作物诊断的叶片图像多重分形方法与建模
|
摘要
叶片是作物的重要生理器官之一,其图像能有效反映作物营养素缺失和病害种类及影响程度。在数字农业中,基于计算机和数学方法的叶片图像处理是研究上述问题的重要途径。如何通过数学算法和机器智能提取叶片图像的有效信息,成为了对作物营养素缺失、病害影响的叶片诊断的关键问题。目前的研究大多集中于作物叶片的颜色、形状特征,对叶片纹理信息的研究较少。而纹理是叶片固有的本质特性,不易受环境因素影响,只有当作物受营养缺失、病害影响时,其叶片灰度图像的纹理会有相应的改变,因此,作物叶片的纹理特征也是研究上述问题的理想对象。多重分形理论是一种描述图像纹理特征的重要手段,近年来在图像处理领域得到了很好的应用。本文利用多重分形理论,针对叶片图像不平稳的特点,提出了一种叶片灰度图像多重分形特征描述方法,得到了一些具有鲁棒性的纹理描述因子,并利用这些特征对上述问题展开了研究。旨在通过机器智能为作物叶片缺素和病害进行无损诊断奠定理论基础。
1.提出了图像平稳性的定义,给出了两种检测图像平稳性的方法。对图像平稳性的讨论是决定用何种多重分形方法提取图像特征的前提工作。由于标准多重分形算法都是基于图像平稳测度而提出的,对于非平稳测度将会得到不准确的结果。而受缺素和病害影响的叶片图像不同于其他图像,其局部灰度值易发生突变,可能产生不平稳测度。针对这一现象,定义了二维灰度图像的平稳性,提出了两种检测平稳性的方法,并利用一组由分形高斯噪声生成的图像和一组由分形布朗运动生成的图像验证了定义和检测方法的有效性。6种玉米病害叶片图像的平稳性检验结果表明它们都是非平稳的。
2.提出了基于多重分形去趋势波动分析(MF-DFA)的纹理图像特征描述方法。采用合适的多重分形特征提取方法是获取叶片图像纹理特征有效信息的保障。针对叶片图像非平稳性和标准多重分形不能解决非平稳测度的缺陷,基于多重分形去趋势波动分析(MF-DFA),提出了一些描述纹理图像特征的算法,获得了全局图像灰度值序列的广义Hurst指数h(q),二维图像表面全局广义Hurst指数H(q)和图像局部广义Hurst指数LHq等新的纹理描述符。一方面,与单一分形维数、标准多重分形谱、基于灰度共生矩阵法的角二阶矩、对比度、熵和自相关系数等传统的纹理特征因子进行对比实验,结果表明提出的h(q)和H(q)具有最好的抗噪性(平均误差<2%)、抗压缩性(平均误差<5%)、抗模糊性(平均误差<7%)。另一方面,与传统的基于差分盒子法的局部广义分形维数及基于三种容量测度的Holder指数进行分割对比实验,结果表明在相同的分类器下,提出的LHq具有最好的分割效果(对不同纹理图像的平均识别率>90%),且具有最好的抗噪性(平均误差率<10%)。
3.提出了基于局部多重分形去趋势波动分析(LMF-DFA)的图像分割方法。图像分割问题是正确反映叶片图像奇异区域,并对其进行缺素、病害诊断的关键问题。针对缺素、病害的叶片图像局部灰度不平稳特征,提出了一种基于LMF-DFA的图像分割方法。该方法以LHq为纹理描述符,以LHq构成子图的计盒分形维数f(LHq)为依据对指定区域进行分割。缺镁素、钾素的油菜叶片图像和玉米小斑病、灰斑病、弯孢菌叶斑病、圆斑病、锈病和褐斑病叶片图像的分割实验表明该算法能有效地分割叶片图像中的奇异区域。通过与现有流行的基于容量测度的多重分形谱分割法及经典的模糊C均值聚类法进行对比实验,结果表明所提方法分割效果最好,既能正确反映上述叶片缺素和病害区域的位置,也能准确识别非缺素、病害的区域,同时具有良好的抗噪性。
4.建立了基于叶片图像的多重分形特征的油菜氮营养诊断模型。基于叶片特征的模型构建是研究作物营养诊断的核心问题。一方面从定量的角度为不同施氮水平下的油菜氮含量建立了回归模型,利用叶片图像的多重分形特征参数为自变量预测氮含量的相对均方根误差最低为10%-20%。另一方面,对大田环境下采集的不同施氮水平下的油菜叶片进行了定性诊断。对基部、中部和顶部及三个部位混合样本进行分类识别。结果表明基于基部叶片和中部叶片的识别效果明显优于顶部叶片。对于混合叶片样本,在5折交叉检验方法下,以支持向量机核方法和随机森林为分类器的平均诊断准确率分别为94.03%和94.90%。
Leaf, as a vital organ of crops, can reflect growth conditions of the crops directly. The type of nutritional deficiency and plant disease can be mirrored by the images of the leaves. The images can also provide critical clues for identifying and diagnosing different level of nutrition. In the research of digital agriculture, it is an important way to solve above problems to process the leaf digital images based on mathematics and computers. How to get the useful information from the leaf images have become the key issues to locate, recognize and diagnose the singular region in the images impacted by the nutritional deficiency and diseases. Current studies are focused on the leaf color and shape characteristics, few studies on the texture information. However, as an inherent nature and characteristics of leaf, the leaf's texture remains relatively stable in the crop growth and less susceptible to outside influence. Meanwhile, the leaf's texture will change when the leaves are affected by nutrient deficiency and disease. By this token, the texture features of leaf image are ideal object for researching the above problems. Multifractal theory is an important tool to describe the texture features, which is widely applied in the field of image processing. Targeting at non-stationary trait of the leaf images, some robust texture descriptors are proposed in our paper by the multifractal theory to study the above problems. It should lay foundation for diagnosing the corps with nutritional deficiency and diseases nondestructively by machine intelligence.
A definition of image stationary and two methods of detecting the image stationary are proposed. The research of the images stationary problem is the premise concern in determining which multifractal technologies to extract the texture feature for the leaf images. Since the existed multifractal methods were proposed based on stationary measures, they cannot solve the non-stationary problems. Unlike the other images, the leaf images with nutritional deficiency and diseases easily lead to mutation of local gray values and may produce not smooth measures. In allusion to this phenomenon, we define the image stationary tentatively and present two methods of stationary detection based on the stationary of one-dimension series. The investigation by two groups of synthetic images generated by fractional Gaussian noise and fractaional Brown motion surface, respectively, shows that the definition and the detection methods of image stationary are effective. In the experiment of detecting the stationary for six corn disease leaf images by the above methods, it shows that they are all non-stationary.
Some texture characterization algorithms based on multifractal detrended fluctuation analysis (MF-DFA) is proposed. Employing right feature extraction method by the multifractal theory is the important safeguard for getting the useful texture information of the leaf images. Targeting at non-stationary trait of the leaf images and the problem of the non-stationary measures cannot be solved by standard multifractal analysis; we propose a texture characterization method based on multifractal detrended fluctuation analysis (MF-DFA). Three new texture descriptors, namely, the generalized Hurst exponent of gray series for global image, denoted as h(q), the generalized Hurst exponent of two-dimension surface for global image, denoted as H(q), and the generalized Hurst exponent of local two-dimension surface for each pixel in the image, denoted as LHq, are obtained. Next, we test the three exponents by two groups of experiments. On one hand, by comparing with the traditional texture descriptors, such as mono-fractal dimension and multifractal spectrum based on mono (multi)-fractal, four statistics calculated by gray occurrence matrix method, the results demonstrate that the proposed h(q) and H(q) have the best noise immunity (the average error is less than2%), best compression resistance (the average error is less than5%) and best anti-ambiguity (the average error is less than7%). The three kinds of errors are less than responding errors calculated by the other texture descriptors significantly. On the other hand, both the proposed texture descriptor LHq and other two multifractal indicators, which are Holder coefficients based on capacity measure and generalized multifractal dimension Dq based on multifractal differential box-counting (MDBC) method have been compared in our segmentation experiments. The first comparative experiment indicates that the segmentation results obtained by the proposed local multifractal detrended fluctuation exponent are as well as the MDBC-based Dq and superior to the Holder coefficients significantly. The results in the second comparative experiment of noise immunity demonstrate that the proposed method can distinguish the texture images more effectively and proazvide more robust segmentations than the MDBC-based Dq significantly.
A novel image segmentation algorithm based on local MF-DFA (LMF-DFA) is proposed. The image segmentation problem is the key problem for illustrating the singular regions in the leaf images. In allusion to non-stationary trait of the leaf images with nutritional deficiency and diseases, we propose a novel image segmentation algorithm based on LMF-DFA. In the proposed algorithm, the local generalized Hurst exponent LHq is calculated firstly. And then, box-counting dimension f(LHq) is calculated for the sub-images constituted by the LHq of some pixels, which come from a specific region. Consequently, series of f(LHq) of the different regions can be obtained. Finally, the singular regions are segmented according to the corresponding f(LHq). The method is used to locate the lesion regions for the six corn disease leaf images, namely, Southern corn leaf blight, Gray leaf spot, Curvularia leaf spot, Round leaf spot, Rust disease and Brown spot. Meanwhile, both the proposed method and other two segmentation methods--multifractal spectrum based and fuzzy C-means clustering have been compared for the six disease images. The results indicate that the proposed method can recognize the lesion regions more effectively and provide more robust segmentations.
A kind of diagnostic model for rapeseed nitrogen based on the multifractal feature of leaf image is proposed. Model construction is the kernel problem in researchingthe crop nutrition diagnosis based on leaf characteristic. On the one hand, we construct some regress models for the rapeseed nitrogen content under the different levels. The least relative square mean root error of predicting the nirtrogen is about10%-20%by using the multifractal parameters as the independent variables. On another hand, a qualitative diagnostic model is proposed for identifying different nitrogen level of rapeseed leaves. In the model, using the selected multifractal parameters as image characteristics, we take diagnosis analysis for base, middle and top of rapeseed plant with different nitrogen levels, which are collected from the field environment. The experiment result shows that the best diagnose accuracy comes from the base of the rapeseed leaves. It is explained that the base leaf is most sensitive to the nitrogen deficiency. In the diagnose of the mixed samples, the accuracy reaches94.03%和94.90%under support vector machines and kernel methods and random forests methods by the5-fold cross validation.
