上海交通大学学报

上海交通大学学报 ›› 2018, Vol. 52 ›› Issue (8): 1003-.doi: 10.16183/j.cnki.jsjtu.2018.08.018

• 学报（中文） • 上一篇    

二维海面红外图像分形维数最优估计

陈瑜1，2,滕克难1,唐金国1,王丽英1   

  1. 1. 海军航空大学, 山东 烟台 264001； 2. 中国人民解放军91213部队， 山东 烟台 264001
  • 发布日期:2025-07-02
  • 通讯作者: 滕克难，男，教授，博士生导师，E-mail:tkn_001@163.com.
  • 作者简介:陈瑜(1982-)，女，山东省烟台市人，博士生，主要研究方向为目标与环境特性.
  • 基金资助:
    国家自然科学基金（51605487）

Optimal Estimation of Fractal Dimension for Two-Dimension Sea Surface Infrared Image

CHEN Yu，TENG Kenan,TANG Jinguo，WANG Liying   

  1. 1. Naval Aeronautical University, Yantai 264001, Shandong, China；2. The 91213 unit of PLA, Yantai 264001, Shandong, China
  • Published:2025-07-02

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摘要： 针对分数布朗运动模型计算分形维数时只适用于海面风速较小、图像谱表现为等方向性的情况，提出了能表现海面红外图像各向同性和异性特征的分形海面随机场模型.针对变分法中尺度范围选择不当，海面红外图像分形维数估计精度不高的问题，首先为了保持红外图像的分形特性和避免图像“混淆”现象的产生，提出了最小尺度的确定准则.然后将所建二维海面模型作为海面红外图像的参考模型，构建了最小目标函数，运用最优的运算准则和最小二乘拟合确定了尺度间隔与海面红外图像的分形维数、图像的基波波长和像素尺寸之间的最优函数关系.最后，通过模拟验证了对尺度范围进行最优估计的必要性.

关键词: 分形模型, 变分法, 分形维数, 海面红外图像

Abstract: 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.

Key words: fractal model, variation method, fractal dimension, sea surface infrared image

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