XX学
科毕业设计（文）
题 目： 基态滤波图雾方法
指导教师：
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学 号：
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日 期： 20XX年X月X日
基态滤波图雾方法
摘
雾霭等天气条件获图模糊清颜色失真影响视觉效果必图进行雾研究图雾通定手段图中雾干扰达快速效雾清晰度恢复作高质量图
图雾方法众态滤波种频域中进行图度增强压缩图亮度范围特殊滤波方法种方法减少低频增加高频量保留低频中灰度级（保存图原貌）锐化细节达雾效果
文基态滤波雾算法全局均衡化图雾算法等方法进行鉴算法优点优化态滤波算法图雾效果更加理想实验结果表明态滤波较锐化细节时保持原图概况图片达更清晰度需结合种算法叠加运行
关键词：图雾图增强态滤波直方图均衡化
Image defog method based on the method of image filterin
Abstract
The image obtained in bad weather conditions such as fog blur color distortion visual effectsTherefore it is necessary to study images defoggingImages defogging is through a certain means of removing fog interference and achieve rapid recovery of fog and clarity of role resulting in high quality images
Homomorphic filtering is an image in the frequency domain of contrast enhancement and special filtering method of image brightness range homomorphic filtering can reduce the frequency and increase the frequency that is try to keep the low frequency of gray levels (save the original image) and sharpen details so as to achieve the effect of fog
This fog based on homomorphic filtering method and global equalization algorithm for images defogging method compares the advantages of other algorithms optimizing the homomorphic filter algorithm making the image to fog effect is more ideal Experimental results show that the homomorphic filtering can be used to sharpen detail while keeping the original profile To make the image better definition should be combined with a variety of algorithms stacking operation
Key words image image enhancement image enhancement image enhancement image enhancement histogram equalization
目录
1 引言 1
11 课题研究背景意义 1
12 图雾研究历史发展现状 2
13 文研究容结构安排 3
131 文研究容 3
132 文结构安排 3
2 图雾概述 5
21 图雾概念 5
22 图雾分类 5
221 基物理模型方法 6
222 基非物理模型方法 8
23 图雾应 12
3 基态滤波图雾方法 13
31 态滤波概念定义 13
32 态滤波原理 13
33 态滤波操作基流程 13
4 实验结果 18
41 灰度版 18
42 彩色版 20
43 实验结果分析评价 22
5 评价改进 24
51 直方图 24
52 暗通道 26
53 改进 29
531 红外处理 29
532 红外态滤波结合优化 29
533 实验结果图 30
结 31
致谢 33
参考文献 34
附录 37
外文资料翻译原文 48
1 引言
图雾图处理中缺少环节遥感航拍水图分析户外视频日常片处理等诸方面着广泛应章图雾技术进行介绍着重阐述基态滤波图雾方法深入研究基态滤波图雾方法雾天退化图增强进行实验验证时增强雾天降质图度色彩保真度提高户外成系统雾霭等天气工作稳定性性章简介绍图雾处理背景意义图雾国外研究现状出文研究容
11 课题研究背景意义
众周知雾霾种常见天气现象雾霾条件拍摄图片清晰必图进行雾研究图雾技术通定手段图中雾干扰高质量图便满意视觉效果获取更效图信息图雾技术图处理领域重研究分支具跨学科前性应前景广阔等特点备受国外批研究者关注目前已成计算机视觉图处理领域研究热点时作门新兴学科雾问题涉天气条件机性复杂性研究起步较晚二十年研究历程目前然新方法量涌现种方法定局限性处断发展中取研究成果然某方面家认需完善改进提高雾天退化图质量需寻找效办法减少雾影响
12 图雾研究历史发展现状
图雾技术跨学科前性课题具广阔应前景年已成计算机视觉图处理领域研究热点问题吸引国外研究员兴趣该技术应计算机视觉初级阶段目标检测踪目标分类识目标行分析理解等中高级阶段基础
图雾技术研究工作开展较晚国外研究机构已取定研究成果然完善研究早追溯1992年L．Bissonnette等针雾雨天气做图雾处John POakley等针恶劣天气航拍降质彩色图进行雾处理取定研究成果McCartney天气条件气粒子类型浓度进行研究NayarNarasimhan气粒子类型浓度造成种天气成进行简单分析Garg等提出雨滴动力学模型利模型约束区分雨类型信号效检测复杂场景中雨滴
国相国外研究工作开展较早研究机构较国外著名研究机构中美国国家航空航天局（NASA）Langley研究中心（LRC）深研究基邻域（surroundbased）Retinex算法雾烟水夜晚图进行增强算法嵌DSP便携式图增强视觉系统中处理分辨率256×256灰度图达30帧／s基满足实时性求哥伦亚学计算机视觉实验室研究利天气条件场景幅图恢复清晰图建立天气条件场景
WILD（Weather and Illumination Database）数库色列联合成实验室研究基偏振滤波方法该方法气成水成均适曼彻斯特学电气电子工程学院传感图信号处理组图度恢复方面进行长期研究英国Dmist公司研究基础开发商业产品C1earVue
国研究机构中微软亚洲研究院香港中文学（Chinese University ofHong Kong）信息工程系媒体实验室合作研究基数假设单幅图雾方法成果较显著实际应存较差距研究高校相关研究工作尚处进步发展中现阶段较优秀雾手段根种算法优缺点进行优势结合般言良雾效果复合层算法进行叠加例基态滤波红外图增强新方法先原红外图适应中值滤波保留原图细节噪声
13 文研究容结构安排
131 文研究容
文介绍基态滤波图雾方法基态滤波雾图全局均衡化直方图图雾算法暗通道雾算法等方法进行鉴红外技术优点优化态滤波算法图雾效果更加理想
132 文结构安排
文分五部分具体结构：
第部分 绪介绍图雾研究背景意义国外研究现状发展前景文研究容
第二部分 图雾原理技术介绍图雾基原理基特征图雾分类纳图雾典型算法应
第三部分 研究基态滤波图雾方法
第四部分 实验结果
第五部分 实验方法评价改进
第六部分 文进行总结
2 图雾概述
21 图雾概念
图雾技术（雾霆等类似气粒子散射现象均米氏散射理描述描述方便简称雾）务天气素图质量影响增强图视见度
22 图雾分类
图雾技术20年研究发展中国外研究学者努力已形成许应实践技术方法目前流方通物理模型非物理模型展开否赖气散射模型现方法分两类：基物理模型方法（MB）非物理模型方法（
NMB）基物理模型方法图复原方法基非物理模型方法图复原方法
雾天图复原研究雾天图退化物理机制建立雾天退化模型反演退化程补偿退化程造成失真便获未干扰退化雾图雾图优估计值改善雾天图质量种方法针性强雾效果然般会信息损失处理关键点模型中参数估计雾天图增强方法考虑图退化原适性广效提高雾天图度增强图细节改善图视觉效果突出部分信息会造成定损失类方法雾方法相似性进步纳子类方法：基图处理雾天图增强方法分全局化图增强方法局部化图增强方法基物理模型雾天图复原方法包括基偏微分方程雾天图复原基深度关系雾天图复原基先验信息雾天图复原
图详细描述种分类层次：
图21 图雾方法分层
221基物理模型方法
图22 基物理模型复原方法
（1）基偏微分方程雾天图复原
利气信息条件场景深度复原雾天图方法局部修正恢复结果场景深度变化较图部分区域度然较低满足应求某图色彩清晰度度较高求场合采偏微分方程图雾方法广泛应
针雾天图处理助气散射模型建立户外图全局雾局部雾量优化模型推导相应包含图梯度场景景深偏微分方程时利户提供简单附加信息消恢复中确定性实现仅幅降质图雾恢复
（2）基深度关系雾天图复原
降质图场景深度信息复原雾天图条重线索根场景深度信息否知种复原
方法分两类类假设场景深度信息已知方法种基物理模型复原场景度方法简单高斯函数场景中光路进行预测取较复原效果需天气预测信息方法需雷达装置获取场景深度类辅助信息进行场景深度提取方法提取场景深度方法存着定局限性利偏振光方法应气散射程度较弱薄雾适雾天气方法需天气状态相景物图需户交互难满足变换场景实时图处理需求
（3）基先验信息雾天图复原
传统雾方法限度提升降质图清晰度忽略真实图雾气分布均事实整体统处理方式雾致图某部分显够清晰某部分度处理失真年众研究者致力针单幅降质图图中雾气浓度变化达彻底雾效果例基暗原色单图雾技术该方法通收集量受雾气影响图发现套识雾气浓度暗原色统计规律图分成子块子块中亮度低素黑点通常存物体阴影黑色物体具鲜艳颜色物体中根规律需雾气浓度局部修复图部分颜色效达雾效果场景目标亮度气光相似时暗原色先验信息失效
222 基非物理模型方法
图23 基非物理模型方法
（1）全局化图增强方法
全局化雾天图增强方法指整幅雾天图统计信息决定灰度值调整考虑调整点处区域雾天场景退化程度深度相关幅图包含复杂景深信息全局化处理方法收理想效果雾天图场景相简单时失种效途径典型全局化雾天图增强方法六种：
1）全局直方图均衡化算法该方法基思想雾图直方图变换均匀分布形式样增加素灰度值动态范围达增强雾天图整体度效果直方图均衡化雾效果进行雾算法时典型参
2）态滤波算法该算法种频率滤灰度变换相结合图增强处理方法种明反射模型作频域处理基础利压缩亮度范围增强度改善图质量处理技术该方法推广彩色图增强方面广泛应
3）波方法波尺度分析度增强应取进展例尺度雾天图细节进行均衡化图细节锐化作
4）Retinex算法Retinex种描述颜色变性模型具动态范围压缩颜色变性特点光均引起低度彩色图具增强效果
5）曲波变换曲波种波变换基础发展起新尺度分析方法特适合异性奇异性特征信号处理够弥补波变换图曲线边缘增强方面局限性
6）基气调制传递函数（Atmospherical Modulation Transfer FunctionMTF）增强雾天图该方法原理：首先通气调制传递函数预测似估计气图质量退化程先验信息时通预测公式计算出相应瑞流调制传递函数气溶胶调制传递函数前两者积总气调制传递函数然利气调制传递函数频域天气退化图进行复原户外景物图中气调制传递函数造成衰减进行补偿天气退化图进行清晰化处理均采气调制传递函数处理
（2）局部化图增强方法
述全局化图增强方法言类方法整幅图进行操作确定变换转移函数时基整图统计量实际应中常常需图某局部区域细节进行增强局部区域素数量相整幅图素数量较参整幅图计算时影响常忽略掉整幅图函数保证关心局部区域需增强效果需根关心局部区域特性计算变换转移函数函数关心区域需增强效果目前三类局部化图增强方法：
1）局部直方图均衡化方法称块重叠直方图均衡化种标准适应直方图均衡化方法（Adaptive Histogram EqualizationAHE）基思想直方图均衡化运算分散图局部区域通局部运算叠加适应增强图局部信息
2）局部度增强方法三种方式：a常数增益（Constant Gain TraceCGT）算法该算法求雾天图局部均值设定例常数雾天图素位置根变换函数放图局部变化b饱度反馈算法该算法雾天图转换HIS色彩空间中进行处理c．适应饱度反馈算法该算法通饱度分量亮度分量局部相关性确定反馈极性程度饱度反馈算法具适应力
3）基局部方差增强方法该算法通计算较局部标准方差判断局部图增强程度然灰度均值基准进行局部灰度拉伸算法样适深度信息变度较低雾天图相局部直方图均衡化算法噪声方面增加增强细节抑制噪声方面找较折中点该方法需进步研究问题
23 图雾应
着图雾技术发展图雾应领域扩展图雾基应领域视频监控形勘测动驾驶等领域目前图雾应集中方面：遥感航拍水图分析户外视频日常片处理等诸方面着广泛应
3 基态滤波图雾方法
31 态滤波概念定义
态滤波频率滤灰度变换结合起种图处理方法图度／反射率模型作频域处理基础利压缩亮度范围增强度改善图质量种方法图处理符合眼亮度响应非线性特性避免直接图进行傅立叶变换处理失真
32 态滤波原理
原灰度值作度反射率两组份产物度相变化作图低频成份反射率高频成份通分处理度反射率元灰度值影响达揭示阴影区细节特征目
33 态滤波操作基流程
①
③FFT
② LOG
④
⑤IFFT
⑦
⑥EXP
图31 态滤波图雾操作流程图
中表示原始图表示雾处理图取数处理取指数处理表示傅里叶变换表示傅里叶变换表示进行态滤波处理
① 二维函数形式表示图特定坐标处值幅度正标量物理意义图源决定幅图物理程产生时 值正物理源辐射量定非零限
（1）
函数两分量表征：
（1）入射观察场景光源总量
（2）场景中物体反射光总量两分量分称入射分量反射分量表示两函数合成
（2）
中 （3）
（式3）指出反射分量限制0（全吸收）1（全反射）间性质取决射源取决成物体表面特性
图灰度仅仅光函数（入射光）决定反射函数关反射函数反映出图具体容光强度般具致性空间通常具缓慢变化性质傅立叶变换表现低频分量然材料物体反射率差异常引起反射光急剧变化图灰度值发生变化种变化高频分量关
消均匀度影响增强图细节采建立频域态滤波器光足光变化图象进行处理减少光足引起图质量降感兴趣景物进行效增强样程度保留图原貌时图细节增强态滤波种频域中进行图度增强压缩图亮度范围特殊滤波方法态滤波够减少低频增加高频减少光变化锐化边缘细节
通光分量反射分量研究知光分量般反映灰度恒定分量类似频域中低频信息减弱光函数（入射光）起缩图灰度范围作反射光物体边界特性密切相关类似频域中高频信息增强反射光起提高图度作态滤波传递函数般低频部分1高频部分1
②进行态滤波处理首先原图取数图模型中法运算转化简单加法运算
（4）
③函数做傅里叶变换函数转换频域
（5）
④选择合适传递函数压缩分量变化范围削弱增强分量度提升增强细节确定合适分析知致形状图32示中代表高频增益代表低频增益表示点滤波中心距离
图32 态滤波处理示意图
利（6）式进行滤波
（6）
⑤滤波结果进行傅立叶反变换⑥指数运算态滤波输出结果⑦．
（7）
（8）
4 实验结果
41 灰度版
图431（a） 雾前 图431（b） 雾
图432（a） 雾前 图432（b） 雾
图433（a） 雾前 图433（b） 雾
图434（a） 雾前 图434（b） 雾
图435（a） 雾前 图435（b） 雾
42 彩色版
图441（a） 雾前 图441（b） 雾
图442（a） 雾前 图442（b） 雾
图443（a） 雾前 图443（b） 雾
图444（a） 雾前 图444（b） 雾
图445（a） 雾前 图445（b） 雾
43实验结果分析评价
进行Matlab操作达图片雾效果时采两种办法分灰度方法彩色方法第种灰度方法图雾彩色图片转化灰度图片进行处理原始图片输入彩色
Matlab处理呈现原始图片雾图均黑白颜色第二种彩色图雾针彩色图片雾处理输入原始图片输出原始图片雾图片成彩色图
处理效果图清晰度两版雾算法达图雾目灰色版黑白颜色差异更加分明原始图清晰彩色版颜色分辨度增强细节细化图片原始图清晰雾效果灰度雾方法更清晰
图片进行Matlab操作程中时运行结果差强意处理灰色版时态滤波处理原色深图片处理图颜色更暗图（a1－1）（a1－2）示细节锐化明显没达较雾处理效果找优配度进行修改相关系数操作改进算法深色图雾效果旧太改善
处理彩色版时做许调研学准备搞懂程序语言时百度相关验方法总结失败原：没真正弄明白样时三色彩维度进行定义总灰度图片转例原灰色版基础图片进行输出前加入段灰色图片变成彩色代码结果出张彩色原图尝试定义三色彩区间图片录入代码定义fR＝rgb（：：1）fG＝rgb（：：2）
fB＝rgb（：：3）结果出两张灰色图学会运正确彩色图定义输入正确代码实现彩色图雾处理
5评价改进
雾效果五幅雾图片进行直方图雾操作暗通道雾操作雾效果评价算法
51 直方图
图511（a） 雾前 图511（b） 雾
图512（a） 雾前 图512（b） 雾
图513（a） 雾前 图513（b） 雾