1.提出了图像平稳性的定义,给出了两种检测图像平稳性的方法。对图像平稳性的讨论是决定用何种多重分形方法提取图像特征的前提工作。由于标准多重分形算法都是基于图像平稳测度而提出的,对于非平稳测度将会得到不准确的结果。而受缺素和病害影响的叶片图像不同于其他图像,其局部灰度值易发生突变,可能产生不平稳测度。针对这一现象,定义了二维灰度图像的平稳性,提出了两种检测平稳性的方法,并利用一组由分形高斯噪声生成的图像和一组由分形布朗运动生成的图像验证了定义和检测方法的有效性。6种玉米病害叶片图像的平稳性检验结果表明它们都是非平稳的。
2.提出了基于多重分形去趋势波动分析(MF-DFA)的纹理图像特征描述方法。采用合适的多重分形特征提取方法是获取叶片图像纹理特征有效信息的保障。针对叶片图像非平稳性和标准多重分形不能解决非平稳测度的缺陷,基于多重分形去趋势波动分析(MF-DFA),提出了一些描述纹理图像特征的算法,获得了全局图像灰度值序列的广义Hurst指数h(q),二维图像表面全局广义Hurst指数H(q)和图像局部广义Hurst指数LHq等新的纹理描述符。一方面,与单一分形维数、标准多重分形谱、基于灰度共生矩阵法的角二阶矩、对比度、熵和自相关系数等传统的纹理特征因子进行对比实验,结果表明提出的h(q)和H(q)具有最好的抗噪性(平均误差<2%)、抗压缩性(平均误差<5%)、抗模糊性(平均误差<7%)。另一方面,与传统的基于差分盒子法的局部广义分形维数及基于三种容量测度的Holder指数进行分割对比实验,结果表明在相同的分类器下,提出的LHq具有最好的分割效果(对不同纹理图像的平均识别率>90%),且具有最好的抗噪性(平均误差率<10%)。
3.提出了基于局部多重分形去趋势波动分析(LMF-DFA)的图像分割方法。图像分割问题是正确反映叶片图像奇异区域,并对其进行缺素、病害诊断的关键问题。针对缺素、病害的叶片图像局部灰度不平稳特征,提出了一种基于LMF-DFA的图像分割方法。该方法以LHq为纹理描述符,以LHq构成子图的计盒分形维数f(LHq)为依据对指定区域进行分割。缺镁素、钾素的油菜叶片图像和玉米小斑病、灰斑病、弯孢菌叶斑病、圆斑病、锈病和褐斑病叶片图像的分割实验表明该算法能有效地分割叶片图像中的奇异区域。通过与现有流行的基于容量测度的多重分形谱分割法及经典的模糊C均值聚类法进行对比实验,结果表明所提方法分割效果最好,既能正确反映上述叶片缺素和病害区域的位置,也能准确识别非缺素、病害的区域,同时具有良好的抗噪性。
4.建立了基于叶片图像的多重分形特征的油菜氮营养诊断模型。基于叶片特征的模型构建是研究作物营养诊断的核心问题。一方面从定量的角度为不同施氮水平下的油菜氮含量建立了回归模型,利用叶片图像的多重分形特征参数为自变量预测氮含量的相对均方根误差最低为10%-20%。另一方面,对大田环境下采集的不同施氮水平下的油菜叶片进行了定性诊断。对基部、中部和顶部及三个部位混合样本进行分类识别。结果表明基于基部叶片和中部叶片的识别效果明显优于顶部叶片。对于混合叶片样本,在5折交叉检验方法下,以支持向量机核方法和随机森林为分类器的平均诊断准确率分别为94.03%和94.90%。
Leaf, as a vital organ of crops, can reflect growth conditions of the crops directly. The type of nutritional deficiency and plant disease can be mirrored by the images of the leaves. The images can also provide critical clues for identifying and diagnosing different level of nutrition. In the research of digital agriculture, it is an important way to solve above problems to process the leaf digital images based on mathematics and computers. How to get the useful information from the leaf images have become the key issues to locate, recognize and diagnose the singular region in the images impacted by the nutritional deficiency and diseases. Current studies are focused on the leaf color and shape characteristics, few studies on the texture information. However, as an inherent nature and characteristics of leaf, the leaf's texture remains relatively stable in the crop growth and less susceptible to outside influence. Meanwhile, the leaf's texture will change when the leaves are affected by nutrient deficiency and disease. By this token, the texture features of leaf image are ideal object for researching the above problems. Multifractal theory is an important tool to describe the texture features, which is widely applied in the field of image processing. Targeting at non-stationary trait of the leaf images, some robust texture descriptors are proposed in our paper by the multifractal theory to study the above problems. It should lay foundation for diagnosing the corps with nutritional deficiency and diseases nondestructively by machine intelligence.
A definition of image stationary and two methods of detecting the image stationary are proposed. The research of the images stationary problem is the premise concern in determining which multifractal technologies to extract the texture feature for the leaf images. Since the existed multifractal methods were proposed based on stationary measures, they cannot solve the non-stationary problems. Unlike the other images, the leaf images with nutritional deficiency and diseases easily lead to mutation of local gray values and may produce not smooth measures. In allusion to this phenomenon, we define the image stationary tentatively and present two methods of stationary detection based on the stationary of one-dimension series. The investigation by two groups of synthetic images generated by fractional Gaussian noise and fractaional Brown motion surface, respectively, shows that the definition and the detection methods of image stationary are effective. In the experiment of detecting the stationary for six corn disease leaf images by the above methods, it shows that they are all non-stationary.
Some texture characterization algorithms based on multifractal detrended fluctuation analysis (MF-DFA) is proposed. Employing right feature extraction method by the multifractal theory is the important safeguard for getting the useful texture information of the leaf images. Targeting at non-stationary trait of the leaf images and the problem of the non-stationary measures cannot be solved by standard multifractal analysis; we propose a texture characterization method based on multifractal detrended fluctuation analysis (MF-DFA). Three new texture descriptors, namely, the generalized Hurst exponent of gray series for global image, denoted as h(q), the generalized Hurst exponent of two-dimension surface for global image, denoted as H(q), and the generalized Hurst exponent of local two-dimension surface for each pixel in the image, denoted as LHq, are obtained. Next, we test the three exponents by two groups of experiments. On one hand, by comparing with the traditional texture descriptors, such as mono-fractal dimension and multifractal spectrum based on mono (multi)-fractal, four statistics calculated by gray occurrence matrix method, the results demonstrate that the proposed h(q) and H(q) have the best noise immunity (the average error is less than2%), best compression resistance (the average error is less than5%) and best anti-ambiguity (the average error is less than7%). The three kinds of errors are less than responding errors calculated by the other texture descriptors significantly. On the other hand, both the proposed texture descriptor LHq and other two multifractal indicators, which are Holder coefficients based on capacity measure and generalized multifractal dimension Dq based on multifractal differential box-counting (MDBC) method have been compared in our segmentation experiments. The first comparative experiment indicates that the segmentation results obtained by the proposed local multifractal detrended fluctuation exponent are as well as the MDBC-based Dq and superior to the Holder coefficients significantly. The results in the second comparative experiment of noise immunity demonstrate that the proposed method can distinguish the texture images more effectively and proazvide more robust segmentations than the MDBC-based Dq significantly.
A novel image segmentation algorithm based on local MF-DFA (LMF-DFA) is proposed. The image segmentation problem is the key problem for illustrating the singular regions in the leaf images. In allusion to non-stationary trait of the leaf images with nutritional deficiency and diseases, we propose a novel image segmentation algorithm based on LMF-DFA. In the proposed algorithm, the local generalized Hurst exponent LHq is calculated firstly. And then, box-counting dimension f(LHq) is calculated for the sub-images constituted by the LHq of some pixels, which come from a specific region. Consequently, series of f(LHq) of the different regions can be obtained. Finally, the singular regions are segmented according to the corresponding f(LHq). The method is used to locate the lesion regions for the six corn disease leaf images, namely, Southern corn leaf blight, Gray leaf spot, Curvularia leaf spot, Round leaf spot, Rust disease and Brown spot. Meanwhile, both the proposed method and other two segmentation methods--multifractal spectrum based and fuzzy C-means clustering have been compared for the six disease images. The results indicate that the proposed method can recognize the lesion regions more effectively and provide more robust segmentations.
A kind of diagnostic model for rapeseed nitrogen based on the multifractal feature of leaf image is proposed. Model construction is the kernel problem in researchingthe crop nutrition diagnosis based on leaf characteristic. On the one hand, we construct some regress models for the rapeseed nitrogen content under the different levels. The least relative square mean root error of predicting the nirtrogen is about10%-20%by using the multifractal parameters as the independent variables. On another hand, a qualitative diagnostic model is proposed for identifying different nitrogen level of rapeseed leaves. In the model, using the selected multifractal parameters as image characteristics, we take diagnosis analysis for base, middle and top of rapeseed plant with different nitrogen levels, which are collected from the field environment. The experiment result shows that the best diagnose accuracy comes from the base of the rapeseed leaves. It is explained that the base leaf is most sensitive to the nitrogen deficiency. In the diagnose of the mixed samples, the accuracy reaches94.03%和94.90%under support vector machines and kernel methods and random forests methods by the5-fold cross validation.
引文
[1]李锦卫.基于计算机视觉的水稻、油菜叶色-氮营养诊断机理与建模[D].长沙：湖南农业大学,2010,12
[2]L. A. Spomer. M. A. L. Smith, J. S. Sawwan. Rapid nondestructive measurement of chlorophyll content in leaves with non-uniform chlorophyll distribution [J]. Photosynth. Res.,1988,16:277-284.
[3]张浩,姚旭国,张小斌等.基于多光谱图像的水稻叶片叶绿素和籽粒氮素含量检测研究[J].中国水稻科学,2008,22(5)：555-558.
[4]祝锦霞,邓劲松,石媛媛等.基于水稻扫描叶片图像特征的氮素营养诊断研究[J].光谱学与光谱分析,2009,29(8)：2171-2175.
[5]祝锦霞,邓劲松,林芬芳等.水稻氮素机器视觉诊断最佳叶位和位点的选择研究[J].农业机械学报,2010,41(4)：179-183.
[6]管鹤卿.基于计算机视觉技术的油菜叶片信息研究[D].湖南农业大学硕士学位论文,2007
[7]李方一.基于数字图像处理技术的油菜叶片氮素营养检测研究[D].湖南农业大学硕士学位论文,2009
[8]张元.基于多光谱机器视觉的油菜氮素营养检测方法研究[D].镇江：江苏大学,硕士学位论文,2005.
[9]张艳诚,毛罕平,胡波.数字图像中作物病斑形状分形特征提取[J].微计算机信息,2007,23,11-3：295-297.
[10]龚国淑,张世熔.植物病害病斑形状的分形研究[J].植物保护,2002,28(6)：9-13.
[11]龚红菊,樊海明,姬长英.基于分形理论的水稻单产计算机视觉预测技术[J].农业机械学报.2010,41(8)：166-170.
[12]江海洋,张建,袁媛,等.基于MDMP-LSM算法的黄瓜叶片病斑分割方法[J].农业工程学报.2012,28(21)：142-148.
[13]温长吉,王生生,于合龙.基于改进蜂群算法优化神经网络的玉米病害图像分割[J].农业工程学报.2013,29(13)：142-149.
