摘要
目的计盒法是一种计算二值图像分形维数的常用方法,传统方法如BCM(box-counting method)对无旋转的图像结构具有较理想的计算结果,但是对具有旋转的图像结构的拟合结果偏差较大,导致同一物体在不同旋转角度下的图像的计算结果存在较大差异。为了减小图像旋转对盒维数的影响,本文提出了一种计算二值位图分形维数的新方法———旋转骨架法。方法将二值图像提取骨架,使位图转换为矢量图,利用遗传算法计算图像中物体的最小包容矩形和旋转角度,然后将矢量图进行旋转使其变为一个无旋转的图形,接下来采用多尺度的盒子覆盖矢量图形得到多个拟合点,最后按最小二乘法对拟合点进行拟合得到盒维数。与BCM方法相比,其核心工作与关键改进为骨架的提取、最小包容体的计算、矢量图的分形维数计算等过程。结果对3种类型的图像进行了分析,在自相似的分形图像中,相比BCM方法,3幅图的平均误差分别降低了0.7252%、3.0605%和2.2985%,变化幅度分别降低了0.0573、0.0883和0.0859;在文字扫描图像中,相比BCM方法,变化幅度降低了0.01275,平均拟合误差降低了0.00128;在植物图像中,与BCM方法相比,分形维数的变化幅度降低了0.01704,平均拟合误差降低了0.0005。结论该方法充分利用了位图易旋转、无厚度的特点,减小了图像旋转对盒维数的影响,评价结果优于BCM方法。
Objective Fractals have been widely used in image processing,signal processing,physics,biology,system science,medicine,geography,material science,and architecture.Fractals have also become an important tool to describe and study complex and irregular geometric features quantitatively.Fractal dimensions are formally defined as the Hausdorff-Besicovitch dimension.However,estimating fractal dimensions can be conducted in several ways,each of which uses a slightly different definition of the dimension.A few of these methods include the box-counting method(BCM),wavelet transform,power spectrum(using the Fourier transform),Hurst coefficient,Bouligand-Minkowski,variation,and capacity dimension methods.Given its high efficiency and easy implementation,BCM has become a widely used method to calculate the fractal dimension of binary images.However,BCM is influenced by many factors,such as range of box sizes,selection of fitting points for calculation,method of box covering,and rotation angle of the image,which lead to the instability of the box-counting dimension.Among the factors that affect the box dimension,the box-counting dimension of binary images change greatly due to image rotation and then leads to the deviation of the box-counting dimension.When the image has rotation,the box dimension calculated by the BCM method is usually smaller than the theoretical fractal dimension.The traditional method(BCM)only has a good estimation of nonrotating images.The estimation of rotating images deviates greatly when the traditional method is used and leads to the large difference in the box-counting dimension of the binary image with different rotating angles of the same object.The average deviation of the box-counting dimension caused by rotation is 3%~5%,and the maximum deviation can reach approximately 8%.To reduce the influence of the image’s rotation on the box-counting dimension,the rotation angle of the image must become 0.If the binary image is directly rotated,then the new binary image generated after rotation is inev
作者
纪佑军
何杰
韩海水
程忠钊
曾保全
Ji Youjun;He Jie;Han Haishui;Cheng Zhongzhao;Zeng Baoquan(School of Geoscience and Technology,Southwest Petroleum University,Chengdu 610500,China;China Petroleum Exploration and Development Institute,Beijing 100083,China;Xi'an Changqing Science and Technology Engineering Co,Ltd,Xi'an 710018,China)
出处
《中国图象图形学报》
CSCD
北大核心
2020年第9期1894-1903,共10页
Journal of Image and Graphics
基金
国家自然科学基金项目(41702340)
国家科技重大专项项目(2017ZX05013-006-002)。
关键词
分形维数
计盒法
旋转骨架法
矢量图
二值图像
fractal dimension
box-counting method(BCM)
skeleton rotating method
vector image
binary image