图514（a） 雾前 图514（b） 雾
图515（a） 雾前 图515（b） 雾
较结：直方图雾色彩失真冷色系颜色突变暖色系颜色细节锐化程度总体态滤波明显图原貌保持方面态滤波雾方法更保持图原貌直方图雾方法图颜色改变细节处理方面态滤波方法细节锐化程度原图光明亮方加强细节暗通道明显相反直方图雾方法原图光较暗方加前细节态滤波明显
52 暗通道
图521 雾
图522 雾
图523 雾
图524 雾
图525 雾
较结：暗通道雾效果良色彩基保留细节锐化明显暗通道处理图颜色会原图颜色加深图原貌保持方面态滤波雾方法更保持图原貌暗通道雾方法图起颜色更加突出细节处理方面态滤波方法原图光明亮方加强细节暗通道明显相反暗通道方法原图光较暗方加前细节态滤波明显
53 改进
531 红外处理
红外成目标背景红外辐射需气传输光学成光电转换电子处理等程转换成红外图红外图产生程分析红外图特点： 1）空间相关性强度低2）表征象温度分布灰度图分辨率较低图较模糊3）噪声干扰较噪声较复杂信噪低4）存器件性非均匀性等
出红外图存缺陷眼说显著特点度低图模糊红外图存散粒噪声机噪声等部分图中高频信息态滤波正处理锐化高频种方法效加强细节
532红外态滤波结合优化
文提出种基态滤波红外图增强新方法先原红外图适应中值滤波保留原图细节噪声利态滤波优势增强红外图细节特征采限制度适应直方图均衡方法进步调整图灰度动态范围方案解决态滤波存缺陷终提高图分辨率度通仿
真验证非常增强效果
533 实验结果图
图531（a） 原图 图531（b） 红外 图531（b） 态滤波
图532（a） 原图 图532（b） 红外 图532（b） 态滤波
图533（a） 原图 图533（b） 红外 图533（b） 态滤波
结
表51 雾方法分析
类
子类
雾方法
优点
缺点
基图处理雾天图増强方法
全局化增强
全局直方图均衡化
⑴算法简单
⑵单景深图复原效果
难反映景深变图中局部景深变化
态滤波
⑴掉光均产生黑斑暗影
⑵较保持图原始貌
需耍两次傅立叶变换占较运算空间
暗通道
较增强图细节
光亮方细节处理效果般
表51雾方法优缺点较方法解决问题思路存着根区种方法优缺点实际应中根需采累试法进行处理幅雾图根研究员判定处理果采增强方法改善灰度度效果釆增强方法采图复原方法行退化模型进行复原处理直观考察种算法清晰化效果述种典型基图处理增强方法新提出基物理模型图复原方法进行实验仿真图13算法清晰化效果示例
图61 原图 图62 态滤波 图63 直方图
图64 暗通道 图65 红外 图66 红外+态滤波
观察图片知雾算法效果优劣图66雾效果应红外技术提高高频应态滤波保持图原貌时图细节处理更加细腻图片达更清晰度需结合种算法叠加运行
致谢
时光飞逝学里学期快历毕业设计整程感觉程中充实愉快
文北方工业学理学院郭芬红老师悉心指导帮助完成选题寻找相关资料开题答辩中期检查程中编程实现文定稿答辩郭老师直耐心竭帮助前期资料查询准备开题答辩书写修改答辩准备代码运行文成文修改郭老师直拽着前进
郭老师总时毕业设计相关信息通知第时间告知文撰写程序设计方面老师非常仔细文老师字句认真仔细阅读帮助标注出恰方指导做出修改帮助精益求精里真诚感谢导师郭芬红私付出
朱喜玲学姐态滤波代码修改中挤出时间私帮助改正代码表深深感谢
学期学程中少学间互相帮助家支持鼓励更少课题刻苦钻研工作者学者付出现做学研究真站巨肩膀更高走更远
谨篇文完成际感谢身边位帮助老师家学朋友致谢
参考文献
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附录
I态滤波代码 灰色版
clcclear allclose all
imgimread('E\Matlab\R2008a\abc\4jpg')
imgrgb2gray(img)
imgimresize(img[256256])
figure(1)
imshow(img)title('原始图片')
imgim2double(img)图片img转换成double型
k18
k28
r161
alf1600
alf161
alf20
nnfloor((r+1)2) nn81尺度C取80合适
for i1r 1循环81
for j1r
h(ij) exp(((inn)^2+(jnn)^2)(k1*alf))(k2*pi*alf*10000) 高斯函数
h(ij) exp(((inn)^2+(jnn)^2)(2*alf^2)) 高斯函数
end
end
gauss hsum(sum(h))
Rconv2(imggauss'same') 灰度
Rlog(R)
Slog(img)R
TS+R
K2exp(T)取指数
K2uint8(K2)
figureimshow(K2)
V变换
V1load('M_256mat')
V1V1y
Fimg1V1*R*V1'
Fimg2V1*S*V1'
傅里叶变换
Fimg1fft(R)傅里叶变换
Fimg2fft(S)傅里叶变换
[MN]size(Fimg1)
figure(2)
imshow(uint8(abs(P))[])title('滤波前频谱图')绘制源图频谱幅度谱
x0floor(M2)取整数
y0floor(N2)
态滤波参数设置
D03
c150
Hh16Hl08Hh>1Hl<1
for u1M
for v1N
D(uv)sqrt((ux0)^2+(vy0)^2)
H(uv)(HhHl)*(1exp(c*(D(uv)^2D0^2)))+Hl态滤波器函数
end
end
Y1Fimg1*H
Y2Fimg2*H
傅里叶逆变换
Q1ifft(Y1)
Q2ifft(Y2)
QQ1+Q2
Jexp(Q)取指数
Jim2uint8(J)
figureimshow(J)title('雾图片')
J1double(J)
[SDENTRAVEGRAD]Sd(J1)
II态滤波第二次修改代码 彩色版
clcclear allclose all
imgimread('E\Matlab\R2008a\aaa\1jpg')
imgimresize(img[256256])
imshow(img)title('原始图片')
Yzeros(2562563)
for ii13
Limg(ii)
img1im2double(L)图片img转换成double型
k18
k28
r161
alf1600
alf161
alf20
nnfloor((r+1)2) nn81尺度C取80合适
for i1r 1循环81
for j1r
h(ij) exp(((inn)^2+(jnn)^2)(k1*alf))(k2*pi*alf*10000) 高斯函数
h(ij) exp(((inn)^2+(jnn)^2)(2*alf^2)) 高斯函数
end
end
gauss hsum(sum(h))
Rconv2(img1gauss'same') 灰度
Rlog(R)
Slog(img1)R
TS+R
K2exp(T)取指数
K2uint8(K2)
figureimshow(K2)
V变换
V1load('M_256mat')
V1V1y
Fimg1V1*R*V1'
Fimg2V1*S*V1'
傅里叶变换
Fimg1fft(R)傅里叶变换
Fimg2fft(S)傅里叶变换
[MN]size(Fimg1)
figure(2)
imshow(uint8(abs(P))[])title('滤波前频谱图')绘制源图频谱幅度谱
x0floor(M2)取整数
y0floor(N2)
态滤波参数设置
D03
c350
Hh16Hl08Hh>1Hl<1
for u1M
for v1N
D(uv)sqrt((ux0)^2+(vy0)^2)
H(uv)(HhHl)*(1exp(c*(D(uv)^2D0^2)))+Hl态滤波器函数
H(uv)(HhHl)*(1(1+(D0c*D(uv))))^2+Hl巴特沃斯
end
end
Y1Fimg1*H
Y2Fimg2*H
傅里叶逆变换
Q1ifft(Y1)
Q2ifft(Y2)
QQ1+Q2
Jexp(Q)取指数
Jim2uint8(J)
Y(ii)J
end
figureimshow(mat2gray(Y))title('雾图')
III直方图均衡化程序
sourcePicimread('E\Matlab\R2008a\abc\22jpg')
[mno]size(sourcePic)
figureimshow(sourcePic[])
title('原图')
grayPicrgb2gray(sourcePic)
grayPicsourcePic(1)
gpzeros(1256) 计算灰度出现概率
for i1256
gp(i)length(find(grayPic(i1)))(m*n)
end
newGpzeros(1256) 计算新灰度出现概率
S1zeros(1256)
S2zeros(1256)
tmp0
for i1256
tmptmp+gp(i)
S1(i)tmp
S2(i)round(S1(i)*256)
end
for i1256
newGp(i)sum(gp(find(S2i)))
end
newGrayPicgrayPic 填充素点新灰度值
for i1256
newGrayPic(find(grayPic(i1)))S2(i)
end
nrnewGrayPic
grayPicsourcePic(2)
gpzeros(1256) 计算灰度出现概率
for i1256
gp(i)length(find(grayPic(i1)))(m*n)
end
newGpzeros(1256) 计算新灰度出现概率
S1zeros(1256)
S2zeros(1256)
tmp0
for i1256
tmptmp+gp(i)
S1(i)tmp
S2(i)round(S1(i)*256)
end
for i1256
newGp(i)sum(gp(find(S2i)))
end
newGrayPicgrayPic 填充素点新灰度值
for i1256
newGrayPic(find(grayPic(i1)))S2(i)
end
ngnewGrayPic
grayPicsourcePic(3)
gpzeros(1256) 计算灰度出现概率
for i1256
gp(i)length(find(grayPic(i1)))(m*n)
end
newGpzeros(1256) 计算新灰度出现概率
S1zeros(1256)
S2zeros(1256)
tmp0
for i1256
tmptmp+gp(i)
S1(i)tmp
S2(i)round(S1(i)*256)
end
for i1256
newGp(i)sum(gp(find(S2i)))
end
newGrayPicgrayPic 填充素点新灰度值
for i1256
newGrayPic(find(grayPic(i1)))S2(i)
end
nbnewGrayPic
rescat(3nrngnb)
figureimshow(res[])
title('处理图')
外文资料翻译原文
灰度直方图
摘
图雾技术利定模型算法处理图雾恢复图原始特征文介绍常霾雾三种方法包括基光分离模型算法提出种基直方图均衡化算法基暗原色先验MATLAB台设计实现种数字图处理系统雾述算法雾天图效果更
关键词：图雾光分离模型直方图均衡化暗通道
11 引言
数字图处理中简单工具灰度直方图该函数概括幅图灰度级容幅图直方图包括观信息某类型图直方图完全描述直方图计算简单特幅图方复制方时直方图计算非常低代价完成
111 定义
灰度直方图灰度级函数描述图中具该灰度级素数：横坐标灰度级坐标该灰度出现频率（素数）图11示例
图11 幅图灰度直方图
灰度直方图种方式定义[1]练更清楚种方法处假设幅函数定义连续图滑中心高度灰度级变化边低灰度级选择定某灰度级然定义条轮廓线该轮廓线连接图具灰度级点轮廓线形成包围灰度级等区域封闭曲线
图12中图条灰度级轮廓线更高灰度级处画第二条轮廓线第条轮廓线包围区域面积样第二条轮廓线包围区域面积
图12 幅图轮廓线
幅连续图中具灰度级D轮廓线包围面积称阈值面积函数直方图定义
(1)
幅连续图直方图面积函数导数负值负号出现着D增加减果图成二维机变量面积函数相累积分布函数灰度直方图相概率密度函数
离散函数固定1等式（1）变
(2)
数字图灰度级D面积函数等灰度值D素数
112 二维直方图
常发现构造高维直方图维直方图更特研究彩色图图13幅数字化显微图中含白血球红血球图白光（a）助滤光片红光（b）蓝光（c）进行数字化右图两幅图红—蓝直方图
二维直方图两变量：红光图灰度值蓝光图灰度值函数坐标处值指红光图中具灰度值时蓝光图中位置具灰度值素（）数种光谱数字图采样点素素变量——处变量数2 二维直方图表示素值两种灰度级组合中分布情况果红光图蓝光图相直方图
斜线位置值外余处值0 果素（）中红分量蓝分量者反直方图分布分斜线
白光图13中显微镜区域显示关彩色许信息红血球呈现粉红色白血球呈现灰色染色处理显示深蓝色核红细胞蓝光吸收蓝光较暗红光透红光较亮样核红光颜色更深红蓝直方图四峰值背景（B）产生红细胞（R）产生核（N）产生白血球细胞质（C）产生
图13 二维直方图示例
（a） 白光图（b）红光图（c）蓝光图（d）红蓝直方图
113 直方图性质
幅图压缩直方图空间信息丢失直方图描述灰度级具素数蛋素图中位置提供线索特定图唯直方图反成立
——极图着相直方图例图中移动物体般直方图没影响直方图确实信息
果换等式（1）变量等式两边D进行积分
(3)
面积函数果令假设灰度级非负
(4)
离散图情形
(5)
中NLNS分图行列数目
果幅图包含灰度均匀致物体背景物体度强规定物体边界灰度级定义轮廓线
(6)
果图包含物体轮廓线处灰度级均公式（6）出物体面积
通图面积化灰度直方图图概率密度函数（PDF）面积函数进行样化处理图累积分布函数（CDF）函数图进行统计处理时
直方图性质该性质定义——灰度级素数——直接：果图两连接区域组成区域直方图已知整幅图直方图该两区域直方图显然该结推广数目连接区域情形
12 直方图途
121 数字化参数
直方图出简单见指示判断幅图否合理利全部允许灰度级范围般幅数字图应该利全部全部灰度级图11否等增加量化间隔旦数学化图级数少256丢失信息（非重新数字化）恢复
果图具超出数字化器处理范围亮度灰度级简单置0255 直方图端两端产生尖峰数字化时直方图进行检查做法直方图快速检查数字化中产生问题早暴露出免浪费量时间
122 边界阈值选择
前述轮廓线提供确立图中简单物体边界效方法轮廓线作边界技术称阈值化合适技术选择灰度阈值图处理中讨课题
假定幅图背景浅色中深色物体图14类图直方图物体中深色素产生直方图左锋背景中量灰度级产生直方图右锋物体边界附具两峰值间灰度级素数目相较少产生两峰间谷选择谷作灰度阈值合理物体边界
图54 双峰直方图
某种意义说应两峰间低点灰度级作阈值确定边界适宜等式（1）知直方图面积函数导数谷底附直方图值相较意味着面积函数阈值灰度级变化缓慢果选择谷底处灰度作阈值物体边界影响达果试图测量物体面积选择谷底处阈值测试量阈值灰度变化敏感降低
123 综合光密度
出（图14）直方图甚没图情况确定物体佳灰度阈值便计算物体面积（等式（6））外种简单图直方图直接计算量综合光密度（IOD）反映图中质量种度量定义
(7)
中ab划定图区域边界果灰度级0背景深色物体IOD反映物体面积密度组合
数字图
(8)
中处素灰度值令代表灰度级k时应素数等式（8）写成
(9)
显然该式幅图素灰度级加起然灰度级k应直方图值公式（9）写成
(10)
灰度级加权直方图令式（8）等式（10）令灰度级增量趋极限0 类似适连续图表达式
(11)
(12)
果图中物体阈值灰度级T边界勾划出物体边界IOD式出
(13)
部灰度级均（mean）值MGL等IOD面积：
(14)
13 直方图图关系
特定图言直方图唯简单图函数形式已知推导出直方图种技术许少直方图更深理解
假定已知幅图函数形式希计算直方图知道直方图面积函数关系等灰度级导数负数（等式（1））果首先图身表达式面积函数求直方图时通观测达目
131 维
简单起见首先考虑维情况 面积实际指长度说明图直方图间关系
考虑维高斯脉（图15）
(15)
图55 高斯脉
注意非负x函数单调面积图函数逆函数非负数x通解方程（15）作灰度级函数x：
(16)
式图右半部分面积函数图左右两半称总面积函数等式（16）两倍直方图表示
(17)
图16示处直方图尖峰较处面积低灰度值点（灰度）处尖峰图处斜率0引起（高斯函数顶部附时坦）
图16 高斯脉直方图
132 二维
通图称性巧妙利样处理程推广二维情形例假定等式（15）维高斯脉实际二维图中条线段果线段样直方图具图16示形状仅仅坐标刻度已
述方法中利圆称性假定图时中心原点圆称高斯脉（图17）
图函数极坐标表示
(18)
图17 圆形高斯点
灰度级常数P轮廓线半径图
(19)
该轮廓线包围面积
(20)
公式（20）表示面积函数微分直方图[1]
(21)
图18 注意然原点处斜率0 够强维情形时样处产生尖峰
图18 图高斯点直方图
更复杂图首先应图划分相邻区域分确定区域面积函数然述方法直方图整图直方图相连区域直方图
14 点总结
1 灰度级直方图阈值面积函数导数负值
2 直方图表明灰度级少素
3 观察直方图出合适数字化
4 简单物体面积IOD通图直方图求
5 具特定函数形式图直方图通面积函数求
参考文献：
1 RJWallAKlingerand KRCastlemanAnalysis of Image HistogramsProcSecond IntCongon Pattern RecognitionCopenhagen1974