[14]贾建楠,吉海彦.基于病斑形状和神经网络的黄瓜病害识别[J].农业工程学报.2013,29(增1)：115-121.
[15]刁智华,：王欢,宋寅卯,等.复杂背景下棉花病叶害螨图像分割方法[J].农业工程学报.2013,29(5)：147-152.
[16]张静,王双喜,董晓志.基于温室植物叶片纹理的病害图像处理及特征值提取方法的研究[J].沈阳农业大学学报2006-06,37(3)：282-285
[17]ZHANG N, CHAISATTAPAGON C.Effective criteria for weed identification in wheat fields using machine vision [J]. ASAE,1995,38(3):965-974.
[18]田有文,王滨,唐晓明.基于纹理特征和支持向量机的玉米病害的识别[J].沈阳农业大学学报,2005-12,36(6)：730-732.
[19]袁媛,李淼,梁青.基于水平集的作物病叶图像分割方法[J].农业工程学报.2011,27(2)：208-212.
[20]Da-ke Wu, Chun-yan Xie, Cheng-wei Ma. The SVM Classification Leafminer-infected Leaves Based on Fractal Dimension Cybernetics and Intelligent Systems, IEEE,2008,9,147-151.
[21]梁淑敏,杨锦忠,李娜娜,等.基于图像处理的玉米分形维数及其种植密度效应评价[J].作物学报,2009,35(4):745-748.
[22]Yan LI, Chun-lei XIA, Yun-ki KIM. Pest Detection Method Using Multi-Fractal Analysis. Journal of Measurement Science and Instrum entation,2011,2(3):240-243.
[23]曹乐平,温芝元,沈陆明.基于色调分形维数的柑橘糖度和有效酸度检测[J].农业机械学报.2010,41(3)：143-148.
[24]曹乐平.基于周长面积分形维数的柑橘品种机器识别[J].农业工程学报,2010,26(2)：351-355.
[25]龚伟,颜晓元,蔡祖聪.长期施肥对小麦-玉米轮作土壤微团聚体组成和分形特征的影响[J].上壤学报,2011,48(6)：1141-1148.
[26]B. B. Mandelbrot, J. W. Van Ness. SIAM Rev.1968,4:422.
[27]Carr J. R, Miranda F. P. The semivariogram in comparison to the co-occurrence matrix for classification of image texture [J]. IEEE Transactions on Geoscience and Remote Sensing,1998,36(6):1945-1952.
[28]Clausi D. A, Yue B. Comparing co-occurrence probabilities and markov random fields for texture analysis of SAR seaice imagery [J]. IEEE Transactions on Geoscience and Remote Sensing,2004,42(1): 215-228.
[29]Ohanian P. P, DubesRC1 Performance evaluation for four classes of textural features[J].Pattern Recognition,1992,25(8):819-833.
[30]刘丽,匡纲要.图像纹理特征提取方法综述[J].中国图象图形学报.2009,14(4)：622-635.
[31]Pentland A P. Fractal based description of natural scenes [J]. IEEE Transactions on Pattern Analysis and Machine Intelligence,1984,6(6):661-674.
[32]Chen S S, Keller JM, Crow nover R M. On the calculation of fractal features from images [J]. IEEE Transactions on Pattern Recognition and Machine Intelligence,1993,15(10):1087-1090.
[33]Sarkar N, Chaudhuri B B. An efficient differential box-counting approach to compute fractal dimension of image [J].IEEE Transactions on Systems, Man, and Cybernetics,1994,24(1):115-120.
[34]谢文录,谢维信.几种分形参数估计方法的性能分析和比较[J].西安电子科技大学学报1997,24(2)：172-179.
[35]Tyler SW, Wheatcraft SW. Application of fractal mathematics to soil water retention estimation [J]. Soil Science Society of America Journal,1989,53:987-996.
[36]冯斌,汪懋华.基于颜色分形的水果计算机视觉分级技术[J].农业工程学报,2002,18(2)：141-144
[37]David A E, Llarion V M,Werner P, et al. Mechanisms of extensive spatiotemporal chaos in Rayleigh 2Benard convection [J]. Nature,2000,404(13):733-736
[38]赵莹,胡静,黎明.基于分形维数的图像纹理特征表示方法[J].上海电机学院学报.2011,14(1)：39-43
[39]B. B. Mandelbrot. The Fractal Geometry of Nature [M]. New York:W. H. Freeman,1983.
[40]工访,尚金城.基于多重分形理论的电力交易价格分时段特征分析[J].电力自动化设备,2013,33(1)：62-69
[41]F. Wang, G. P. Liao, X. Y. Zhou et.al. Multifractal detrended cross-correlation analysis for power markets [J]. Nonlinear Dynamics 72(1-2):353-363 (2013)
[42]Sun Xia, Chen Huiping, Wu Ziqin, et al. Multifractal analysis of Hang Seng index in Hong Kong stock market [J]. Physica A,2001,291:553-562.
[43]陈军.多重分形局部奇异性分析方法及其在矿产资源信息提取中的应用[D].武汉：中国地质大学,2007.
[44]李会方.多重分形理论及其在图象处理中应用的研究[D].西安：西北工业大学,2004.
[45]Kantelhardt J. W.2008 Fractal and multifractal time series, to be published in Springer Encyclopaedia of Complexity and System Science preprint arXiv:0804.0747(2008)
[46]ZANG Bao-jiang, SHANG Peng-jian. Multi-fractal analysis of the Yellow River flows [J].Chinese Physics,2007,3(16):565-569.
[47]DING Liang-jin, PENG Hu, et al. Multifractal analysisof human heart beat in sleep [J]. Chin Phys Lett, 2007,24(7):2149-2152.
[48]Zhou L.Q., Yu Z.G.,Deng J.Q.,Anh V.and Long S.C.,A fractal method to distinguish coding and non-coding sequences in a complete genome based on a number sequence representation, J.Theor.Biol., 2005,232:559-567.
[49]Ma D.K,Wu M.and Liu C.J.,The entropies and multifractal spectrum of some compact systems [J], Chaos, Solitons & Fractals,2008,38:840-851.
[50]M Sadegh Movahed, G R Jafari, F Ghasemi, Sohrab Rahvar and M Reza Rahimi Tabar. Multifractal detrended fluctuation analysis of sunspot time series [J]. Journal of Statistical Mechanics:Theory and Experiment.2006,2:1-15.
[51]Jian-Yi Yang, Zu-Guo Yu a,b, Vo Anh. Clustering structures of large proteins using multifractal analyses based on a 6-letter model and hydrophobicity scale of amino acids [J]. Chaos, Solitons and Fractals 40 (2009) 607-620.
[52]Kapan L M, Ku o C-C. Extending self-similarity for fractional Brownian motion [J]. IEEE Transactions on Signal Processing,1994,42(12):3526-3530.
[53]Kaplan L M. Extend fractal analysis for texture classification and segmentation [J]. IEEE Transactions on Image Processing,1999,8(11):1572-1585.
[54]蒋爱平,杨悦华,杨兴全.基于多重加权法的多重分形图像分割研究[J].中国图象图形学报,2007,12(10)：1889-1992.
[55]刘元永,罗晓曙,陈全斌.多重分形谱在叶片图像处理中的应用[J].计算机工程与应用.2008, 44(28)：190-192.
[56]Wendt H, Roux S G, Jaffard S, et al. Wavelet leaders and bootstrap for multifractal analysis of images [J]. Signal Processing.2009,89:1100-1114.
[57]Ouahabi A. Multifractal analysis for texture characterization:A new approach based on DWT [J]. ISSPA 2010:698-703
[58]Xu P F, Yao H X, Ji R R, et al. A robust texture descriptor using multifractal analysis with Gabor filter [C]. In 2010 Proceedings of the Second International Conference on Internet Multimedia Computing and Service (ICIMCS'10).
[59]李会方,俞卞章.一种基于多重分形新特征的图像分割算法[J].光学精密程,2003,11(6)：627-631
[60]Lopes R, Dubois P, Bhouri I, et al. Local fractal and multifractal features for volumic texture characterization [J]. Pattern Recognition,2011,44(8):1690-1697
[61]Yong Xia, Dagan Feng, Rongchun Zhao. Morphology-Based Multifractal Estimation for Texture Segmentation [J]. IEEE Transactions on Image Processing,2006,15(3):614-622.
[62]Lei Yu, Da-wei Qi. Analysis and Processing of decayed Log CT image based on multifractal theory. Computers and Electronics in Agriculture.2008,63(2):147-154.
[63]Lei Yu, Da-wei Qi. Applying Multifractal Spectrum Combined with Fractal Discrete Brownian Motion Model to Wood Defects Recognition [J]. Wood Science and Technology,2011,45,511-519.
[64]韩书霞,戚大伟.多重分形理论在原木图像处理中的应用[J].东北林业大学学报.2011,39(10)：132-133.
[65]孔平,严广乐,孙继佳.基于多重分形的肝脏边缘粗糙度分析[J].计算机应用研究,2011,28(6)：2398-2400.
[66]J. Grazzini, A. Turiel, H. Yahia, I. Heriin. A multifractal Approach for Extracting Relevant Textural Areas in Satellite Meteorologieal Images [J]. Environmental Modelling & Software.2006,22(3):1-12.
[67]D. Gan, Y. Tat-soon. A Multifractal Approach for Auto-segmentation of SAR Images [J]. IEEE.2001: 2301-2303.
[68]C. K. Peng, S. V. Buldyrev, S. Havlin, M. Simons, H. E. Stanley, and A. L. Goldberger, Mosaic Organization of DN A Nucleotides [J], Phys. Rev. E 49,1685-1689 (1994)
[69]J. W. Kantelhardt, S. A. Zschiegner, E. K. Bunde, et al. Multifractal detrended fluctuation analysis of non-stationary time series [J]. Physica A,2002,316:87-114.
[70]Lin, A.-j., Shang, P., Zhao, X.:The cross-correlations of stock markets based on DCCA and time-delay DCCA [J]. Nonlinear Dyn.67,425-434 (2012)
[71]Xu, N., Shang, P., Kamae, S.:Modeling traffic flow correlation using DFA and DCCA [J]. Nonlinear Dyn. 61,207-216(2010)
[72]D. Horvatic, H. Eugene Stanley, B. Podobnik. Detrended cross-Correlation analysis for non-stationary time series with periodic trends [J]. Europhysics Letters 94,18007 (2011)
[73]Gu G F, Zhou W X. Detrended fluctuation analysis for fractals and multifractals in higher dimensions [J]. Phys. Rev. E 2008,74,061104.
[1]B.B.Mandelbrot, The Fractal Geometry of Nature [M]. New York:W. H. Freeman,1983.
[2]B. B. Mandelbrot. A multifractal walk down Wall Street [J]. Scientific American,1999,298:70-73.
[3]蒋爱平,杨悦华,杨兴全.基于多重加权法的多重分形图像分割研究[J].中国图象图形学报,2007,12(10)：1889-1992.
