基于自相关函数的自然纹理图像分形维数的估计

王华; 王祁; 孙金玮

基于自相关函数的自然纹理图像分形维数的估计

哈尔滨工业大学自动化测试与控制系, 哈尔滨 150001

详细信息

中图分类号: TP 391
计量
- 文章访问数: 3114
- HTML全文浏览量: 235
- PDF下载量: 1245
- 被引次数: 0
出版历程
- 收稿日期: 2003-05-26
- 网络出版日期: 2004-08-31

Auto-correlation function based estimation of the fractal dimension of natural texture images

Dept. of Automatic Measurement and Control, Harbin Institute of Technology, Harbin 150001, China

摘要

摘要: 提出了一种估计分形维数的新方法,并利用该方法估计自然纹理图像的分形维数.分形维数是描述图像粗糙程度的主要参数.将分数布朗运动推广到离散情况,研究离散高斯噪声的自相关函数的性质.根据自相关函数的性质,获得估计分形维数的自相关函数方法.合成分形图像和自然纹理图像被用来检验该方法的准确性,并与计盒方法进行了比较,结果显示自相关法是准确的和有效的.
- 自相关函数 /
- 分形维数 /
- 分数布朗运动 /
- 自然纹理
Abstract: A novel method for estimating the fractal dimension has been proposed and the method has been applied to estimate the fractal dimension in natural texture images. Fractal dimension is an important parameter to characterize roughness in an image. Extending the basic theory of fractional Brownian motion to the discrete case, the characteristics of auto-correlation function of fractional Gauss noise has been studied. Based on the characteristics, an auto-correlation function method is obtained to estimate fractal dimension. Both synthesis images of fractal and natural texture images are used to test the proposed method. The method is compared with the box-counting method and the results show that the auto-correlation function method is accurate and efficient.
- autocorrelation functions /
- fractal dimension /
- fractional Brownian motion /
- natural texture

HTML全文

参考文献(1)

[1] Haralick R M. Statistical and structural approaches to texture[J]. Proceedings of the IEEE, 1979, 67(5):786~804 [2] Laws K I. Rapid texture identification . SPIE,1980.276~380 [3] Pentland P. Fractal based description of natural scenes[J]. IEEE Transactions on Pattern analysis and Machine Intelligence, 1984, 6(6):661~674 [4] Chaudhuri B B, Nirupam Sarkar. Texture segmentation using fractal dimension[J]. IEEE Transactions on Pattern analysis and Machine Intelligence, 1995,17(1):72~77 [5] Aura Conci, Claudia Belmiro Proenca. A fractal image analysis system for fabric inspection based on a box-counting method[J]. Computer Networks and ISDN Systems, 1998, 30(20-21):1887~1895 [6] 吴高洪,章毓晋,林行刚. 基于分形的自然纹理自相关描述和分类[J]. 清华大学学报(自然科学版), 2000,40(3):90~93 Wu Gaohong, Zhang Yujin, Lin Xinggang. Fractal-based auto-correlation description and classification of natural texture images[J]. Journal of Tsinghua University(Science and Technology), 2000, 40(3):90~93(in Chinese) [7] Mandelbrot B B. The fractal geometry of nature[M]. New York:Freeman&Co,1982 [8] Mandelbrot B B. Fractals:form, chance and dimension[M]. New York:Freeman&Co, 1977 [9] Gangepain J J, Roques-Carmes C. Fractal approach to two dimensional and three dimensional surface roughness[J]. Wear, 1986,109:119~126 [10] Voss R. Random fractals:characterization and measurement[M]. In:Pynn R, Skjeltop A, eds. Scaling Phenomena in Disordered Systems, Plenum, New York, 1985 [11] Sarkar H, Chaudhuri B B. An efficient approach to estimate fractal dimension of texture images[J]. Pattern Recognition, 1992,25(9):1035~1041 [12] Sarkar H, Chaudhuri B B. An efficient differential box-counting fractal dimension of textural images[J]. IEEE Transactions on Systems, Man, and Cybernetics, 1994,24(1):115~120 [13] Lundahl T, Ohley W J, Kay S M, et al. Fractional Brownian motion:a maximum likelihood estimator and its application to image texture[J]. IEEE Transactions on Medical Imaging, 1986,5(3):152~161 [14] Lundahl T, Ohley W J, Kay S M, et al. Texture analysis of diagnostic xray images by use of fractals . SPIE Visual Communications and Image Processing . 1986,707:23~30 [15] Wen C Y, Acharya R. Self-similar texture characterization using a Fourier-domain maximum likelihood estimation method[J]. Pattern Recognition Letters, 1998,19:735~739 [16] Mandelbrot B B, Ness J W Van. Fractional Brownian Motions, fractional noises and applications[J]. SIAM Rev, 1968,10(4):422~437 [17] 肯尼思·法尔科内.分形几何——数学基础及其应用[M]. 曾文曲,刘世耀,戴连贵,等译.沈阳:东北大学出版社, 2001 Falconer K. Fractal geometry:Mathematical foundations and applications[M]. Translated by Zeng Wenqu, Liu Shiyue, Dai Liangui, et al. Shen Yang:North East University Press, 2001(in Chinese) [18] Harsh Potlapalli, Ren C L. Fractal-based classification of natural textures[J]. IEEE Transactions on Industrial Electronics, 1998,45(1):142~150 [19] Kaplan L M, Jay Kuo C C. An improved method for 2-D self-similar image synthesis[J]. IEEE Transactions on Image Processing, 1998,5(5):754~761 [20] Brodatz P. Textures:A photographic album for artists and designer[M]. New York:Dover, 1966

施引文献

资源附件(0)

访问统计