2 CLNovak and SAShaferAnatomy of a Color HistogramProceedings of the 1992 IEEE Computer Society Conference on Computer Vision and Pattern Recognnition599—605IEEE Computer Society PressLos AlamitosCA1992
3 JPrewitt and MMendelsohnThe Analysis of Cell Images Annals of the New York Academy of Sciences1281035—1053January 1966
4 MMendelsohnBMayallJPrewittRBostromand RHolcombDigital Transformation and Computer Analysisi of Microscope Imagesin RBarer and VCossletedsAdvances in Optical and Electron Microscopy 2 Academic Press London 1968
Research on Image Defogging Methods
ZHANG Chi
School of Computer and SoftwareNanjing University of Information Science and TechnologyNanjing 210044
ABSTRACT
Image dehazing is to use a certain model or algorithm to process the defogging image to restore the original features of the imageThe paper introduces three methods commonly used to haze the fog including an algorithm based on light separation modelan algorithm based on histogram equalization and an algorithm based on dark channel prior In the MATLAB platform design and implementation of a digital image processing system to fog to use the above algorithm to the fog image the effect is better
Key words image defogging light separation model histogram equalization dark channel prior
The GrayLevel Histogram
11 INTRODUCTION
One of the simplest and most useful tools in digital image processing is the graylevel histogram The function summarizes the graylevel content of an image While the histogram of any image contians considerable informationcertain types of images are completely specified by their histograms Computation of the histogram is simple and may be done at little apparent cost when an image is copied from one place to another
111 Definition
The graylevel histogram is a function showingfor each gray levelthe number of pixels in the image that have that gray level The abscissa is gray level and the ordinate is frequency of occurrence(number of pixels) Figure 11 shows an example
There is another way to define the graylevel histogram[1]and the following exercise yields insight into the usefulness of this function Suppose we have a continuous imagedefined by the function that varies smoothly from high gray level at the center to low gray level at the borders We can select some gray level and define a set of contour lines connecting all points in the image with value The resulting contour lines from closed curves that surround regions in which the gray level is greater than or equal to
Figure 12 shows an image containing one contour line at the gram level A second contour line has been drawn at a higher gray level
is the area of the region inside the first contour line and similarly is the area inside the second line
The threshold area function of a continuous image is the area enclosed by all contour lines of gray level D Now the histogram may be
defined as
(1)
Thus the histogram of a continuous image is the negative of the derivatives of its area function The minus sign results from the fact that decreases with increasing D If the image is considered a random variable of two dimensions the area function is proportional to its cumulative distribution function and the gray level histogram to its probability density density function
Figure 11 An image and its graylevel histogram
Figure 12 Contour lines in an image
For the case of discrete functions we fix at unity and E(1) becomes
(2)
The area function of a digital image is merely the number of pixels having gray level greater than or equal to D for any gray level D
112 The TwoDimensional Histogram
Frequently one finds it useful to construct histograms of higher dimension than one This is particularly useful for color images [2]as discussed in Chapter 21figure 13 shows images digitized from a microscope field containing a white blood cell and several red blood cells The field was digitized in white light and through colored filters
in red and blue light At the lower right is the twodimensional redversusblue histogram of the latter two images
The twodimensional histogram is a function of two variables gray level in the red image and gray level in the blue image Its value at the coordinate is the number of corresponding pixel pairs having gray level in the red image and gray level in the blue image Recall that a multispectral digital image such as this can be thought of as having a single pixel at each sample point but each pixel has multiple values —in this case two The twodimensional histogram shows how the pixels are distributed among combinations of two gray levels If the red and blue component images were identical the histogram would have zero value except on the diagonal Pixels having higher red than blue gray level and vice versa contribute to the histogram above and below the diagonal line respectively
In white light the microscope field of Figure 13 shows considerable information in color The red blood cells appear pinkish Thus the red cells appear dark in blue light which they absorb and light in red light which they transmit Similarly the nucleus is much denser in red light The redversusblue histogram therefore has four distinct peaks one each due to the background the red blood cells and the nucleus and cytoplasm
of the white cell The analysis of twodimensional histograms is discussed further in Chapter 21
113 Propertise of the Histogram
When an image is condensed into a histogram all spatial information is discarded The histogram specifies the number of pixels having each gray level but gives no hint as to where those pixels are located within the image Thus the histogram is unique for any particular image but the reverse is not true Vastly different images could have identical histograms Such operations as moving objects around within an image typically have no effect on the histogram The histogram does Nevertheless possess some useful properties
If we change variables in Fq(1) and integrate both sides from D to infinity we find that
(3)
The area function If we then set assuming nonnegative gray levels we obtain
area of image (4)
Figure 13 Example twodimensional histogram
(a)whitelight image(b)redlight image(c)bluelight image(d)redblue histogram
Or in the discrete case
(5)
Where NL and NS are the number of rows and columns respectivelyin the image
If an image contains a single uniformly gray object on a contrasting background and we stipulate that the boundary of that object is the contour line defined by gray level then
area of object (6)
If the image contains multiple objects All of whose boundaries are contour lines at gray level Then Eq(6) gives the aggregate area of all the objects
Normalizing the graylevel histogram by dividing by the area of the image produces the probability density function(PDF) of the image A similar normalization of the area function produces the cumulative distribution function (CDF) of the image These functions are useful in the statistical treatment of images As illustrated in chapter 6
The histogram has another useful propertywhich follows directly from its definition as the number of pixels having each gray level if an image consists of two disjoint regions And the histogram of each region is known then the histogram of the entire image is the sum of the two regional histograms Clearly this can be extended to any number of disjoint regions