[4]李会方,俞卞章.一种基于多重分形新特征的图像分割算法[J].光学精密程,2003,11(6)：627-631.
[5]刘元永,罗晓曙,陈全斌.多重分形谱在叶片图像处理中的应用[J].计算机工程与应用.2008,44(28)：190-192.
[6]Wendt H, Roux S G, Jaffard S, et al. Wavelet leaders and bootstrap for multifractal analysis of images [J]. Signal Processing.2009,89:1100-1114.
[7]Ouahabi A. Multifractal analysis for texture characterization:A new approach based on DWT [J].ISSPA 2010:698-703
[8]Xu P F, Yao H X, Ji R R, et al. A robust texture descriptor using multifractal analysis with Gabor filter [C]. In 2010 Proceedings of the Second International Conference on Internet Multimedia Computing and Service (ICIMCS'10).
[9]Lopes R, Dubois P, Bhouri I, et al. Local fractal and multifractal features for volumic texture characterization [J]. Pattern Recognition,2011,44(8):1690-1697
[10]Xia Y, Feng Dagan, Rongchun Zhao. Morphology-Based Multifractal Estimation for Texture Segmentation [J]. IEEE Transactions on Image Processing,2006,15(3):614-622.
[11]M. Sadegh Movahed, E. Hermanis. Fractal analysis of river flow fluctuations [J]. Physica A,2008,387 (4):915-932
[12]Lei Yu, Da-wei Qi. Analysis and Processing of decayed Log CT image based on multifractal theory. Computers and Electronics in Agriculture.2008,63(2):147-154
[13]Lei Yu, Da-wei Qi. Applying Multifractal Spectrum Combined with Fractal Discrete Brownian Motion Model to Wood Defects Recognition [J]. Wood Science and Technology,2011,45,511-519.
[14]M. Sadegh Movahed, G R Jafari, F Ghasemi, et al. Multifractal detrended fluctuation analysis of sunspot time series [J]. Journal of Statistical Mechanics:Theory and Experiment.2006, P02003
15]Kantelhardt J W, Zschiegner S A, Koscielny-Bunde, et al. Multifractal detrended fluctuation analysis of non-stationary time series [J]. Physica A 2002,316:87-114
[16]Ruey S. Tsay著,王远林,潘家柱译.金融时间序列分析[M].2012,北京：人民邮电出版社
[17]http://www.mathworks.com/matlabcentral/fileexchange/27078-zig-zag-scan/content/zigzag.m
[18]张善文、雷英杰、冯有前MATLAB在时间序列分析中的应用[M].2007,西安：西安电子科技大学
[19]D. R. McGaughey, G. J. M. Aitken. Generating two-dimensional fractional Brownian motion using the fractional Gaussian process (FGp) algorithm. Physica A,2002,311(3-4):369-380
[20]中国玉米http://www.chinamaize.com.cn/
[1]B. B. Mandelbrot, How long is the coast of Britain? Statistical self-similarity and fractal dimension [J], Science,1967,156:636-638.
[2]B.B.Mandelbrot, The Fractal Geometry of Nature [M]. New York:W. H. Freeman,1983.
[3]Pentland A P. Fractal based description of natural scenes [J]. IEEE Transactions on Pattern Analysis and Machine Intelligence,1984,6 (6):661-674.
[4]B. B. Mandelbrot. A multifractal walk down Wall Street [J]. Scientific American,1999,298:70-73.
[5]J. W. Kantelhardt,Fractal and Multifractal Time Series. Encyclopedia of Complexity and Systems Science 2009, pp:3754-3779
[6]谢和平等,分形几何：数学基础与应用[M].重庆：重庆大学出版社,1991.
[7]J. W. Kantelhardt, S. A. Zschiegner, E. K. Bunde, et al. Multifractal detrended fluctuation analysis of non-stationary time series [J]. Physica A,2002,316:87-114.
[8]C. K. Peng, S. V. Buldyrev, S. Havlin, M. Simons, H. E. Stanley, and A. L. Goldberger, Mosaic Organization of DNA Nucleotides [J], Phys. Rev. E 49,1685-1689 (1994)
[9]J. F. Muzy, E. Bacry, A. Arneodo. Wavelets and multifractal formalism for singular signals:application to turbulence data [J]. Phys. Rev. Lett.,1991,67:3515
[10]工访,尚金城.基于多重分形理论的电力交易价格分时段特征分析[J].电力自动化设备,2013,33(1)：62-69
[11]F. Wang, G. P. Liao, X. Y. Zhou et.al. Multifractal detrended cross-correlation analysis for power markets [J]. Nonlinear Dynamics 72(1-2):353-363 (2013)
[12]袁晓辉,王云燕,谢俊等.电力市场中电价长程相关性的去趋势波动分析[J].华东电力.2009,37(6)：982-984.
[13]M. S. Movahed, G. R. Jafari, F. Ghasemi, et.al. Multifractal detrended fluctuation analysis of sunspot time series [J]. Journal of Statistical Mechanics:Theory and Experiment.2,1-15 (2006)
[14]Lin, A.-j., Shang, P., Zhao, X.:The cross-correlations of stock markets based on DCCA and time-delay DCCA [J]. Nonlinear Dyn.67,425-434 (2012)
[15]Podobnik, B., Jiang, Z.-Q., Zhou, W.-X., Stanley, H.E.:Statistical tests for power-law cross-correlated processes [J]. Phys. Rev. E 84,066118 (2011)
[16]Buldyrev S V, Goldberger A L, Havlin S, Mantegna R N, Matsa M E, Peng C K, Simons M and Stanley H E,1995 Phys. Rev. E 51,5084; Buldyrev S V, Dokholyan N V, Goldberger A L, Havlin S, Peng C K, Stanley H E and Viswanathan G M,1998 Physica A 249,430
[17]Xu, N., Shang, P., Kamae, S.:Modeling traffic flow correlation using DFA and DCCA [J]. Nonlinear Dyn. 61,207-216(2010)
[18]Podobnik, B., Horvatic, D., Lam, A.N., Stanley, H.E., Ivanov, P.C.:Modeling long-range cross-correlations in two-component ARFIMA and FIARCH processes [J]. Physica A 387,3954-3959 (2008)
[19]D. Horvatic, H. Eugene Stanley, B. Podobnik. Detrended cross-Correlation analysis for non-stationary time series with periodic trends [J]. Europhysics Letters 94,18007 (2011)
[20]Z. Chen, K. Hu, P. Carpena, P. Bernaola-Galvan, H. E. Stanley, et.al. Effect of Nonlinear Filters on Detrended Fluctuation Analysis [J]. Phys. Rev. E 71,011104 (2005)
[21]L. Hedayatifar, M. Vahabi, and G. R. Jafari. Coupling detrended fluctuation analysis for analyzing coupled non-stationary signals [J]. Phys. Rev. E 84,021138 (2011)
[22]J. W. Kantelhardt. Fractal and multifractal time series. Encyclopaedia of Complexity and System Science preprint arXiv:2008,0804,0747
[23]G. F Gu, W. X. Zhou. Detrended fluctuation analysis for fractals and multifractals in higher dimensions [J]. Physical Review E,2006,74,061104
[24]P. Brodatz, Texture:A Photographic Album for Artists and Designers [M]. New York:Dover,1966
[25]赵莹,高隽,陈果,等.一种基于分形理论的多尺度多方向纹理特征提取方法[J].仪器仪表学报.2008,29(4)：787-791
[26]B. B. Chaudhuri, N. Sarkar. Texture segmentation using fractal dimension [J], IEEE Trans. Pattern Anal. Mach. Intell.,1995,17(1):72-77
[27]R. Haralick. Statistical and structural approaches to texture [J]. Proc. IEEE,1979,67(5), pp.786-804.
[28]Y. Xia, D. G. Feng, R. C. Zhao. Morpholgy-based multifractal estimation for texture segmentation [J]. IEEE transactions on image processing,2006,15(3):614-622
[29]T. Hastie, R.Tibshirani, J. Friedman. ming F. et al. translate. The elements of statistical learning data mining, inference, and prediction [M]. Beijing:Electronic Industry Press,2007
[30]L. Yu, D. W. Qi. Applying multifraetal spectrum combined with fractal discrete brownian motion model to wood defects recognition [J]. Wood Science and Technology.2009,45(3):511-519
[31]T. Stojic, I. Reljin, B. Reljin. Adaptation of multifractal analysis to segmentation of micro-calcifications in digital mammograms [J]. Physica A.2006,367(15):494-508
[32]R. Lopes, P. Dubois, I. Bhouri, et al. Local fractal and multifractal features for volumic texture characterization. Pattern Recognition,2011,44(8):1690-1697
[33]李厚强,刘政凯,林峰.基于分形理论和Kohonen神经网络的纹理图像分割方法[J].计算机工程与应用.2001,37：44-46
[34]D. Bremner, E. Demaine, J. Erickson, et.al. Output-sensitive algorithms for computing nearest-neighbor decision boundaries [J]. Discrete and Computational Geometry 2005,33 (4):593-604. Doi: 10.1007/s00454-004-1152-0
[35]Ho, T. Kam. Random Decision Forest. Proc. of the 3rd Int'l Conf. on Document Analysis and Recognition [C], Montreal, Canada, August 14-18,1995,278-282
[1]Xiao T J, Guang-X X, Xin-P C, et al. Reducing environmental risk by improving N management in intensive Chinese agricultural systems [J].PNAS,2009:106(9):3041-3046.
[2]李锦卫.基于计算机视觉的水稻、油菜叶色-氮营养诊断机理与建模[D].长沙：湖南农业大学博士论文,2010,12.
[3]B. B. Mandelbrot, How long is the coast of Britain? Statistical self-similarity and fractal dimension [J], Science,1967,156:636-638.
[4]Pentland A P. Fractal based description of natural scenes [J]. IEEE Transactions on Pattern Analysis and Machine Intelligence,1984,6(6):661-674.
[5]B.B.Mandelbrot, The Fractal Geometry of Nature [M]. New York:W. H. Freeman,1983.
[6]王访,尚金城.基于多重分形理论的电力交易价格分时段特征分析[J].电力自动化设备,2013,33(1)：62-69.
[7]Yang J Y, Yu Z G, Anh V. Clustering structures of large proteins using multifractal analyses based on a 6-letter model and hydrophobicity scale of amino acids [J]. Chaos, Solitons & Fractals 2009,40:607-620.
[8]Yu Z G, Anh V, Eastes R. Multifractal analysis of geomagnetic storm and solar flare indices and their class dependence[J]. J. Geophys. Res.2009:114, A05214.
[9]Hedayatifar L, Vahabi M, Jafari G R. Coupling detrended fluctuation analysis for analyzing coupled non- stationary signals [J]. Phys. Rev. E 2011:84,021138.
[10]P. Shang, Y. Lu, S. Kama. The application of Holder exponent to traffic congestion waming [J]. Physica A: Statistical Mechanics and its Applications.2006,370(2):769-776.
