Aiming at the problem that fractional Brownian motion model can only calculate the fractal dimension when the sea surface wind speed is slow and the image spectrum is isotropic, the fractal model of the sea surface with the isotropic and anisotropic characteristics of sea surface infrared image was proposed. In view of the improper selection of scale range in variation method, the fractal dimension of sea surface infrared image can not be accurately estimated. First the selection criterion of the minimum scale was proposed for maintaining the fractal property of infrared image and avoiding the aliasing effect of image. Then the optimal function relationship among scale interval and the fractal dimension of sea infrared image, fundamental spatial wavelength of image and pixel size was determined by choosing the established sea surface model as reference model of sea infrared image, building minimum costs as target function, using the optimization of the algorithm and least square fitting. Finally, the necessity of the optimal estimation for scale range is proved by simulation.
CHEN Yu，TENG Kenan,TANG Jinguo，WANG Liying
. Optimal Estimation of Fractal Dimension for Two-Dimension Sea Surface Infrared Image[J]. Journal of Shanghai Jiaotong University, 2018
, 52(8)
: 1003
.
DOI: 10.16183/j.cnki.jsjtu.2018.08.018
［1］LO T, LEUNG H, LITVA J. Fractal characterization of sea scattered signals and detection of sea-surface targets［J］. IEE Proceedings F-Radar and Signal Processing, 1993, 140(4): 243-250.
［2］PENTLAND A P. Fractal-based description of natural scenes［J］. IEEE Transactions on Pattern Analysis and Machine Intelligence, 1984, 6(6): 661-674.
［3］STEWART C V, MOGHADDAM B, HINTZ K. Fractional Brownian motion models for synthetic aperture radar imagery scene segmentation［J］. Proceedings of IEEE, 1993, 81(10): 1511-1523.
［4］BERIZZI F, BERTINI G, MARTORELLA M. Two-dimensional variation algorithm for fractal analysis of sea SAR images［J］. IEEE Transactions on Geoscience and Remote Sensing, 2006, 44(9): 2361-2370.
［5］陈洪科, 杨晓玲. 基于分形理论的改进型二维最大熵红外图像分割算法［J］. 红外, 2012, 33(8): 27-31.
CHEN Hongke, YANG Xiaoling. Improved two-dimensional maximum entropy segmentation algorithm for infrared images based on fractal theory［J］. Infrared, 2012, 33(8): 27-31.
［6］郭同健, 高慧斌, 宋立维. 云背景下红外小目标检测的分形方法［J］. 激光与红外, 2014, 44(11): 1278-1281.
GUO Tongjian, GAO Huibin, SONG Liwei. Fractal method of infrared small targets under cloud background［J］. Laser & Infrared, 2014, 44(11): 1278-1281.
［7］孙汉昌, 武毅, 高峰. 基于分形理论和相关匹配的快速目标检测技术［J］. 测绘通报, 2014(S0), 159-162.
SUN Hanchang, WU Yi, GAO Feng. A fast object detection method based on fractal theory and correlation matching［J］. Bulletin of Surveying, 2014(S0): 159-162.
［8］关卿, 张卫. 基于分形维数的图像边缘提取［J］. 计算机科学, 2015, 42(6): 296-298.
GUAN Qing, ZHANG Wei. Image edge detection based on fractal dimension［J］. Computer Science, 2015, 42(6): 296-298.
［9］谷雨, 刘晶红, 孙明超. 基于分形特征和导引滤波的可见光与红外图像融合算法［J］. 光电工程, 2015, 42(4): 62-67.
GU Yu, LIU Jinghong, SUN Mingchao. Visible and infrared image fusion algorithm by fractal feature and guided filtering［J］. Opto-Electronic Engineering, 2015, 42(4): 62-67.
［10］王立地, 黄莎白, 史泽林. 基于小波和分形的海面红外小目标自动检测方法［J］. 激光与红外, 2004, 34(6): 481-483.
WANG Lidi, HUANG Shabai, SHI Zelin. Automatic detection of the infrared small sea target based on wavelet and fractal［J］. Laser and Infrared, 2004, 34(6): 481-483.
［11］LONGUET-HIGGINS M S. The distribution of intervals between zeros of a stationary random function［J］. Philosophical Transactions for the Royal Society of London, 1962, 254: 557-599.
［12］陈瑜, 胡云安, 林涛. 二维改进分形海面模型及海谱分析［J］. 通信学报, 2013, 34(2): 177-184.
CHEN Yu, HU Yunan, Lin Tao. Two-dimensional improved fractal model of the sea surface and sea spectrum evaluation［J］. Journal of Communication, 2013, 34(2): 177-184.
［13］陈瑜, 胡云安, 林涛. 改进分形海面模型散射信号分形特性分析［J］. 遥感学报, 2013, 17(6): 1345-1358.
CHEN Yu, HU Yunan, Lin Tao. Fractal characteristics analysis of the scattering signal from the improved fractal model of the sea surface［J］. Journal of Remote Sensing, 2013, 17(6): 1345-1358.
［14］TRICOT C. Curves and fractal dimension［M］. Berlin: Springer-Verlag, 1995.
［15］MARAGOS P, SUN F K. Measuring the fractal dimension of signals: Morphological covers and iterative optimization［J］. IEEE Transactions on Signal Processing, 1993, 41(1): 108-121.