12 USES OF THE HISTOGRAM
121 Digitizing Parameters
The histogram gives a simple visual indication as to whether or not an image is properly scaled within the available range of gray levels Ordinarily a digital image should make use of all or almost all of the available gray levels as in Figure 11 Failure to do so increases the effective quantizing interval Once the image has been digitized to fewer than 256 gray levels the lost information cannot be restored without redigitizing
Likewise if the image has a greater brightness range than the digitizeris set to handle then the gray levels will be clipped at 0 andor 255 Producing spikes at one or both ends of the histogram It is a good practice routinely to review the histogram when digitizing A quick check of the histogram can bring digitizing problems into the open before much time has been wasted
122 Boundary Threshold Selection
As mentioned earliercontour lines provide an effective way to establish the boundary of a simple object within an image The technique of using contour lines as boundaries is called thresholding The use of optimal techniques for selecting threshold gray levels is a subject of considerable discussion in the literature and is treated in Chapter 18
Suppose an image contains a dark object on a light background Figure 14 illustrates the appearance of the histogram of such an image The dark pixels inside the object produce the rightmost peak in the histogram The leftmost peak is due to the large number of gray levels in the background The relatively few mid level gray pixels around the edge of the object produce the dip betwee
n the two peaks A threshold gray level chosen in the area of the dip will produce a reasonable boundary for the object
Figure 14 a bimodal histogram
In one sense the gray level corresponding to the minimun between the two peaks is optimal for defining the boundary Recall from Eq(1) that the histogram is the derivative of the area function In the vicinity of the dip the histogram takes on relatively small values implying gray level at the dip we minimize its effect upon the boundary of the object If we are concerned with measuring the object's area selecting a threshold at the dip in the histogram minimizes the sensitivity of the area measurement to variations in threshold gray level
123 Integrated Optical Density
Given the histogram in Figure 14 we could determine an optimal threshold gray level for the object and compute its area [Eq(6)] without ever seeing the image Another measurement that can be computed directly from the histogram of simple images is the integrated optical density (IOD)
A useful measure of the mass of an image it is defined as
(7)
Where a and b delimit the region of the image When the image consists of a dark object situated on a background of zero gray level the IOD reflects a combination of the area and density of that object
For a digital image
(8)
Where is the gray level of the pixel at line i sample j Let be the number of pixels in the image whit gray level equal to k Then Eq(8) can be written as
(9)
Since clearly this adds up the gray levels of all pixels within the image However is merely the histogram evaluated at gray level k Thus Eq(9) can be written as
(10)
That is a graylevelweighted summation of the histogram By equating Eqs(8)and (10)and taking a limit as the increment between gray levels approaches zero we derive similar expressions for continuous images
(11)
And
(12)
If an object within the image is delineated by a threshold boundary at gray level T the IOD within the object boundary is given by
(13)
The mean interior gray level is the ratio of IOD to area
(14)
13 RELATIONSHIP BETWEEN HISTOGRAM AND IMAGE
Since the histogram of a particular image is unique it is possible to derive the histogram of simple images whose functional from is known While this technique is perhaps seldom used it does yield insight into the histogram and it establishes a basis for further study of threshold selection in chapter 18
Suppose we have an image of given functional from and we desire to computer its histogram We know that this is the negative of the derivative with respect to gray level of the area funcyion [Eq(1)] Thus we may derive the histogram if we first derive the area function from the expression for the image itself Sometimes this can be done simply by observation
131 One Dimension
For simplicity we first address the onedimensional case Here the area is actually a length but it demonstrates the relationship between a histogram and its image
Consider the onedimensional Gaussian pulse (Figure 15 )given by
(15)
Notice that for nonnegative x the function is monotonic Furthermore the area is merely the inverse of the image function Thus for nonnegative values of x we may solve Eq(15) for x as a function of gray level to yield
(16)
Which is the area function for the right half of the image Since the two halves of the image
Figure 15 the gaussian pulse
are symmetrical the overall area function is twice that of Eq(16) The histogram is given by
(17)
And is shown in Figure 16 The histogram builds up to a spike at because of the large areas of low gray level at large positive and negative values of x The small spike at results from the image having zero slope at (iethe Gaussian is locally flat at the very top)
Figure 16 histogram of the Gaussian pulse
132 Two Dimensions
The same procedure may be extended to twodimensional images by judicious use of symmetry within the image For example suppose that the onedimensional Gaussian pulse of Eq(15) is actually one line of a twodimensional image Then if all lines are identical the histogram will have the same shape as that in Figure 16 differing only in ordinate scale
One may take advantage of circular symmetry in the following way Suppose the image is a circularly symmetric Gaussian pulse centered on the origin (Figure 17) The image function in polar coordinates is given by
(18)
Figure 17 the circular Gaussian spot
A contour of constant gray level P is a circle of radius
(19)
Such a contour encloses an area
(20)
The area function of Eq(20) may now be differentiated to yield the histogram [1]
(21)
Shown in Figure 18 Notice that the point of zero slope at the origin is not powerful enough to produce a spike at As it did in the onedimensional case
For more complex images the histogram may be derived by first partitioning the imageinto disjoint regions over which the area function may be determined The histogram of the complete image is then the sum of the histograms of all the disjoint regions
Figure 18 histogram of the circular Gaussian spot
14 SUMMARY OF IMPORTANT POINTS
6 The graylevel histogram is the negative of the derivative of the threshold area function
7 The histogram shows how many pixels occur at each gray level
8 Inspection of the histogram points out improper digitization
9 The area and IOD of a simple object can be computed from the histogram of its image
10 The histogram of an image of specified functional from can be derived with the aid of the area function
REFERENCES
1 RJWallAKlingerand KRCastlemanAnalysis of Image HistogramsProcSecond IntCongon Pattern RecognitionCopenhagen1974
2 CLNovak and SAShaferAnatomy of a Color HistogramProceedings of the 1992 IEEE Computer Society Conference on Computer Vision and Pattern Recognnition599—605IEEE Computer Society PressLos AlamitosCA1992