[11]蒋爱平,杨悦华,杨兴全.基于多重加权法的多重分形图像分割研究[J].中国图像图形学报,2007,12(10)：1889-1992.
[12]刘元永,罗晓曙,陈全斌,等.多重分形谱在叶片图像处理中的应用[J].计算机工程与应用.2008,44(28)：190-192.
[13]Wendt H, Roux S G, Jaffard S, et al. Wavelet leaders and bootstrap for multifractal analysis of images [J]. Signal Processing.2009,89:1100-1114.
[14]Ouahabi A. Multifractal analysis for texture characterization:A new approach based on DWT [J].ISSPA 2010:698-703.
[15]Xu P F, Yao H X, Ji R R, et al. A robust texture descriptor using multifractal analysis with Gabor filter [C]. In 2010 Proceedings of the Second International Conference on Internet Multimedia Computing and Service (ICIMCS'10).
[16]李会方,俞卞章.一种基于多重分形新特征的图像分割算法[J].光学精密程,2003,11(6)：627-631.
[17]Lopes R, Dubois P, Bhouri I, et al. Local fractal and multifractal features for volumic texture characterization [J]. Pattern Recognition,2011,44(8):1690-1697.
[18]Xia Y, Feng Dagan, Rongchun Zhao. Morphology-Based Multifractal Estimation for Texture Segmentation [J]. IEEE Transactions on Image Processing,2006,15(3):614-622.
[19]Xia Y, Feng Dagan, Rongchun Zhao, et al. Multifractal signature estimation for textured image segmentation [J]. Pattern Recognition Letters.2010,31:163-169.
[20]Lei Yu, Da-wei Qi. Analysis and Processing of decayed Log CT image based on multifractal theory. Computers and Electronics in Agriculture.2008,63(2):147-154.
[21]Lei Yu, Da-wei Qi. Applying Multifractal Spectrum Combined with Fractal Discrete Brownian Motion Model to Wood Defects Recognition [J]. Wood Science and Technology,2011,45,511-519.
[22]Lei Yu, Da-wei Qi. Applying Multifractal Spectrum Combined with Fractal Discrete Brownian Motion Model to Wood Defects Recognition for Sawing [C]. IEEE International Conference on Automation and Logistics Shenyang, China, August 2009,309-314.
[23]韩书霞,戚大伟.多重分形理论在原木图像处理中的应用[J].东北林业大学学报.2011,39(10)：132-133.
[24]孔平,严广乐,孙继佳.基于多重分形的肝脏边缘粗糙度分析[J].计算机应用研究,2011,28(6)：2398-2400.
[25]金春兰,黄华,刘圹彬.基于多重分形的医学图像分割方法[J].中国组织工程研究与临床康复.2010,14(9)：135-1538.
[26]J. Grazzini, A. Turiel, H. Yahia, I. Heriin. A multifractal Approach for Extracting Relevant Textural Areas in Satellite Meteorologieal Images [J]. Environmental Modelling & Software.2006,22(3):1-12.
[27]D. Gan, Y. Tat-soon. A Multifractal Approach for Auto-segmentation of SAR Images [J]. IEEE.2001: 2301-2303.
[28]李会方,徐瑞萍,庞文俊.基于相对多重分形谱的感兴趣区域图像压缩[J].计算机应用,2005,25(12)：2840-2542.
[29]J. W. Kantelhardt, S. A. Zschiegner, E. K. Bunde, el al. Multifractal detrended fluctuation analysis of non-stationary time series [J]. Physica A,2002,316:87-114.
[30]Gu G F, Zhou W X. Detrended fluctuation analysis for fractals and multifractals in higher dimensions [J]. Phys. Rev. E 2006,74,061104.
[31]冈萨雷斯,伍兹著,阮秋琦等译.数字图像处理(第三版)[M].2011北京：电子工业出版社.
[32]Bezdek J C. Pattern recognition with fuzzy objection function algorithms[M]. New York:Plenum Press, 1981.
[33]T Poggio. H Voorhees, A Yuille. A Regularized Solution to Edge Detection[R]. Tech Rep MA, Rep AIM-833, MIT Artificial Intell Lab,1985.
[34]华中农业信息网http://ccain.hzau.edu.cn
[35]中国玉米http://www.chinamaize.com.cn/
[l]张浩,姚旭国,张小斌等.基于多光谱图像的水稻叶片叶绿素和籽粒氮素含量检测研究[J].中国水稻科学,2008,22(5)：555-558.
[2]祝锦霞,邓劲松,石媛媛等.基于水稻扫描叶片图像特征的氮素营养诊断研究[J].光谱学与光谱分析,2009,29(8)：2171-2175.
[3]祝锦霞,邓劲松,林芬芳等.水稻氮素机器视觉诊断最佳叶位和位点的选择研究[J].农业机械学报,2010,41(4)：179-183.
[4]李锦卫.基于计算机视觉的水稻、油菜叶色-氮营养诊断机理与建模[D].长沙：湖南农业大学,2010,12
[5]管鹤卿.基于计算机视觉技术的油菜叶片信息研究[D].湖南农业大学硕士学位论文,2007
[6]李方一.基于数字图像处理技术的油菜叶片氮素营养检测研究[D].湖南农业大学硕士学位论文,2009
[7]张元.基于多光谱机器视觉的油菜氮素营养检测方法研究[D].镇江：江苏大学,硕士学位论文,2005.
[8]J.S. Cope, et al., Plant species identification using digital morphometrics:a review [J], Expert Syst. Appl., 39(2012),7562-7573.
[9]J.S. Cope, et al., Plant texture classification using Gabor co-occurrences [J], In International symposium on visual computing, Las Vegas, Nevada, USA, Springer-Verlag,2010.
[10]J. Liu, S. Zhang, S. Deng, A method of plant classification based on wavelet transforms and support vector machines [J], Emerging Intelligent Computing Technology and Applications,5754 (2009), 253-260.
[11]O.M. Bruno, et al., Fractal dimension applied to plant identification [J], Inform. Sciences,178 (2008), 2722-2733.
[12]Y. Kong, S.H. Wang, C.W. Ma, et.al. Effect of image processing of a leaf photograph on the calculated fractal dimension of leaf veins [J], Computer and Computing Technologies in Agriculture,259(2008): 755-760.
[13]D.R. Rossatto, D. Casanova, R.M. Kolb, Fractal 267 analysis of leaf-texture properties as a tool for taxonomic and identification purposes:a case study with species from Neotropical Melastomataceae (Miconieae tribe) [J], Plant Syst. Evol.,29(2011):103-116.
[14]A.R. Backes, O.M. Bruno, Plant leaf identification using color and multi-scale fractal [J], Dimension Image and Signal Processing,6134 (2010):463-470.
[15]A.R. Backes, O.M. Bruno, Plant leaf identification using multi-scale fractal dimension [J], Image Analysis and Processing,5716 (2009):143-150.
[16]A. Ouahabi:Multifractal analysis for texture characterization:A new approach based on DWT [J]. ISSPA, 2010:698-703
[17]Y. Xia, D.G. Feng, R.C. Zhao, et al., Multifractal signature estimation for textured image segmentation [J], Pattern Recogn. Lett.,31(2010):163-169.
[18]R. Lopes, P. Dubois, I. Bhouri, et al., Local fractal and multifractal features for volumic texture characterization [J], Pattern Recogn.,44(2011):1690-1697.
[19]J. W. Kantelhardt, S.A. Zschiegner, E.K. Bunde, et al., Multifractal detrended fluctuation analysis of nonstationary time series [J], Phys. A,316(2002):87-114.
[20]G. F. Gu, W. X. Zhou. Detrended fluctuation analysis for fractals and multifractals in higher dimensions [J]. Physical Review E,2006,74,061104
[21]O. J. O. So"derkvist, Computer Vision Classification of Leaf from Swedish Trees, Master Thesis, Linko"ping University,2001.
[22]范金城,梅长林.数据分析[M].北京：科学出版社,2002
[23]R. O. Duda, P. E. Hart., D. G. Stork. Pattern classification [M].2nd. New York:John Wiley & Sons,2001
[24]G. B. Huang, Q. Y. Zhu, CKSIEW. Extreme learning machine:theory and applications [J]. Neuro-computing,2006,12(1):489-501.
[25]G. B. Huang, Q. Y. Zhu, CKSIEW. Extreme learning machine:a new learning scheme of feedfoward neural networks [J]. Neuro-computing,2004,2(2):985-990
[27]Vladimir N.Vapnik.统计学习理论[M].北京：电子工业出版社,2009.
[28]Nello Cristianini, John Shawe, Taylor. An Introduction to Support Vector Machines and Other Kernel-based Learning Methods (支持向量机导论)[M].北京：电子工业出版社,2004.
[29]S. Canu, Y. Grandvalet, V. Guigue, et.al. SVM and Kernel Methods MatlabToolbox. Perception Systems Information, INSA de Rouen, Rouen, France,2005. Software available at http://asi.insa-rouen.fr/ enseignants/～arakotom/toolbox/index.html.
[30]Ho, T. Kam. Random Decision Forest. Proc. of the 3rd Int'l Conf. on Document Analysis and Recognition [C], Montreal, Canada, August 14-18,1995,278-282
[31]D. Bremner, E. Demaine, J. Erickson, et.al. Output-sensitive algorithms for computing nearest-neighbor decision boundaries [J]. Discrete and Computational Geometry 2005,33 (4):593-604. Doi:10.1007/ s00454-004-1152-0
[32]T. Hastie, R.Tibshirani, J. Friedman.范明,柴玉梅等译.统计学习基础-数据挖掘[M].北京：电子工业出版社,2007
[33]苏金明,阮沈勇,王永利.Matlab工程数学[M].北京：电子工业出版社,2005.
[2]L. A. Spomer. M. A. L. Smith, J. S. Sawwan. Rapid nondestructive measurement of chlorophyll content in leaves with non-uniform chlorophyll distribution [J]. Photosynth. Res.,1988,16:277-284.
[3]张浩,姚旭国,张小斌等.基于多光谱图像的水稻叶片叶绿素和籽粒氮素含量检测研究[J].中国水稻科学,2008,22(5)：555-558.
[4]祝锦霞,邓劲松,石媛媛等.基于水稻扫描叶片图像特征的氮素营养诊断研究[J].光谱学与光谱分析,2009,29(8)：2171-2175.
[5]祝锦霞,邓劲松,林芬芳等.水稻氮素机器视觉诊断最佳叶位和位点的选择研究[J].农业机械学报,2010,41(4)：179-183.
[6]管鹤卿.基于计算机视觉技术的油菜叶片信息研究[D].湖南农业大学硕士学位论文,2007
[7]李方一.基于数字图像处理技术的油菜叶片氮素营养检测研究[D].湖南农业大学硕士学位论文,2009
[8]张元.基于多光谱机器视觉的油菜氮素营养检测方法研究[D].镇江：江苏大学,硕士学位论文,2005.
