved texture recognition

Fractal dimension measures the geometrical complexity of images. Lacunarity being a measure of spatial heterogeneity can be used to differentiate between images that have similar fractal dimensions but different appearances. This paper presents a method to combine fractal dimension (FD) and lacunarity for better texture recognition. For the estimation of the fractal dimension an improved algorithm is presented. This algorithm uses new box-counting measure based on the statistical distribution of the gray levels of the “boxes”. Also for the lacunarity estimation, new and faster gliding-box method is proposed, which utilizes summed area tables and Levenberg-Marquardt method. Methods are tested using Brodatz texture database (complete set), a subset of the Oulu rotation invariant texture database (Brodatz subset), and UIUC texture database (partial). Results from the tests showed that combining fractal dimension and lacunarity can improve recognition of textures.     

利用改进分形特征对SAR图像目标检测方法的研究

改进分形特征是用指数小波在一个尺度上对检测图像滤波,针对特定大小目标用能量关系函数求得各像素点的分形特征。该文研究了利用改进分形特征对SAR图像进行目标检测的方法,分别使用改进特征与扩展分形特征对单一背景和复杂背景条件下的SAR图像进行目标检测,结果表明:改进分形特征能够在这两种背景条件下以更低虚警率检测出全部特定大小的目标,目标空间可分辨性好、位置指示准确;但在复杂背景条件下的检测虚警率比单一背景下的检测虚警率有所上升。     

Au-MgF2团簇薄膜TEM图像二值化阈值选取的研究

用透射电镜(TEM)观察磁控溅射制备Au-MgF2团簇薄膜的形貌,对团簇薄膜TEM图像采用灰度平均值法和Boltzmann拟合参数法进行二值化处理,并用分形理论表征薄膜中Au团簇的分布规律.结果显示:随着Au体积分数从6.0%增加到49.0%,用灰度平均值法所得分形维数由1.851增大到1.869,而由Boltzmann拟合参数法所得分形维数从1.669逐渐增大到1.941.两种方法所得分形参数均能表征Au团簇的尺寸和分布复杂程度随体积分数的变化规律,而由Boltzmann拟合参数法所得结果还能很好地表征不同体积分数薄膜Au团簇分布的差异性.     

基于分形理论的红外图像边缘检测

提出了利用分形理论进行红外图像边缘检测的方法,比较了根据单一分形维数和根据多尺度分形维数两种方法的边缘检测结果,从而得出：分表理论可以用于红外图像的边缘检测,并且根据多尺度维数的方法能获得较好的边缘检测结果。     

A Power Differentiation Method of Fractal Dimension Estimation for 2-D Signals

Fractal dimension has been used for texture analysis as it is highly correlated with the human perception of surface roughness. Several methods have been proposed for the estimation of the fractal dimension of an image. One of the most popular is via its power spectrum density, provided that it is modeled as a fractional Brownian function. In this paper, a new method, called the power differentiation method (PDM), for estimating the fractal dimension of a two-variable signal from its power spectrum density is presented. The method is first applied to noise-free data of known fractal dimension. It is also tested with noise-corrupted and quantized data. Particularly, in the case of noise-corrupted data, the modified power differentiation method (MPDM) is developed, resulting in more accurate estimation of the fractal dimension. The results obtained by the PDM and the MPDM are compared directly to those obtained using four other well-known methods of fractal dimension. Finally, preliminary results for the classification of ultrasonic liver images, obtained by applying the new method, are presented.     

真实孔径雷达海洋图像的分形特征分析

结合海洋雷达图像的电磁散射机理,采用小波分析方法对真实孔径雷达海洋图像的分形维数和特征进行分析,发现虽然海洋表面波具有分形的特征,但是海洋雷达图像在布拉格散射机制主导的情况下,不具备分形特征.为了准确计算雷达图像的分形维数,还对差分盒计数法、数学形态学方法和小波分析方法三种分形维数的计算方法进行了评估,通过对已知维数的模拟图像进行分形维数的计算,分析了三种方法的优缺点.     

Fractal feature analysis and classification in medical imaging

Following B.B. Mandelbrot's fractal theory (1982), it was found that the fractal dimension could be obtained in medical images by the concept of fractional Brownian motion. An estimation concept for determination of the fractal dimension based upon the concept of fractional Brownian motion is discussed. Two applications are found: (1) classification; (2) edge enhancement and detection. For the purpose of classification, a normalized fractional Brownian motion feature vector is defined from this estimation concept. It represented the normalized average absolute intensity difference of pixel pairs on a surface of different scales. The feature vector uses relatively few data items to represent the statistical characteristics of the medial image surface and is invariant to linear intensity transformation. For edge enhancement and detection application, a transformed image is obtained by calculating the fractal dimension of each pixel over the whole medical image. The fractal dimension value of each pixel is obtained by calculating the fractal dimension of 7x7 pixel block centered on this pixel.     

图像分形维数的差分盒方法的改进研究

分形可以提供大量关于自然景象复杂程度的信息,差分盒算法作为一种图像分形维数提取算法被广泛应用.针对差分盒算法计算精度不高和计算量大等问题,基于动态规划和残差分析的思想,提出了改进的差分盒分形维数计算方法.实验结果表明,该算法能够有效地区分不同类型的地貌,能够应用于遥感图像的地物分类.     