3 JPrewitt and MMendelsohnThe Analysis of Cell Images Annals of the New York Academy of Sciences1281035—1053January 1966
4 MMendelsohnBMayallJPrewittRBostromand RHolcombDigital Transformation and Computer Analysisi of Microscope Imagesin RBarer and VCossletedsAdvances in Optical and Electron Microscopy 2 Academic Press London 1968
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XX学
科毕业设计（文）
题 目： 基态滤波图雾方法
指导教师：
专业班级：
学 号：
姓 名：
日 期： 20XX年X月X日
基态滤波图雾方法
摘
雾霭等天气条件获图模糊清颜色失真影响视觉效果必图进行雾研究图雾通定手段图中雾干扰达快速效雾清晰度恢复作高质量图
图雾方法众态滤波种频域中进行图度增强压缩图亮度范围特殊滤波方法种方法减少低频增加高频量保留低频中灰度级（保存图原貌）锐化细节达雾效果
文基态滤波雾算法全局均衡化图雾算法等方法进行鉴算法优点优化态滤波算法图雾效果更加理想实验结果表明态滤波较锐化细节时保持原图概况图片达更清晰度需结合种算法叠加运行
关键词：图雾图增强态滤波直方图均衡化
Image defog method based on the method of image filterin
Abstract
The image obtained in bad weather conditions such as fog blur color distortion visual effectsTherefore it is necessary to study images defoggingImages defogging is through a certain means of removing fog interference and achieve rapid recovery of fog and clarity of role resulting in high quality images
Homomorphic filtering is an image in the frequency domain of contrast enhancement and special filtering method of image brightness range homomorphic filtering can reduce the frequency and increase the frequency that is try to keep the low frequency of gray levels (save the original image) and sharpen details so as to achieve the effect of fog
This fog based on homomorphic filtering method and global equalization algorithm for images defogging method compares the advantages of other algorithms optimizing the homomorphic filter algorithm making the image to fog effect is more ideal Experimental results show that the homomorphic filtering can be used to sharpen detail while keeping the original profile To make the image better definition should be combined with a variety of algorithms stacking operation
Key words image image enhancement image enhancement image enhancement image enhancement histogram equalization
目录
1 引言 1
11 课题研究背景意义 1
12 图雾研究历史发展现状 2
13 文研究容结构安排 3
131 文研究容 3
132 文结构安排 3
2 图雾概述 5
21 图雾概念 5
22 图雾分类 5
221 基物理模型方法 6
222 基非物理模型方法 8
23 图雾应 12
3 基态滤波图雾方法 13
31 态滤波概念定义 13
32 态滤波原理 13
33 态滤波操作基流程 13
4 实验结果 18
41 灰度版 18
42 彩色版 20
43 实验结果分析评价 22
5 评价改进 24
51 直方图 24
52 暗通道 26
53 改进 29
531 红外处理 29
532 红外态滤波结合优化 29
533 实验结果图 30
结 31
致谢 33
参考文献 34
附录 37
外文资料翻译原文 48
1 引言
图雾图处理中缺少环节遥感航拍水图分析户外视频日常片处理等诸方面着广泛应章图雾技术进行介绍着重阐述基态滤波图雾方法深入研究基态滤波图雾方法雾天退化图增强进行实验验证时增强雾天降质图度色彩保真度提高户外成系统雾霭等天气工作稳定性性章简介绍图雾处理背景意义图雾国外研究现状出文研究容
11 课题研究背景意义
众周知雾霾种常见天气现象雾霾条件拍摄图片清晰必图进行雾研究图雾技术通定手段图中雾干扰高质量图便满意视觉效果获取更效图信息图雾技术图处理领域重研究分支具跨学科前性应前景广阔等特点备受国外批研究者关注目前已成计算机视觉图处理领域研究热点时作门新兴学科雾问题涉天气条件机性复杂性研究起步较晚二十年研究历程目前然新方法量涌现种方法定局限性处断发展中取研究成果然某方面家认需完善改进提高雾天退化图质量需寻找效办法减少雾影响
12 图雾研究历史发展现状
图雾技术跨学科前性课题具广阔应前景年已成计算机视觉图处理领域研究热点问题吸引国外研究员兴趣该技术应计算机视觉初级阶段目标检测踪目标分类识目标行分析理解等中高级阶段基础
图雾技术研究工作开展较晚国外研究机构已取定研究成果然完善研究早追溯1992年L．Bissonnette等针雾雨天气做图雾处John POakley等针恶劣天气航拍降质彩色图进行雾处理取定研究成果McCartney天气条件气粒子类型浓度进行研究NayarNarasimhan气粒子类型浓度造成种天气成进行简单分析Garg等提出雨滴动力学模型利模型约束区分雨类型信号效检测复杂场景中雨滴
国相国外研究工作开展较早研究机构较国外著名研究机构中美国国家航空航天局（NASA）Langley研究中心（LRC）深研究基邻域（surroundbased）Retinex算法雾烟水夜晚图进行增强算法嵌DSP便携式图增强视觉系统中处理分辨率256×256灰度图达30帧／s基满足实时性求哥伦亚学计算机视觉实验室研究利天气条件场景幅图恢复清晰图建立天气条件场景
WILD（Weather and Illumination Database）数库色列联合成实验室研究基偏振滤波方法该方法气成水成均适曼彻斯特学电气电子工程学院传感图信号处理组图度恢复方面进行长期研究英国Dmist公司研究基础开发商业产品C1earVue
国研究机构中微软亚洲研究院香港中文学（Chinese University ofHong Kong）信息工程系媒体实验室合作研究基数假设单幅图雾方法成果较显著实际应存较差距研究高校相关研究工作尚处进步发展中现阶段较优秀雾手段根种算法优缺点进行优势结合般言良雾效果复合层算法进行叠加例基态滤波红外图增强新方法先原红外图适应中值滤波保留原图细节噪声
13 文研究容结构安排
131 文研究容
文介绍基态滤波图雾方法基态滤波雾图全局均衡化直方图图雾算法暗通道雾算法等方法进行鉴红外技术优点优化态滤波算法图雾效果更加理想
132 文结构安排
文分五部分具体结构：
第部分 绪介绍图雾研究背景意义国外研究现状发展前景文研究容
第二部分 图雾原理技术介绍图雾基原理基特征图雾分类纳图雾典型算法应
第三部分 研究基态滤波图雾方法
第四部分 实验结果
第五部分 实验方法评价改进
第六部分 文进行总结
2 图雾概述
21 图雾概念
图雾技术（雾霆等类似气粒子散射现象均米氏散射理描述描述方便简称雾）务天气素图质量影响增强图视见度
22 图雾分类
图雾技术20年研究发展中国外研究学者努力已形成许应实践技术方法目前流方通物理模型非物理模型展开否赖气散射模型现方法分两类：基物理模型方法（MB）非物理模型方法（
NMB）基物理模型方法图复原方法基非物理模型方法图复原方法
雾天图复原研究雾天图退化物理机制建立雾天退化模型反演退化程补偿退化程造成失真便获未干扰退化雾图雾图优估计值改善雾天图质量种方法针性强雾效果然般会信息损失处理关键点模型中参数估计雾天图增强方法考虑图退化原适性广效提高雾天图度增强图细节改善图视觉效果突出部分信息会造成定损失类方法雾方法相似性进步纳子类方法：基图处理雾天图增强方法分全局化图增强方法局部化图增强方法基物理模型雾天图复原方法包括基偏微分方程雾天图复原基深度关系雾天图复原基先验信息雾天图复原
图详细描述种分类层次：
图21 图雾方法分层
221基物理模型方法
图22 基物理模型复原方法
（1）基偏微分方程雾天图复原
利气信息条件场景深度复原雾天图方法局部修正恢复结果场景深度变化较图部分区域度然较低满足应求某图色彩清晰度度较高求场合采偏微分方程图雾方法广泛应
针雾天图处理助气散射模型建立户外图全局雾局部雾量优化模型推导相应包含图梯度场景景深偏微分方程时利户提供简单附加信息消恢复中确定性实现仅幅降质图雾恢复
（2）基深度关系雾天图复原
降质图场景深度信息复原雾天图条重线索根场景深度信息否知种复原
方法分两类类假设场景深度信息已知方法种基物理模型复原场景度方法简单高斯函数场景中光路进行预测取较复原效果需天气预测信息方法需雷达装置获取场景深度类辅助信息进行场景深度提取方法提取场景深度方法存着定局限性利偏振光方法应气散射程度较弱薄雾适雾天气方法需天气状态相景物图需户交互难满足变换场景实时图处理需求
（3）基先验信息雾天图复原
传统雾方法限度提升降质图清晰度忽略真实图雾气分布均事实整体统处理方式雾致图某部分显够清晰某部分度处理失真年众研究者致力针单幅降质图图中雾气浓度变化达彻底雾效果例基暗原色单图雾技术该方法通收集量受雾气影响图发现套识雾气浓度暗原色统计规律图分成子块子块中亮度低素黑点通常存物体阴影黑色物体具鲜艳颜色物体中根规律需雾气浓度局部修复图部分颜色效达雾效果场景目标亮度气光相似时暗原色先验信息失效
222 基非物理模型方法
图23 基非物理模型方法
（1）全局化图增强方法
全局化雾天图增强方法指整幅雾天图统计信息决定灰度值调整考虑调整点处区域雾天场景退化程度深度相关幅图包含复杂景深信息全局化处理方法收理想效果雾天图场景相简单时失种效途径典型全局化雾天图增强方法六种：
1）全局直方图均衡化算法该方法基思想雾图直方图变换均匀分布形式样增加素灰度值动态范围达增强雾天图整体度效果直方图均衡化雾效果进行雾算法时典型参
2）态滤波算法该算法种频率滤灰度变换相结合图增强处理方法种明反射模型作频域处理基础利压缩亮度范围增强度改善图质量处理技术该方法推广彩色图增强方面广泛应
3）波方法波尺度分析度增强应取进展例尺度雾天图细节进行均衡化图细节锐化作
4）Retinex算法Retinex种描述颜色变性模型具动态范围压缩颜色变性特点光均引起低度彩色图具增强效果
5）曲波变换曲波种波变换基础发展起新尺度分析方法特适合异性奇异性特征信号处理够弥补波变换图曲线边缘增强方面局限性
6）基气调制传递函数（Atmospherical Modulation Transfer FunctionMTF）增强雾天图该方法原理：首先通气调制传递函数预测似估计气图质量退化程先验信息时通预测公式计算出相应瑞流调制传递函数气溶胶调制传递函数前两者积总气调制传递函数然利气调制传递函数频域天气退化图进行复原户外景物图中气调制传递函数造成衰减进行补偿天气退化图进行清晰化处理均采气调制传递函数处理
（2）局部化图增强方法
述全局化图增强方法言类方法整幅图进行操作确定变换转移函数时基整图统计量实际应中常常需图某局部区域细节进行增强局部区域素数量相整幅图素数量较参整幅图计算时影响常忽略掉整幅图函数保证关心局部区域需增强效果需根关心局部区域特性计算变换转移函数函数关心区域需增强效果目前三类局部化图增强方法：
1）局部直方图均衡化方法称块重叠直方图均衡化种标准适应直方图均衡化方法（Adaptive Histogram EqualizationAHE）基思想直方图均衡化运算分散图局部区域通局部运算叠加适应增强图局部信息
2）局部度增强方法三种方式：a常数增益（Constant Gain TraceCGT）算法该算法求雾天图局部均值设定例常数雾天图素位置根变换函数放图局部变化b饱度反馈算法该算法雾天图转换HIS色彩空间中进行处理c．适应饱度反馈算法该算法通饱度分量亮度分量局部相关性确定反馈极性程度饱度反馈算法具适应力
3）基局部方差增强方法该算法通计算较局部标准方差判断局部图增强程度然灰度均值基准进行局部灰度拉伸算法样适深度信息变度较低雾天图相局部直方图均衡化算法噪声方面增加增强细节抑制噪声方面找较折中点该方法需进步研究问题
23 图雾应
着图雾技术发展图雾应领域扩展图雾基应领域视频监控形勘测动驾驶等领域目前图雾应集中方面：遥感航拍水图分析户外视频日常片处理等诸方面着广泛应
3 基态滤波图雾方法
31 态滤波概念定义
态滤波频率滤灰度变换结合起种图处理方法图度／反射率模型作频域处理基础利压缩亮度范围增强度改善图质量种方法图处理符合眼亮度响应非线性特性避免直接图进行傅立叶变换处理失真
32 态滤波原理
原灰度值作度反射率两组份产物度相变化作图低频成份反射率高频成份通分处理度反射率元灰度值影响达揭示阴影区细节特征目
33 态滤波操作基流程
①
③FFT
② LOG
④
⑤IFFT
⑦
⑥EXP
图31 态滤波图雾操作流程图
中表示原始图表示雾处理图取数处理取指数处理表示傅里叶变换表示傅里叶变换表示进行态滤波处理
① 二维函数形式表示图特定坐标处值幅度正标量物理意义图源决定幅图物理程产生时 值正物理源辐射量定非零限
（1）
函数两分量表征：
（1）入射观察场景光源总量
（2）场景中物体反射光总量两分量分称入射分量反射分量表示两函数合成
（2）
中 （3）
（式3）指出反射分量限制0（全吸收）1（全反射）间性质取决射源取决成物体表面特性
图灰度仅仅光函数（入射光）决定反射函数关反射函数反映出图具体容光强度般具致性空间通常具缓慢变化性质傅立叶变换表现低频分量然材料物体反射率差异常引起反射光急剧变化图灰度值发生变化种变化高频分量关
消均匀度影响增强图细节采建立频域态滤波器光足光变化图象进行处理减少光足引起图质量降感兴趣景物进行效增强样程度保留图原貌时图细节增强态滤波种频域中进行图度增强压缩图亮度范围特殊滤波方法态滤波够减少低频增加高频减少光变化锐化边缘细节
通光分量反射分量研究知光分量般反映灰度恒定分量类似频域中低频信息减弱光函数（入射光）起缩图灰度范围作反射光物体边界特性密切相关类似频域中高频信息增强反射光起提高图度作态滤波传递函数般低频部分1高频部分1
②进行态滤波处理首先原图取数图模型中法运算转化简单加法运算
（4）
③函数做傅里叶变换函数转换频域
（5）
④选择合适传递函数压缩分量变化范围削弱增强分量度提升增强细节确定合适分析知致形状图32示中代表高频增益代表低频增益表示点滤波中心距离
图32 态滤波处理示意图
利（6）式进行滤波
（6）
⑤滤波结果进行傅立叶反变换⑥指数运算态滤波输出结果⑦．
（7）
（8）
4 实验结果
41 灰度版
图431（a） 雾前 图431（b） 雾
图432（a） 雾前 图432（b） 雾
图433（a） 雾前 图433（b） 雾
图434（a） 雾前 图434（b） 雾
图435（a） 雾前 图435（b） 雾
42 彩色版
图441（a） 雾前 图441（b） 雾
图442（a） 雾前 图442（b） 雾
图443（a） 雾前 图443（b） 雾
图444（a） 雾前 图444（b） 雾
图445（a） 雾前 图445（b） 雾
43实验结果分析评价
进行Matlab操作达图片雾效果时采两种办法分灰度方法彩色方法第种灰度方法图雾彩色图片转化灰度图片进行处理原始图片输入彩色
Matlab处理呈现原始图片雾图均黑白颜色第二种彩色图雾针彩色图片雾处理输入原始图片输出原始图片雾图片成彩色图
处理效果图清晰度两版雾算法达图雾目灰色版黑白颜色差异更加分明原始图清晰彩色版颜色分辨度增强细节细化图片原始图清晰雾效果灰度雾方法更清晰
图片进行Matlab操作程中时运行结果差强意处理灰色版时态滤波处理原色深图片处理图颜色更暗图（a1－1）（a1－2）示细节锐化明显没达较雾处理效果找优配度进行修改相关系数操作改进算法深色图雾效果旧太改善