[9]张艳诚,毛罕平,胡波.数字图像中作物病斑形状分形特征提取[J].微计算机信息,2007,23,11-3：295-297.
[10]龚国淑,张世熔.植物病害病斑形状的分形研究[J].植物保护,2002,28(6)：9-13.
[11]龚红菊,樊海明,姬长英.基于分形理论的水稻单产计算机视觉预测技术[J].农业机械学报.2010,41(8)：166-170.
[12]江海洋,张建,袁媛,等.基于MDMP-LSM算法的黄瓜叶片病斑分割方法[J].农业工程学报.2012,28(21)：142-148.
[13]温长吉,王生生,于合龙.基于改进蜂群算法优化神经网络的玉米病害图像分割[J].农业工程学报.2013,29(13)：142-149.
[14]贾建楠,吉海彦.基于病斑形状和神经网络的黄瓜病害识别[J].农业工程学报.2013,29(增1)：115-121.
[15]刁智华,：王欢,宋寅卯,等.复杂背景下棉花病叶害螨图像分割方法[J].农业工程学报.2013,29(5)：147-152.
[16]张静,王双喜,董晓志.基于温室植物叶片纹理的病害图像处理及特征值提取方法的研究[J].沈阳农业大学学报2006-06,37(3)：282-285
[17]ZHANG N, CHAISATTAPAGON C.Effective criteria for weed identification in wheat fields using machine vision [J]. ASAE,1995,38(3):965-974.
[18]田有文,王滨,唐晓明.基于纹理特征和支持向量机的玉米病害的识别[J].沈阳农业大学学报,2005-12,36(6)：730-732.
[19]袁媛,李淼,梁青.基于水平集的作物病叶图像分割方法[J].农业工程学报.2011,27(2)：208-212.
[20]Da-ke Wu, Chun-yan Xie, Cheng-wei Ma. The SVM Classification Leafminer-infected Leaves Based on Fractal Dimension Cybernetics and Intelligent Systems, IEEE,2008,9,147-151.
[21]梁淑敏,杨锦忠,李娜娜,等.基于图像处理的玉米分形维数及其种植密度效应评价[J].作物学报,2009,35(4):745-748.
[22]Yan LI, Chun-lei XIA, Yun-ki KIM. Pest Detection Method Using Multi-Fractal Analysis. Journal of Measurement Science and Instrum entation,2011,2(3):240-243.
[23]曹乐平,温芝元,沈陆明.基于色调分形维数的柑橘糖度和有效酸度检测[J].农业机械学报.2010,41(3)：143-148.
[24]曹乐平.基于周长面积分形维数的柑橘品种机器识别[J].农业工程学报,2010,26(2)：351-355.
[25]龚伟,颜晓元,蔡祖聪.长期施肥对小麦-玉米轮作土壤微团聚体组成和分形特征的影响[J].上壤学报,2011,48(6)：1141-1148.
[26]B. B. Mandelbrot, J. W. Van Ness. SIAM Rev.1968,4:422.
[27]Carr J. R, Miranda F. P. The semivariogram in comparison to the co-occurrence matrix for classification of image texture [J]. IEEE Transactions on Geoscience and Remote Sensing,1998,36(6):1945-1952.
[28]Clausi D. A, Yue B. Comparing co-occurrence probabilities and markov random fields for texture analysis of SAR seaice imagery [J]. IEEE Transactions on Geoscience and Remote Sensing,2004,42(1): 215-228.
[29]Ohanian P. P, DubesRC1 Performance evaluation for four classes of textural features[J].Pattern Recognition,1992,25(8):819-833.
[30]刘丽,匡纲要.图像纹理特征提取方法综述[J].中国图象图形学报.2009,14(4)：622-635.
[31]Pentland A P. Fractal based description of natural scenes [J]. IEEE Transactions on Pattern Analysis and Machine Intelligence,1984,6(6):661-674.
[32]Chen S S, Keller JM, Crow nover R M. On the calculation of fractal features from images [J]. IEEE Transactions on Pattern Recognition and Machine Intelligence,1993,15(10):1087-1090.
[33]Sarkar N, Chaudhuri B B. An efficient differential box-counting approach to compute fractal dimension of image [J].IEEE Transactions on Systems, Man, and Cybernetics,1994,24(1):115-120.
[34]谢文录,谢维信.几种分形参数估计方法的性能分析和比较[J].西安电子科技大学学报1997,24(2)：172-179.
[35]Tyler SW, Wheatcraft SW. Application of fractal mathematics to soil water retention estimation [J]. Soil Science Society of America Journal,1989,53:987-996.
[36]冯斌,汪懋华.基于颜色分形的水果计算机视觉分级技术[J].农业工程学报,2002,18(2)：141-144
[37]David A E, Llarion V M,Werner P, et al. Mechanisms of extensive spatiotemporal chaos in Rayleigh 2Benard convection [J]. Nature,2000,404(13):733-736
[38]赵莹,胡静,黎明.基于分形维数的图像纹理特征表示方法[J].上海电机学院学报.2011,14(1)：39-43
[39]B. B. Mandelbrot. The Fractal Geometry of Nature [M]. New York:W. H. Freeman,1983.
[40]工访,尚金城.基于多重分形理论的电力交易价格分时段特征分析[J].电力自动化设备,2013,33(1)：62-69
[41]F. Wang, G. P. Liao, X. Y. Zhou et.al. Multifractal detrended cross-correlation analysis for power markets [J]. Nonlinear Dynamics 72(1-2):353-363 (2013)
[42]Sun Xia, Chen Huiping, Wu Ziqin, et al. Multifractal analysis of Hang Seng index in Hong Kong stock market [J]. Physica A,2001,291:553-562.
[43]陈军.多重分形局部奇异性分析方法及其在矿产资源信息提取中的应用[D].武汉：中国地质大学,2007.
[44]李会方.多重分形理论及其在图象处理中应用的研究[D].西安：西北工业大学,2004.
[45]Kantelhardt J. W.2008 Fractal and multifractal time series, to be published in Springer Encyclopaedia of Complexity and System Science preprint arXiv:0804.0747(2008)
[46]ZANG Bao-jiang, SHANG Peng-jian. Multi-fractal analysis of the Yellow River flows [J].Chinese Physics,2007,3(16):565-569.
[47]DING Liang-jin, PENG Hu, et al. Multifractal analysisof human heart beat in sleep [J]. Chin Phys Lett, 2007,24(7):2149-2152.
[48]Zhou L.Q., Yu Z.G.,Deng J.Q.,Anh V.and Long S.C.,A fractal method to distinguish coding and non-coding sequences in a complete genome based on a number sequence representation, J.Theor.Biol., 2005,232:559-567.
[49]Ma D.K,Wu M.and Liu C.J.,The entropies and multifractal spectrum of some compact systems [J], Chaos, Solitons & Fractals,2008,38:840-851.
[50]M Sadegh Movahed, G R Jafari, F Ghasemi, Sohrab Rahvar and M Reza Rahimi Tabar. Multifractal detrended fluctuation analysis of sunspot time series [J]. Journal of Statistical Mechanics:Theory and Experiment.2006,2:1-15.
[51]Jian-Yi Yang, Zu-Guo Yu a,b, Vo Anh. Clustering structures of large proteins using multifractal analyses based on a 6-letter model and hydrophobicity scale of amino acids [J]. Chaos, Solitons and Fractals 40 (2009) 607-620.
[52]Kapan L M, Ku o C-C. Extending self-similarity for fractional Brownian motion [J]. IEEE Transactions on Signal Processing,1994,42(12):3526-3530.
[53]Kaplan L M. Extend fractal analysis for texture classification and segmentation [J]. IEEE Transactions on Image Processing,1999,8(11):1572-1585.
[54]蒋爱平,杨悦华,杨兴全.基于多重加权法的多重分形图像分割研究[J].中国图象图形学报,2007,12(10)：1889-1992.
[55]刘元永,罗晓曙,陈全斌.多重分形谱在叶片图像处理中的应用[J].计算机工程与应用.2008, 44(28)：190-192.
[56]Wendt H, Roux S G, Jaffard S, et al. Wavelet leaders and bootstrap for multifractal analysis of images [J]. Signal Processing.2009,89:1100-1114.
[57]Ouahabi A. Multifractal analysis for texture characterization:A new approach based on DWT [J]. ISSPA 2010:698-703
[58]Xu P F, Yao H X, Ji R R, et al. A robust texture descriptor using multifractal analysis with Gabor filter [C]. In 2010 Proceedings of the Second International Conference on Internet Multimedia Computing and Service (ICIMCS'10).
[59]李会方,俞卞章.一种基于多重分形新特征的图像分割算法[J].光学精密程,2003,11(6)：627-631
[60]Lopes R, Dubois P, Bhouri I, et al. Local fractal and multifractal features for volumic texture characterization [J]. Pattern Recognition,2011,44(8):1690-1697
[61]Yong Xia, Dagan Feng, Rongchun Zhao. Morphology-Based Multifractal Estimation for Texture Segmentation [J]. IEEE Transactions on Image Processing,2006,15(3):614-622.
[62]Lei Yu, Da-wei Qi. Analysis and Processing of decayed Log CT image based on multifractal theory. Computers and Electronics in Agriculture.2008,63(2):147-154.
[63]Lei Yu, Da-wei Qi. Applying Multifractal Spectrum Combined with Fractal Discrete Brownian Motion Model to Wood Defects Recognition [J]. Wood Science and Technology,2011,45,511-519.
[64]韩书霞,戚大伟.多重分形理论在原木图像处理中的应用[J].东北林业大学学报.2011,39(10)：132-133.
[65]孔平,严广乐,孙继佳.基于多重分形的肝脏边缘粗糙度分析[J].计算机应用研究,2011,28(6)：2398-2400.
[66]J. Grazzini, A. Turiel, H. Yahia, I. Heriin. A multifractal Approach for Extracting Relevant Textural Areas in Satellite Meteorologieal Images [J]. Environmental Modelling & Software.2006,22(3):1-12.
[67]D. Gan, Y. Tat-soon. A Multifractal Approach for Auto-segmentation of SAR Images [J]. IEEE.2001: 2301-2303.
[68]C. K. Peng, S. V. Buldyrev, S. Havlin, M. Simons, H. E. Stanley, and A. L. Goldberger, Mosaic Organization of DN A Nucleotides [J], Phys. Rev. E 49,1685-1689 (1994)
[69]J. W. Kantelhardt, S. A. Zschiegner, E. K. Bunde, et al. Multifractal detrended fluctuation analysis of non-stationary time series [J]. Physica A,2002,316:87-114.