多孔电极材料表面微孔显微形貌数字图像分析研究

本文利用微空间三角形重构、图像灰度阈值分割及聚类统计等数字图像处理技术,实现了基于SEM像的多孔电极材料有效表面积、表面微孔统计分布及表面形貌分形维数的表征。该方法方便、快捷,可应用于多孔电极材料制备过程的在线监测/检测及结构优化。     

A novel approach to diagnose diabetes based on the fractal characteristics of retinal images

A novel diagnostic scheme to develop quantitative indexes of diabetes is introduced in this paper. The fractal dimension of the vascular distribution is estimated because we discovered that the fractal dimension of a severe diabetic patient's retinal vascular distribution appears greater than that of a normal human's. The issue of how to yield an accurate fractal dimension is to use high-quality images. To achieve a better image-processing result, an appropriate image-processing algorithm is adopted in this paper. Another important fractal feature introduced in this paper is the measure of lacunarity, which describes the characteristics of fractals that have the same fractal dimension but different appearances. For those vascular distributions in the same fractal dimension, further classification can be made using the degree of lacunarity. In addition to the image-processing technique, the resolution of original image is also discussed here. In this paper, the influence of the image resolution upon the fractal dimension is explored. We found that a low-resolution image cannot yield an accurate fractal dimension. Therefore, an approach for examining the lower bound of image resolution is also proposed in this paper. As for the classification of diagnosis results, four different approaches are compared to achieve higher accuracy. In this study, the fractal dimension and the measure of lacunarity have shown their significance in the classification of diabetes and are adequate for use as quantitative indexes.     

Texture-based classification of atherosclerotic carotid plaques

There are indications that the morphology of atherosclerotic carotid plaques, obtained by high-resolution ultrasound imaging, has prognostic implications. The objective of this study was to develop a computer-aided system that will facilitate the characterization of carotid plaques for the identification of individuals with asymptomatic carotid stenosis at risk of stroke. A total of 230 plaque images were collected which were classified into two types: symptomatic because of ipsilateral hemispheric symptoms, or asymptomatic because they were not connected with ipsilateral hemispheric events. Ten different texture feature sets were extracted from the manually segmented plaque images using the following algorithms: first-order statistics, spatial gray level dependence matrices, gray level difference statistics, neighborhood gray tone difference matrix, statistical feature matrix, Laws texture energy measures, fractal dimension texture analysis, Fourier power spectrum and shape parameters. For the classification task a modular neural network composed of self-organizing map (SOM) classifiers, and combining techniques based on a confidence measure were used. Combining the classification results of the ten SOM classifiers inputted with the ten feature sets improved the classification rate of the individual classifiers, reaching an average diagnostic yield (DY) of 73.1%. The same modular system was implemented using the statistical k-nearest neighbor (KNN) classifier. The combined DY for the KNN system was 68.8%. The results of this paper show that it is possible to identify a group of patients at risk of stroke based on texture features extracted from ultrasound images of carotid plaques. This group of patients may benefit from a carotid endarterectomy whereas other patients may be spared from an unnecessary operation.     

Fast calculation of co-occurrence matrix parameters for image segmentation

Image segmentation methods based only on grey level information are not suitable for pictures in which regions exhibit almost the same average grey level and differ only for local variations or texture. By extending these methods to textural features, better results are expected. Among textural features, those extracted from co-occurrence matrices are quite effective. A fast algorithm for the calculation of these parameters for windows centred on each pixel of the image is presented.<>     

基于分形理论的改进型二维最大熵红外图像分割算法

提出了一种基于分形理论的改进型二维最大熵红外图像阈值分割算法。该算法利用图像分形维数挖掘像素的空间分布信息,然后将原图像灰度及其分形维数映射图像灰度相结合组成二维随机向量,并构造出联合离散概率分布。在此基础上,以二维最大熵原则来确定一个最佳二维分割阈值,进而取得分割结果。实验结果表明,该算法在分割效果上优于传统的二维最大熵分割算法。     

Co-occurrence matrices for image analysis

The authors present a range of techniques for image segmentation and edge detection based on co-occurrence matrices. Co-occurrence matrices are described and transforms are defined which adapt to global image characteristics and emphasise the differences between typical and atypical image features using co-occurrence matrices as look-up tables. The techniques are extended by analysing the matrices and labelling them, with the result that a labelled matrix can be used to segment the regions of an image and to simultaneously detect prominent edges. Examples are given for a variety of images: synthetic, infrared, multispectral and temporal. It is also shown that the techniques presented can be integrated easily with a variety of postprocessing techniques such as hysteresis and relaxation labelling for enhanced performance     

Contribution of the fractal dimension to multiscale adaptive filtering of SAR imagery

Radar images can show great variability from pixel to pixel, which is an obstacle to effective processing. This variability, due to speckle created by the radar wave coherence, necessitates the use of more adapted filters. Previous studies have shown that multiresolution wavelet analysis yields better results but produces artefacts due to multiscale decomposition. This paper proposes a method that reduces these effects by introducing the fractal dimension. The resultant filter combines wavelet decomposition and variance change model based on the level of variance estimated by studying the fractal dimension of the image.     

基于分形特征的高频雷达目标检测技术

在现代化战争中,高频雷达起着越来越重要的作用,同时由于各种强杂波的干扰,对高频雷达目标(小目标)的检测需要寻找更好的算法.针对传统相干积累算法对高频雷达舰船目标检测的不足,文中提出了一种基于分形特征的高频雷达目标检测的新方法,利用合维数法计算分形维数,给出了自适应检测门限.在实测数据基础上对分形算法进行验证,实验结果表...     

Detection of radio transmitter turn-on transients

The use of a fractal dimension measure in conjunction with a Bayesian step change detector for the detection of radio transmitter turn-on transients is described. Fractal dimensions from radio transmission samples are calculated. The Bayesian change detector is then used to detect the change in the fractal trajectory in order to locate the transition point from channel noise to the start of a transient