处理彩色版时做许调研学准备搞懂程序语言时百度相关验方法总结失败原：没真正弄明白样时三色彩维度进行定义总灰度图片转例原灰色版基础图片进行输出前加入段灰色图片变成彩色代码结果出张彩色原图尝试定义三色彩区间图片录入代码定义fR＝rgb（：：1）fG＝rgb（：：2）
fB＝rgb（：：3）结果出两张灰色图学会运正确彩色图定义输入正确代码实现彩色图雾处理
5评价改进
雾效果五幅雾图片进行直方图雾操作暗通道雾操作雾效果评价算法
51 直方图
图511（a） 雾前 图511（b） 雾
图512（a） 雾前 图512（b） 雾
图513（a） 雾前 图513（b） 雾
图514（a） 雾前 图514（b） 雾
图515（a） 雾前 图515（b） 雾
较结：直方图雾色彩失真冷色系颜色突变暖色系颜色细节锐化程度总体态滤波明显图原貌保持方面态滤波雾方法更保持图原貌直方图雾方法图颜色改变细节处理方面态滤波方法细节锐化程度原图光明亮方加强细节暗通道明显相反直方图雾方法原图光较暗方加前细节态滤波明显
52 暗通道
图521 雾
图522 雾
图523 雾
图524 雾
图525 雾
较结：暗通道雾效果良色彩基保留细节锐化明显暗通道处理图颜色会原图颜色加深图原貌保持方面态滤波雾方法更保持图原貌暗通道雾方法图起颜色更加突出细节处理方面态滤波方法原图光明亮方加强细节暗通道明显相反暗通道方法原图光较暗方加前细节态滤波明显
53 改进
531 红外处理
红外成目标背景红外辐射需气传输光学成光电转换电子处理等程转换成红外图红外图产生程分析红外图特点： 1）空间相关性强度低2）表征象温度分布灰度图分辨率较低图较模糊3）噪声干扰较噪声较复杂信噪低4）存器件性非均匀性等
出红外图存缺陷眼说显著特点度低图模糊红外图存散粒噪声机噪声等部分图中高频信息态滤波正处理锐化高频种方法效加强细节
532红外态滤波结合优化
文提出种基态滤波红外图增强新方法先原红外图适应中值滤波保留原图细节噪声利态滤波优势增强红外图细节特征采限制度适应直方图均衡方法进步调整图灰度动态范围方案解决态滤波存缺陷终提高图分辨率度通仿
真验证非常增强效果
533 实验结果图
图531（a） 原图 图531（b） 红外 图531（b） 态滤波
图532（a） 原图 图532（b） 红外 图532（b） 态滤波
图533（a） 原图 图533（b） 红外 图533（b） 态滤波
结
表51 雾方法分析
类
子类
雾方法
优点
缺点
基图处理雾天图増强方法
全局化增强
全局直方图均衡化
⑴算法简单
⑵单景深图复原效果
难反映景深变图中局部景深变化
态滤波
⑴掉光均产生黑斑暗影
⑵较保持图原始貌
需耍两次傅立叶变换占较运算空间
暗通道
较增强图细节
光亮方细节处理效果般
表51雾方法优缺点较方法解决问题思路存着根区种方法优缺点实际应中根需采累试法进行处理幅雾图根研究员判定处理果采增强方法改善灰度度效果釆增强方法采图复原方法行退化模型进行复原处理直观考察种算法清晰化效果述种典型基图处理增强方法新提出基物理模型图复原方法进行实验仿真图13算法清晰化效果示例
图61 原图 图62 态滤波 图63 直方图
图64 暗通道 图65 红外 图66 红外+态滤波
观察图片知雾算法效果优劣图66雾效果应红外技术提高高频应态滤波保持图原貌时图细节处理更加细腻图片达更清晰度需结合种算法叠加运行
致谢
时光飞逝学里学期快历毕业设计整程感觉程中充实愉快
文北方工业学理学院郭芬红老师悉心指导帮助完成选题寻找相关资料开题答辩中期检查程中编程实现文定稿答辩郭老师直耐心竭帮助前期资料查询准备开题答辩书写修改答辩准备代码运行文成文修改郭老师直拽着前进
郭老师总时毕业设计相关信息通知第时间告知文撰写程序设计方面老师非常仔细文老师字句认真仔细阅读帮助标注出恰方指导做出修改帮助精益求精里真诚感谢导师郭芬红私付出
朱喜玲学姐态滤波代码修改中挤出时间私帮助改正代码表深深感谢
学期学程中少学间互相帮助家支持鼓励更少课题刻苦钻研工作者学者付出现做学研究真站巨肩膀更高走更远
谨篇文完成际感谢身边位帮助老师家学朋友致谢
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[14]张锐雾天背光条件图清晰化算法研究硬件实现[D]哈尔滨：哈尔滨工业学2008．
[15]王恒进基波遥感图薄云研究实现[D西安：西北工业学2002．
[16]冈萨雷斯数字图处理（MATLAB版）[M]（阮秋琦译）北京：电子工业出版社20145578．
[17]Oakley J PSatherley B LImproving image quality in poor visibility conditions using a physical model for contract degradation[J]IEEE Transactions on Image Processing19987（2）：167179．
[18]Narasimhan S GNayar S KContrast restoration of weather degraded image[J]IEEE Transactions on Pattern Analysis and Machine Intelligence200325（6）：713724．
[19]Ebner MEvolving color constancy[J]Pattern Recognition Letters200627（11）：12201229．
[20]JoungYoun KimLeeSuP KimSeungHo HwangAn advanced Contrast
Enhaneement Using Partially Overlap Ped SubBlock Histogram Equalization
[J]IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS FOR VIDEO
TECHNOLOGY200111(4)：475483．
[21]OAKLEY JPBUHONGCorrection of simple contrast loss in color images[J]Image Processing200716(2)：511522．
[22]TAN R TVisiblity in bad weather from a single image [C]Proceedings of Computer Society Conference on Computer Vision and Pattern Recognition 2008：18．
[23]Hongbo Yang Jiuhe WangColor Image Contrast Enhancement by
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附录
I态滤波代码 灰色版
clcclear allclose all
imgimread('E\Matlab\R2008a\abc\4jpg')
imgrgb2gray(img)
imgimresize(img[256256])
figure(1)
imshow(img)title('原始图片')
imgim2double(img)图片img转换成double型
k18
k28
r161
alf1600
alf161
alf20
nnfloor((r+1)2) nn81尺度C取80合适
for i1r 1循环81
for j1r
h(ij) exp(((inn)^2+(jnn)^2)(k1*alf))(k2*pi*alf*10000) 高斯函数
h(ij) exp(((inn)^2+(jnn)^2)(2*alf^2)) 高斯函数
end
end
gauss hsum(sum(h))
Rconv2(imggauss'same') 灰度
Rlog(R)
Slog(img)R
TS+R
K2exp(T)取指数
K2uint8(K2)
figureimshow(K2)
V变换
V1load('M_256mat')
V1V1y
Fimg1V1*R*V1'
Fimg2V1*S*V1'
傅里叶变换
Fimg1fft(R)傅里叶变换
Fimg2fft(S)傅里叶变换
[MN]size(Fimg1)
figure(2)
imshow(uint8(abs(P))[])title('滤波前频谱图')绘制源图频谱幅度谱
x0floor(M2)取整数
y0floor(N2)
态滤波参数设置
D03
c150
Hh16Hl08Hh>1Hl<1
for u1M
for v1N
D(uv)sqrt((ux0)^2+(vy0)^2)
H(uv)(HhHl)*(1exp(c*(D(uv)^2D0^2)))+Hl态滤波器函数
end
end
Y1Fimg1*H
Y2Fimg2*H
傅里叶逆变换
Q1ifft(Y1)
Q2ifft(Y2)
QQ1+Q2
Jexp(Q)取指数
Jim2uint8(J)
figureimshow(J)title('雾图片')
J1double(J)
[SDENTRAVEGRAD]Sd(J1)
II态滤波第二次修改代码 彩色版
clcclear allclose all
imgimread('E\Matlab\R2008a\aaa\1jpg')
imgimresize(img[256256])
imshow(img)title('原始图片')
Yzeros(2562563)
for ii13
Limg(ii)
img1im2double(L)图片img转换成double型
k18
k28
r161
alf1600
alf161
alf20
nnfloor((r+1)2) nn81尺度C取80合适
for i1r 1循环81
for j1r
h(ij) exp(((inn)^2+(jnn)^2)(k1*alf))(k2*pi*alf*10000) 高斯函数
h(ij) exp(((inn)^2+(jnn)^2)(2*alf^2)) 高斯函数
end
end
gauss hsum(sum(h))
Rconv2(img1gauss'same') 灰度
Rlog(R)
Slog(img1)R
TS+R
K2exp(T)取指数
K2uint8(K2)
figureimshow(K2)
V变换
V1load('M_256mat')
V1V1y
Fimg1V1*R*V1'
Fimg2V1*S*V1'
傅里叶变换
Fimg1fft(R)傅里叶变换
Fimg2fft(S)傅里叶变换
[MN]size(Fimg1)
figure(2)
imshow(uint8(abs(P))[])title('滤波前频谱图')绘制源图频谱幅度谱
x0floor(M2)取整数
y0floor(N2)
态滤波参数设置
D03
c350
Hh16Hl08Hh>1Hl<1
for u1M
for v1N
D(uv)sqrt((ux0)^2+(vy0)^2)
H(uv)(HhHl)*(1exp(c*(D(uv)^2D0^2)))+Hl态滤波器函数
H(uv)(HhHl)*(1(1+(D0c*D(uv))))^2+Hl巴特沃斯
end
end
Y1Fimg1*H
Y2Fimg2*H
傅里叶逆变换
Q1ifft(Y1)
Q2ifft(Y2)
QQ1+Q2
Jexp(Q)取指数
Jim2uint8(J)
Y(ii)J
end
figureimshow(mat2gray(Y))title('雾图')
III直方图均衡化程序
sourcePicimread('E\Matlab\R2008a\abc\22jpg')
[mno]size(sourcePic)
figureimshow(sourcePic[])
title('原图')
grayPicrgb2gray(sourcePic)
grayPicsourcePic(1)
gpzeros(1256) 计算灰度出现概率
for i1256
gp(i)length(find(grayPic(i1)))(m*n)
end
newGpzeros(1256) 计算新灰度出现概率
S1zeros(1256)
S2zeros(1256)
tmp0
for i1256
tmptmp+gp(i)
S1(i)tmp
S2(i)round(S1(i)*256)
end
for i1256
newGp(i)sum(gp(find(S2i)))
end
newGrayPicgrayPic 填充素点新灰度值
for i1256
newGrayPic(find(grayPic(i1)))S2(i)
end
nrnewGrayPic
grayPicsourcePic(2)
gpzeros(1256) 计算灰度出现概率
for i1256
gp(i)length(find(grayPic(i1)))(m*n)
end
newGpzeros(1256) 计算新灰度出现概率
S1zeros(1256)
S2zeros(1256)
tmp0
for i1256
tmptmp+gp(i)
S1(i)tmp
S2(i)round(S1(i)*256)
end
for i1256
newGp(i)sum(gp(find(S2i)))
end
newGrayPicgrayPic 填充素点新灰度值
for i1256
newGrayPic(find(grayPic(i1)))S2(i)
end
ngnewGrayPic
grayPicsourcePic(3)
gpzeros(1256) 计算灰度出现概率
for i1256
gp(i)length(find(grayPic(i1)))(m*n)
end
newGpzeros(1256) 计算新灰度出现概率
S1zeros(1256)
S2zeros(1256)
tmp0
for i1256
tmptmp+gp(i)
S1(i)tmp
S2(i)round(S1(i)*256)
end
for i1256
newGp(i)sum(gp(find(S2i)))
end
newGrayPicgrayPic 填充素点新灰度值
for i1256
newGrayPic(find(grayPic(i1)))S2(i)
end
nbnewGrayPic
rescat(3nrngnb)
figureimshow(res[])
title('处理图')
外文资料翻译原文
灰度直方图
摘
图雾技术利定模型算法处理图雾恢复图原始特征文介绍常霾雾三种方法包括基光分离模型算法提出种基直方图均衡化算法基暗原色先验MATLAB台设计实现种数字图处理系统雾述算法雾天图效果更
关键词：图雾光分离模型直方图均衡化暗通道
11 引言
数字图处理中简单工具灰度直方图该函数概括幅图灰度级容幅图直方图包括观信息某类型图直方图完全描述直方图计算简单特幅图方复制方时直方图计算非常低代价完成
111 定义
灰度直方图灰度级函数描述图中具该灰度级素数：横坐标灰度级坐标该灰度出现频率（素数）图11示例
图11 幅图灰度直方图
灰度直方图种方式定义[1]练更清楚种方法处假设幅函数定义连续图滑中心高度灰度级变化边低灰度级选择定某灰度级然定义条轮廓线该轮廓线连接图具灰度级点轮廓线形成包围灰度级等区域封闭曲线
图12中图条灰度级轮廓线更高灰度级处画第二条轮廓线第条轮廓线包围区域面积样第二条轮廓线包围区域面积
图12 幅图轮廓线
幅连续图中具灰度级D轮廓线包围面积称阈值面积函数直方图定义
(1)
幅连续图直方图面积函数导数负值负号出现着D增加减果图成二维机变量面积函数相累积分布函数灰度直方图相概率密度函数
离散函数固定1等式（1）变
(2)
数字图灰度级D面积函数等灰度值D素数
112 二维直方图
常发现构造高维直方图维直方图更特研究彩色图图13幅数字化显微图中含白血球红血球图白光（a）助滤光片红光（b）蓝光（c）进行数字化右图两幅图红—蓝直方图
二维直方图两变量：红光图灰度值蓝光图灰度值函数坐标处值指红光图中具灰度值时蓝光图中位置具灰度值素（）数种光谱数字图采样点素素变量——处变量数2 二维直方图表示素值两种灰度级组合中分布情况果红光图蓝光图相直方图
斜线位置值外余处值0 果素（）中红分量蓝分量者反直方图分布分斜线
白光图13中显微镜区域显示关彩色许信息红血球呈现粉红色白血球呈现灰色染色处理显示深蓝色核红细胞蓝光吸收蓝光较暗红光透红光较亮样核红光颜色更深红蓝直方图四峰值背景（B）产生红细胞（R）产生核（N）产生白血球细胞质（C）产生
图13 二维直方图示例
（a） 白光图（b）红光图（c）蓝光图（d）红蓝直方图
113 直方图性质
幅图压缩直方图空间信息丢失直方图描述灰度级具素数蛋素图中位置提供线索特定图唯直方图反成立
——极图着相直方图例图中移动物体般直方图没影响直方图确实信息
果换等式（1）变量等式两边D进行积分
(3)
面积函数果令假设灰度级非负
(4)
离散图情形
(5)
中NLNS分图行列数目
果幅图包含灰度均匀致物体背景物体度强规定物体边界灰度级定义轮廓线
(6)
果图包含物体轮廓线处灰度级均公式（6）出物体面积
通图面积化灰度直方图图概率密度函数（PDF）面积函数进行样化处理图累积分布函数（CDF）函数图进行统计处理时
直方图性质该性质定义——灰度级素数——直接：果图两连接区域组成区域直方图已知整幅图直方图该两区域直方图显然该结推广数目连接区域情形
12 直方图途
121 数字化参数