[70]Lin, A.-j., Shang, P., Zhao, X.:The cross-correlations of stock markets based on DCCA and time-delay DCCA [J]. Nonlinear Dyn.67,425-434 (2012)
[71]Xu, N., Shang, P., Kamae, S.:Modeling traffic flow correlation using DFA and DCCA [J]. Nonlinear Dyn. 61,207-216(2010)
[72]D. Horvatic, H. Eugene Stanley, B. Podobnik. Detrended cross-Correlation analysis for non-stationary time series with periodic trends [J]. Europhysics Letters 94,18007 (2011)
[73]Gu G F, Zhou W X. Detrended fluctuation analysis for fractals and multifractals in higher dimensions [J]. Phys. Rev. E 2008,74,061104.
[1]B.B.Mandelbrot, The Fractal Geometry of Nature [M]. New York:W. H. Freeman,1983.
[2]B. B. Mandelbrot. A multifractal walk down Wall Street [J]. Scientific American,1999,298:70-73.
[3]蒋爱平,杨悦华,杨兴全.基于多重加权法的多重分形图像分割研究[J].中国图象图形学报,2007,12(10)：1889-1992.
[4]李会方,俞卞章.一种基于多重分形新特征的图像分割算法[J].光学精密程,2003,11(6)：627-631.
[5]刘元永,罗晓曙,陈全斌.多重分形谱在叶片图像处理中的应用[J].计算机工程与应用.2008,44(28)：190-192.
[6]Wendt H, Roux S G, Jaffard S, et al. Wavelet leaders and bootstrap for multifractal analysis of images [J]. Signal Processing.2009,89:1100-1114.
[7]Ouahabi A. Multifractal analysis for texture characterization:A new approach based on DWT [J].ISSPA 2010:698-703
[8]Xu P F, Yao H X, Ji R R, et al. A robust texture descriptor using multifractal analysis with Gabor filter [C]. In 2010 Proceedings of the Second International Conference on Internet Multimedia Computing and Service (ICIMCS'10).
[9]Lopes R, Dubois P, Bhouri I, et al. Local fractal and multifractal features for volumic texture characterization [J]. Pattern Recognition,2011,44(8):1690-1697
[10]Xia Y, Feng Dagan, Rongchun Zhao. Morphology-Based Multifractal Estimation for Texture Segmentation [J]. IEEE Transactions on Image Processing,2006,15(3):614-622.
[11]M. Sadegh Movahed, E. Hermanis. Fractal analysis of river flow fluctuations [J]. Physica A,2008,387 (4):915-932
[12]Lei Yu, Da-wei Qi. Analysis and Processing of decayed Log CT image based on multifractal theory. Computers and Electronics in Agriculture.2008,63(2):147-154
[13]Lei Yu, Da-wei Qi. Applying Multifractal Spectrum Combined with Fractal Discrete Brownian Motion Model to Wood Defects Recognition [J]. Wood Science and Technology,2011,45,511-519.
[14]M. Sadegh Movahed, G R Jafari, F Ghasemi, et al. Multifractal detrended fluctuation analysis of sunspot time series [J]. Journal of Statistical Mechanics:Theory and Experiment.2006, P02003
15]Kantelhardt J W, Zschiegner S A, Koscielny-Bunde, et al. Multifractal detrended fluctuation analysis of non-stationary time series [J]. Physica A 2002,316:87-114
[16]Ruey S. Tsay著,王远林,潘家柱译.金融时间序列分析[M].2012,北京：人民邮电出版社
[17]http://www.mathworks.com/matlabcentral/fileexchange/27078-zig-zag-scan/content/zigzag.m
[18]张善文、雷英杰、冯有前MATLAB在时间序列分析中的应用[M].2007,西安：西安电子科技大学
[19]D. R. McGaughey, G. J. M. Aitken. Generating two-dimensional fractional Brownian motion using the fractional Gaussian process (FGp) algorithm. Physica A,2002,311(3-4):369-380
[20]中国玉米http://www.chinamaize.com.cn/
[1]B. B. Mandelbrot, How long is the coast of Britain? Statistical self-similarity and fractal dimension [J], Science,1967,156:636-638.
[2]B.B.Mandelbrot, The Fractal Geometry of Nature [M]. New York:W. H. Freeman,1983.
[3]Pentland A P. Fractal based description of natural scenes [J]. IEEE Transactions on Pattern Analysis and Machine Intelligence,1984,6 (6):661-674.
[4]B. B. Mandelbrot. A multifractal walk down Wall Street [J]. Scientific American,1999,298:70-73.
[5]J. W. Kantelhardt,Fractal and Multifractal Time Series. Encyclopedia of Complexity and Systems Science 2009, pp:3754-3779
[6]谢和平等,分形几何：数学基础与应用[M].重庆：重庆大学出版社,1991.
[7]J. W. Kantelhardt, S. A. Zschiegner, E. K. Bunde, et al. Multifractal detrended fluctuation analysis of non-stationary time series [J]. Physica A,2002,316:87-114.
[8]C. K. Peng, S. V. Buldyrev, S. Havlin, M. Simons, H. E. Stanley, and A. L. Goldberger, Mosaic Organization of DNA Nucleotides [J], Phys. Rev. E 49,1685-1689 (1994)
[9]J. F. Muzy, E. Bacry, A. Arneodo. Wavelets and multifractal formalism for singular signals:application to turbulence data [J]. Phys. Rev. Lett.,1991,67:3515
[10]工访,尚金城.基于多重分形理论的电力交易价格分时段特征分析[J].电力自动化设备,2013,33(1)：62-69
[11]F. Wang, G. P. Liao, X. Y. Zhou et.al. Multifractal detrended cross-correlation analysis for power markets [J]. Nonlinear Dynamics 72(1-2):353-363 (2013)
[12]袁晓辉,王云燕,谢俊等.电力市场中电价长程相关性的去趋势波动分析[J].华东电力.2009,37(6)：982-984.
[13]M. S. Movahed, G. R. Jafari, F. Ghasemi, et.al. Multifractal detrended fluctuation analysis of sunspot time series [J]. Journal of Statistical Mechanics:Theory and Experiment.2,1-15 (2006)
[14]Lin, A.-j., Shang, P., Zhao, X.:The cross-correlations of stock markets based on DCCA and time-delay DCCA [J]. Nonlinear Dyn.67,425-434 (2012)
[15]Podobnik, B., Jiang, Z.-Q., Zhou, W.-X., Stanley, H.E.:Statistical tests for power-law cross-correlated processes [J]. Phys. Rev. E 84,066118 (2011)
[16]Buldyrev S V, Goldberger A L, Havlin S, Mantegna R N, Matsa M E, Peng C K, Simons M and Stanley H E,1995 Phys. Rev. E 51,5084; Buldyrev S V, Dokholyan N V, Goldberger A L, Havlin S, Peng C K, Stanley H E and Viswanathan G M,1998 Physica A 249,430
[17]Xu, N., Shang, P., Kamae, S.:Modeling traffic flow correlation using DFA and DCCA [J]. Nonlinear Dyn. 61,207-216(2010)
[18]Podobnik, B., Horvatic, D., Lam, A.N., Stanley, H.E., Ivanov, P.C.:Modeling long-range cross-correlations in two-component ARFIMA and FIARCH processes [J]. Physica A 387,3954-3959 (2008)
[19]D. Horvatic, H. Eugene Stanley, B. Podobnik. Detrended cross-Correlation analysis for non-stationary time series with periodic trends [J]. Europhysics Letters 94,18007 (2011)
[20]Z. Chen, K. Hu, P. Carpena, P. Bernaola-Galvan, H. E. Stanley, et.al. Effect of Nonlinear Filters on Detrended Fluctuation Analysis [J]. Phys. Rev. E 71,011104 (2005)
[21]L. Hedayatifar, M. Vahabi, and G. R. Jafari. Coupling detrended fluctuation analysis for analyzing coupled non-stationary signals [J]. Phys. Rev. E 84,021138 (2011)
[22]J. W. Kantelhardt. Fractal and multifractal time series. Encyclopaedia of Complexity and System Science preprint arXiv:2008,0804,0747
[23]G. F Gu, W. X. Zhou. Detrended fluctuation analysis for fractals and multifractals in higher dimensions [J]. Physical Review E,2006,74,061104
[24]P. Brodatz, Texture:A Photographic Album for Artists and Designers [M]. New York:Dover,1966
[25]赵莹,高隽,陈果,等.一种基于分形理论的多尺度多方向纹理特征提取方法[J].仪器仪表学报.2008,29(4)：787-791
[26]B. B. Chaudhuri, N. Sarkar. Texture segmentation using fractal dimension [J], IEEE Trans. Pattern Anal. Mach. Intell.,1995,17(1):72-77
[27]R. Haralick. Statistical and structural approaches to texture [J]. Proc. IEEE,1979,67(5), pp.786-804.
[28]Y. Xia, D. G. Feng, R. C. Zhao. Morpholgy-based multifractal estimation for texture segmentation [J]. IEEE transactions on image processing,2006,15(3):614-622
[29]T. Hastie, R.Tibshirani, J. Friedman. ming F. et al. translate. The elements of statistical learning data mining, inference, and prediction [M]. Beijing:Electronic Industry Press,2007
[30]L. Yu, D. W. Qi. Applying multifraetal spectrum combined with fractal discrete brownian motion model to wood defects recognition [J]. Wood Science and Technology.2009,45(3):511-519
[31]T. Stojic, I. Reljin, B. Reljin. Adaptation of multifractal analysis to segmentation of micro-calcifications in digital mammograms [J]. Physica A.2006,367(15):494-508
[32]R. Lopes, P. Dubois, I. Bhouri, et al. Local fractal and multifractal features for volumic texture characterization. Pattern Recognition,2011,44(8):1690-1697
[33]李厚强,刘政凯,林峰.基于分形理论和Kohonen神经网络的纹理图像分割方法[J].计算机工程与应用.2001,37：44-46
[34]D. Bremner, E. Demaine, J. Erickson, et.al. Output-sensitive algorithms for computing nearest-neighbor decision boundaries [J]. Discrete and Computational Geometry 2005,33 (4):593-604. Doi: 10.1007/s00454-004-1152-0
[35]Ho, T. Kam. Random Decision Forest. Proc. of the 3rd Int'l Conf. on Document Analysis and Recognition [C], Montreal, Canada, August 14-18,1995,278-282
[1]Xiao T J, Guang-X X, Xin-P C, et al. Reducing environmental risk by improving N management in intensive Chinese agricultural systems [J].PNAS,2009:106(9):3041-3046.
[2]李锦卫.基于计算机视觉的水稻、油菜叶色-氮营养诊断机理与建模[D].长沙：湖南农业大学博士论文,2010,12.
[3]B. B. Mandelbrot, How long is the coast of Britain? Statistical self-similarity and fractal dimension [J], Science,1967,156:636-638.
[4]Pentland A P. Fractal based description of natural scenes [J]. IEEE Transactions on Pattern Analysis and Machine Intelligence,1984,6(6):661-674.
[5]B.B.Mandelbrot, The Fractal Geometry of Nature [M]. New York:W. H. Freeman,1983.