直方图出简单见指示判断幅图否合理利全部允许灰度级范围般幅数字图应该利全部全部灰度级图11否等增加量化间隔旦数学化图级数少256丢失信息（非重新数字化）恢复
果图具超出数字化器处理范围亮度灰度级简单置0255 直方图端两端产生尖峰数字化时直方图进行检查做法直方图快速检查数字化中产生问题早暴露出免浪费量时间
122 边界阈值选择
前述轮廓线提供确立图中简单物体边界效方法轮廓线作边界技术称阈值化合适技术选择灰度阈值图处理中讨课题
假定幅图背景浅色中深色物体图14类图直方图物体中深色素产生直方图左锋背景中量灰度级产生直方图右锋物体边界附具两峰值间灰度级素数目相较少产生两峰间谷选择谷作灰度阈值合理物体边界
图54 双峰直方图
某种意义说应两峰间低点灰度级作阈值确定边界适宜等式（1）知直方图面积函数导数谷底附直方图值相较意味着面积函数阈值灰度级变化缓慢果选择谷底处灰度作阈值物体边界影响达果试图测量物体面积选择谷底处阈值测试量阈值灰度变化敏感降低
123 综合光密度
出（图14）直方图甚没图情况确定物体佳灰度阈值便计算物体面积（等式（6））外种简单图直方图直接计算量综合光密度（IOD）反映图中质量种度量定义
(7)
中ab划定图区域边界果灰度级0背景深色物体IOD反映物体面积密度组合
数字图
(8)
中处素灰度值令代表灰度级k时应素数等式（8）写成
(9)
显然该式幅图素灰度级加起然灰度级k应直方图值公式（9）写成
(10)
灰度级加权直方图令式（8）等式（10）令灰度级增量趋极限0 类似适连续图表达式
(11)
(12)
果图中物体阈值灰度级T边界勾划出物体边界IOD式出
(13)
部灰度级均（mean）值MGL等IOD面积：
(14)
13 直方图图关系
特定图言直方图唯简单图函数形式已知推导出直方图种技术许少直方图更深理解
假定已知幅图函数形式希计算直方图知道直方图面积函数关系等灰度级导数负数（等式（1））果首先图身表达式面积函数求直方图时通观测达目
131 维
简单起见首先考虑维情况 面积实际指长度说明图直方图间关系
考虑维高斯脉（图15）
(15)
图55 高斯脉
注意非负x函数单调面积图函数逆函数非负数x通解方程（15）作灰度级函数x：
(16)
式图右半部分面积函数图左右两半称总面积函数等式（16）两倍直方图表示
(17)
图16示处直方图尖峰较处面积低灰度值点（灰度）处尖峰图处斜率0引起（高斯函数顶部附时坦）
图16 高斯脉直方图
132 二维
通图称性巧妙利样处理程推广二维情形例假定等式（15）维高斯脉实际二维图中条线段果线段样直方图具图16示形状仅仅坐标刻度已
述方法中利圆称性假定图时中心原点圆称高斯脉（图17）
图函数极坐标表示
(18)
图17 圆形高斯点
灰度级常数P轮廓线半径图
(19)
该轮廓线包围面积
(20)
公式（20）表示面积函数微分直方图[1]
(21)
图18 注意然原点处斜率0 够强维情形时样处产生尖峰
图18 图高斯点直方图
更复杂图首先应图划分相邻区域分确定区域面积函数然述方法直方图整图直方图相连区域直方图
14 点总结
1 灰度级直方图阈值面积函数导数负值
2 直方图表明灰度级少素
3 观察直方图出合适数字化
4 简单物体面积IOD通图直方图求
5 具特定函数形式图直方图通面积函数求
参考文献：
1 RJWallAKlingerand KRCastlemanAnalysis of Image HistogramsProcSecond IntCongon Pattern RecognitionCopenhagen1974
2 CLNovak and SAShaferAnatomy of a Color HistogramProceedings of the 1992 IEEE Computer Society Conference on Computer Vision and Pattern Recognnition599—605IEEE Computer Society PressLos AlamitosCA1992
3 JPrewitt and MMendelsohnThe Analysis of Cell Images Annals of the New York Academy of Sciences1281035—1053January 1966
4 MMendelsohnBMayallJPrewittRBostromand RHolcombDigital Transformation and Computer Analysisi of Microscope Imagesin RBarer and VCossletedsAdvances in Optical and Electron Microscopy 2 Academic Press London 1968
Research on Image Defogging Methods
ZHANG Chi
School of Computer and SoftwareNanjing University of Information Science and TechnologyNanjing 210044
ABSTRACT
Image dehazing is to use a certain model or algorithm to process the defogging image to restore the original features of the imageThe paper introduces three methods commonly used to haze the fog including an algorithm based on light separation modelan algorithm based on histogram equalization and an algorithm based on dark channel prior In the MATLAB platform design and implementation of a digital image processing system to fog to use the above algorithm to the fog image the effect is better
Key words image defogging light separation model histogram equalization dark channel prior
The GrayLevel Histogram
11 INTRODUCTION
One of the simplest and most useful tools in digital image processing is the graylevel histogram The function summarizes the graylevel content of an image While the histogram of any image contians considerable informationcertain types of images are completely specified by their histograms Computation of the histogram is simple and may be done at little apparent cost when an image is copied from one place to another
111 Definition
The graylevel histogram is a function showingfor each gray levelthe number of pixels in the image that have that gray level The abscissa is gray level and the ordinate is frequency of occurrence(number of pixels) Figure 11 shows an example
There is another way to define the graylevel histogram[1]and the following exercise yields insight into the usefulness of this function Suppose we have a continuous imagedefined by the function that varies smoothly from high gray level at the center to low gray level at the borders We can select some gray level and define a set of contour lines connecting all points in the image with value The resulting contour lines from closed curves that surround regions in which the gray level is greater than or equal to
Figure 12 shows an image containing one contour line at the gram level A second contour line has been drawn at a higher gray level
is the area of the region inside the first contour line and similarly is the area inside the second line
The threshold area function of a continuous image is the area enclosed by all contour lines of gray level D Now the histogram may be
defined as
(1)
Thus the histogram of a continuous image is the negative of the derivatives of its area function The minus sign results from the fact that decreases with increasing D If the image is considered a random variable of two dimensions the area function is proportional to its cumulative distribution function and the gray level histogram to its probability density density function
Figure 11 An image and its graylevel histogram
Figure 12 Contour lines in an image
For the case of discrete functions we fix at unity and E(1) becomes
(2)
The area function of a digital image is merely the number of pixels having gray level greater than or equal to D for any gray level D
112 The TwoDimensional Histogram
Frequently one finds it useful to construct histograms of higher dimension than one This is particularly useful for color images [2]as discussed in Chapter 21figure 13 shows images digitized from a microscope field containing a white blood cell and several red blood cells The field was digitized in white light and through colored filters
in red and blue light At the lower right is the twodimensional redversusblue histogram of the latter two images
The twodimensional histogram is a function of two variables gray level in the red image and gray level in the blue image Its value at the coordinate is the number of corresponding pixel pairs having gray level in the red image and gray level in the blue image Recall that a multispectral digital image such as this can be thought of as having a single pixel at each sample point but each pixel has multiple values —in this case two The twodimensional histogram shows how the pixels are distributed among combinations of two gray levels If the red and blue component images were identical the histogram would have zero value except on the diagonal Pixels having higher red than blue gray level and vice versa contribute to the histogram above and below the diagonal line respectively
In white light the microscope field of Figure 13 shows considerable information in color The red blood cells appear pinkish Thus the red cells appear dark in blue light which they absorb and light in red light which they transmit Similarly the nucleus is much denser in red light The redversusblue histogram therefore has four distinct peaks one each due to the background the red blood cells and the nucleus and cytoplasm
of the white cell The analysis of twodimensional histograms is discussed further in Chapter 21
113 Propertise of the Histogram
When an image is condensed into a histogram all spatial information is discarded The histogram specifies the number of pixels having each gray level but gives no hint as to where those pixels are located within the image Thus the histogram is unique for any particular image but the reverse is not true Vastly different images could have identical histograms Such operations as moving objects around within an image typically have no effect on the histogram The histogram does Nevertheless possess some useful properties