[6]王访,尚金城.基于多重分形理论的电力交易价格分时段特征分析[J].电力自动化设备,2013,33(1)：62-69.
[7]Yang J Y, Yu Z G, Anh V. Clustering structures of large proteins using multifractal analyses based on a 6-letter model and hydrophobicity scale of amino acids [J]. Chaos, Solitons & Fractals 2009,40:607-620.
[8]Yu Z G, Anh V, Eastes R. Multifractal analysis of geomagnetic storm and solar flare indices and their class dependence[J]. J. Geophys. Res.2009:114, A05214.
[9]Hedayatifar L, Vahabi M, Jafari G R. Coupling detrended fluctuation analysis for analyzing coupled non- stationary signals [J]. Phys. Rev. E 2011:84,021138.
[10]P. Shang, Y. Lu, S. Kama. The application of Holder exponent to traffic congestion waming [J]. Physica A: Statistical Mechanics and its Applications.2006,370(2):769-776.
[11]蒋爱平,杨悦华,杨兴全.基于多重加权法的多重分形图像分割研究[J].中国图像图形学报,2007,12(10)：1889-1992.
[12]刘元永,罗晓曙,陈全斌,等.多重分形谱在叶片图像处理中的应用[J].计算机工程与应用.2008,44(28)：190-192.
[13]Wendt H, Roux S G, Jaffard S, et al. Wavelet leaders and bootstrap for multifractal analysis of images [J]. Signal Processing.2009,89:1100-1114.
[14]Ouahabi A. Multifractal analysis for texture characterization:A new approach based on DWT [J].ISSPA 2010:698-703.
[15]Xu P F, Yao H X, Ji R R, et al. A robust texture descriptor using multifractal analysis with Gabor filter [C]. In 2010 Proceedings of the Second International Conference on Internet Multimedia Computing and Service (ICIMCS'10).
[16]李会方,俞卞章.一种基于多重分形新特征的图像分割算法[J].光学精密程,2003,11(6)：627-631.
[17]Lopes R, Dubois P, Bhouri I, et al. Local fractal and multifractal features for volumic texture characterization [J]. Pattern Recognition,2011,44(8):1690-1697.
[18]Xia Y, Feng Dagan, Rongchun Zhao. Morphology-Based Multifractal Estimation for Texture Segmentation [J]. IEEE Transactions on Image Processing,2006,15(3):614-622.
[19]Xia Y, Feng Dagan, Rongchun Zhao, et al. Multifractal signature estimation for textured image segmentation [J]. Pattern Recognition Letters.2010,31:163-169.
[20]Lei Yu, Da-wei Qi. Analysis and Processing of decayed Log CT image based on multifractal theory. Computers and Electronics in Agriculture.2008,63(2):147-154.
[21]Lei Yu, Da-wei Qi. Applying Multifractal Spectrum Combined with Fractal Discrete Brownian Motion Model to Wood Defects Recognition [J]. Wood Science and Technology,2011,45,511-519.
[22]Lei Yu, Da-wei Qi. Applying Multifractal Spectrum Combined with Fractal Discrete Brownian Motion Model to Wood Defects Recognition for Sawing [C]. IEEE International Conference on Automation and Logistics Shenyang, China, August 2009,309-314.
[23]韩书霞,戚大伟.多重分形理论在原木图像处理中的应用[J].东北林业大学学报.2011,39(10)：132-133.
[24]孔平,严广乐,孙继佳.基于多重分形的肝脏边缘粗糙度分析[J].计算机应用研究,2011,28(6)：2398-2400.
[25]金春兰,黄华,刘圹彬.基于多重分形的医学图像分割方法[J].中国组织工程研究与临床康复.2010,14(9)：135-1538.
[26]J. Grazzini, A. Turiel, H. Yahia, I. Heriin. A multifractal Approach for Extracting Relevant Textural Areas in Satellite Meteorologieal Images [J]. Environmental Modelling & Software.2006,22(3):1-12.
[27]D. Gan, Y. Tat-soon. A Multifractal Approach for Auto-segmentation of SAR Images [J]. IEEE.2001: 2301-2303.
[28]李会方,徐瑞萍,庞文俊.基于相对多重分形谱的感兴趣区域图像压缩[J].计算机应用,2005,25(12)：2840-2542.
[29]J. W. Kantelhardt, S. A. Zschiegner, E. K. Bunde, el al. Multifractal detrended fluctuation analysis of non-stationary time series [J]. Physica A,2002,316:87-114.
[30]Gu G F, Zhou W X. Detrended fluctuation analysis for fractals and multifractals in higher dimensions [J]. Phys. Rev. E 2006,74,061104.
[31]冈萨雷斯,伍兹著,阮秋琦等译.数字图像处理(第三版)[M].2011北京：电子工业出版社.
[32]Bezdek J C. Pattern recognition with fuzzy objection function algorithms[M]. New York:Plenum Press, 1981.
[33]T Poggio. H Voorhees, A Yuille. A Regularized Solution to Edge Detection[R]. Tech Rep MA, Rep AIM-833, MIT Artificial Intell Lab,1985.
[34]华中农业信息网http://ccain.hzau.edu.cn
[35]中国玉米http://www.chinamaize.com.cn/
[l]张浩,姚旭国,张小斌等.基于多光谱图像的水稻叶片叶绿素和籽粒氮素含量检测研究[J].中国水稻科学,2008,22(5)：555-558.
[2]祝锦霞,邓劲松,石媛媛等.基于水稻扫描叶片图像特征的氮素营养诊断研究[J].光谱学与光谱分析,2009,29(8)：2171-2175.
[3]祝锦霞,邓劲松,林芬芳等.水稻氮素机器视觉诊断最佳叶位和位点的选择研究[J].农业机械学报,2010,41(4)：179-183.
[4]李锦卫.基于计算机视觉的水稻、油菜叶色-氮营养诊断机理与建模[D].长沙：湖南农业大学,2010,12
[5]管鹤卿.基于计算机视觉技术的油菜叶片信息研究[D].湖南农业大学硕士学位论文,2007
[6]李方一.基于数字图像处理技术的油菜叶片氮素营养检测研究[D].湖南农业大学硕士学位论文,2009
[7]张元.基于多光谱机器视觉的油菜氮素营养检测方法研究[D].镇江：江苏大学,硕士学位论文,2005.
[8]J.S. Cope, et al., Plant species identification using digital morphometrics:a review [J], Expert Syst. Appl., 39(2012),7562-7573.
[9]J.S. Cope, et al., Plant texture classification using Gabor co-occurrences [J], In International symposium on visual computing, Las Vegas, Nevada, USA, Springer-Verlag,2010.
[10]J. Liu, S. Zhang, S. Deng, A method of plant classification based on wavelet transforms and support vector machines [J], Emerging Intelligent Computing Technology and Applications,5754 (2009), 253-260.
[11]O.M. Bruno, et al., Fractal dimension applied to plant identification [J], Inform. Sciences,178 (2008), 2722-2733.
[12]Y. Kong, S.H. Wang, C.W. Ma, et.al. Effect of image processing of a leaf photograph on the calculated fractal dimension of leaf veins [J], Computer and Computing Technologies in Agriculture,259(2008): 755-760.
[13]D.R. Rossatto, D. Casanova, R.M. Kolb, Fractal 267 analysis of leaf-texture properties as a tool for taxonomic and identification purposes:a case study with species from Neotropical Melastomataceae (Miconieae tribe) [J], Plant Syst. Evol.,29(2011):103-116.
[14]A.R. Backes, O.M. Bruno, Plant leaf identification using color and multi-scale fractal [J], Dimension Image and Signal Processing,6134 (2010):463-470.
[15]A.R. Backes, O.M. Bruno, Plant leaf identification using multi-scale fractal dimension [J], Image Analysis and Processing,5716 (2009):143-150.
[16]A. Ouahabi:Multifractal analysis for texture characterization:A new approach based on DWT [J]. ISSPA, 2010:698-703
[17]Y. Xia, D.G. Feng, R.C. Zhao, et al., Multifractal signature estimation for textured image segmentation [J], Pattern Recogn. Lett.,31(2010):163-169.
[18]R. Lopes, P. Dubois, I. Bhouri, et al., Local fractal and multifractal features for volumic texture characterization [J], Pattern Recogn.,44(2011):1690-1697.
[19]J. W. Kantelhardt, S.A. Zschiegner, E.K. Bunde, et al., Multifractal detrended fluctuation analysis of nonstationary time series [J], Phys. A,316(2002):87-114.
[20]G. F. Gu, W. X. Zhou. Detrended fluctuation analysis for fractals and multifractals in higher dimensions [J]. Physical Review E,2006,74,061104
[21]O. J. O. So"derkvist, Computer Vision Classification of Leaf from Swedish Trees, Master Thesis, Linko"ping University,2001.
[22]范金城,梅长林.数据分析[M].北京：科学出版社,2002
[23]R. O. Duda, P. E. Hart., D. G. Stork. Pattern classification [M].2nd. New York:John Wiley & Sons,2001
[24]G. B. Huang, Q. Y. Zhu, CKSIEW. Extreme learning machine:theory and applications [J]. Neuro-computing,2006,12(1):489-501.
[25]G. B. Huang, Q. Y. Zhu, CKSIEW. Extreme learning machine:a new learning scheme of feedfoward neural networks [J]. Neuro-computing,2004,2(2):985-990
[27]Vladimir N.Vapnik.统计学习理论[M].北京：电子工业出版社,2009.
[28]Nello Cristianini, John Shawe, Taylor. An Introduction to Support Vector Machines and Other Kernel-based Learning Methods (支持向量机导论)[M].北京：电子工业出版社,2004.
[29]S. Canu, Y. Grandvalet, V. Guigue, et.al. SVM and Kernel Methods MatlabToolbox. Perception Systems Information, INSA de Rouen, Rouen, France,2005. Software available at http://asi.insa-rouen.fr/ enseignants/～arakotom/toolbox/index.html.
[30]Ho, T. Kam. Random Decision Forest. Proc. of the 3rd Int'l Conf. on Document Analysis and Recognition [C], Montreal, Canada, August 14-18,1995,278-282
[31]D. Bremner, E. Demaine, J. Erickson, et.al. Output-sensitive algorithms for computing nearest-neighbor decision boundaries [J]. Discrete and Computational Geometry 2005,33 (4):593-604. Doi:10.1007/ s00454-004-1152-0
[32]T. Hastie, R.Tibshirani, J. Friedman.范明,柴玉梅等译.统计学习基础-数据挖掘[M].北京：电子工业出版社,2007
[33]苏金明,阮沈勇,王永利.Matlab工程数学[M].北京：电子工业出版社,2005.
© 2004-2018 中国地质图书馆版权所有 京ICP备05064691号 京公网安备11010802017129号 地址：北京市海淀区学院路29号 邮编：100083 电话：办公室：(+86 10)66554848；文献借阅、咨询服务、科技查新：66554700 |