If we change variables in Fq(1) and integrate both sides from D to infinity we find that
(3)
The area function If we then set assuming nonnegative gray levels we obtain
area of image (4)
Figure 13 Example twodimensional histogram
(a)whitelight image(b)redlight image(c)bluelight image(d)redblue histogram
Or in the discrete case
(5)
Where NL and NS are the number of rows and columns respectivelyin the image
If an image contains a single uniformly gray object on a contrasting background and we stipulate that the boundary of that object is the contour line defined by gray level then
area of object (6)
If the image contains multiple objects All of whose boundaries are contour lines at gray level Then Eq(6) gives the aggregate area of all the objects
Normalizing the graylevel histogram by dividing by the area of the image produces the probability density function(PDF) of the image A similar normalization of the area function produces the cumulative distribution function (CDF) of the image These functions are useful in the statistical treatment of images As illustrated in chapter 6
The histogram has another useful propertywhich follows directly from its definition as the number of pixels having each gray level if an image consists of two disjoint regions And the histogram of each region is known then the histogram of the entire image is the sum of the two regional histograms Clearly this can be extended to any number of disjoint regions
12 USES OF THE HISTOGRAM
121 Digitizing Parameters
The histogram gives a simple visual indication as to whether or not an image is properly scaled within the available range of gray levels Ordinarily a digital image should make use of all or almost all of the available gray levels as in Figure 11 Failure to do so increases the effective quantizing interval Once the image has been digitized to fewer than 256 gray levels the lost information cannot be restored without redigitizing
Likewise if the image has a greater brightness range than the digitizeris set to handle then the gray levels will be clipped at 0 andor 255 Producing spikes at one or both ends of the histogram It is a good practice routinely to review the histogram when digitizing A quick check of the histogram can bring digitizing problems into the open before much time has been wasted
122 Boundary Threshold Selection
As mentioned earliercontour lines provide an effective way to establish the boundary of a simple object within an image The technique of using contour lines as boundaries is called thresholding The use of optimal techniques for selecting threshold gray levels is a subject of considerable discussion in the literature and is treated in Chapter 18
Suppose an image contains a dark object on a light background Figure 14 illustrates the appearance of the histogram of such an image The dark pixels inside the object produce the rightmost peak in the histogram The leftmost peak is due to the large number of gray levels in the background The relatively few mid level gray pixels around the edge of the object produce the dip betwee
n the two peaks A threshold gray level chosen in the area of the dip will produce a reasonable boundary for the object
Figure 14 a bimodal histogram
In one sense the gray level corresponding to the minimun between the two peaks is optimal for defining the boundary Recall from Eq(1) that the histogram is the derivative of the area function In the vicinity of the dip the histogram takes on relatively small values implying gray level at the dip we minimize its effect upon the boundary of the object If we are concerned with measuring the object's area selecting a threshold at the dip in the histogram minimizes the sensitivity of the area measurement to variations in threshold gray level
123 Integrated Optical Density
Given the histogram in Figure 14 we could determine an optimal threshold gray level for the object and compute its area [Eq(6)] without ever seeing the image Another measurement that can be computed directly from the histogram of simple images is the integrated optical density (IOD)
A useful measure of the mass of an image it is defined as
(7)
Where a and b delimit the region of the image When the image consists of a dark object situated on a background of zero gray level the IOD reflects a combination of the area and density of that object
For a digital image
(8)
Where is the gray level of the pixel at line i sample j Let be the number of pixels in the image whit gray level equal to k Then Eq(8) can be written as
(9)
Since clearly this adds up the gray levels of all pixels within the image However is merely the histogram evaluated at gray level k Thus Eq(9) can be written as
(10)
That is a graylevelweighted summation of the histogram By equating Eqs(8)and (10)and taking a limit as the increment between gray levels approaches zero we derive similar expressions for continuous images
(11)
And
(12)
If an object within the image is delineated by a threshold boundary at gray level T the IOD within the object boundary is given by
(13)
The mean interior gray level is the ratio of IOD to area
(14)
13 RELATIONSHIP BETWEEN HISTOGRAM AND IMAGE
Since the histogram of a particular image is unique it is possible to derive the histogram of simple images whose functional from is known While this technique is perhaps seldom used it does yield insight into the histogram and it establishes a basis for further study of threshold selection in chapter 18
Suppose we have an image of given functional from and we desire to computer its histogram We know that this is the negative of the derivative with respect to gray level of the area funcyion [Eq(1)] Thus we may derive the histogram if we first derive the area function from the expression for the image itself Sometimes this can be done simply by observation
131 One Dimension
For simplicity we first address the onedimensional case Here the area is actually a length but it demonstrates the relationship between a histogram and its image
Consider the onedimensional Gaussian pulse (Figure 15 )given by
(15)
Notice that for nonnegative x the function is monotonic Furthermore the area is merely the inverse of the image function Thus for nonnegative values of x we may solve Eq(15) for x as a function of gray level to yield
(16)
Which is the area function for the right half of the image Since the two halves of the image
Figure 15 the gaussian pulse
are symmetrical the overall area function is twice that of Eq(16) The histogram is given by
(17)
And is shown in Figure 16 The histogram builds up to a spike at because of the large areas of low gray level at large positive and negative values of x The small spike at results from the image having zero slope at (iethe Gaussian is locally flat at the very top)
Figure 16 histogram of the Gaussian pulse
132 Two Dimensions
The same procedure may be extended to twodimensional images by judicious use of symmetry within the image For example suppose that the onedimensional Gaussian pulse of Eq(15) is actually one line of a twodimensional image Then if all lines are identical the histogram will have the same shape as that in Figure 16 differing only in ordinate scale
One may take advantage of circular symmetry in the following way Suppose the image is a circularly symmetric Gaussian pulse centered on the origin (Figure 17) The image function in polar coordinates is given by
(18)
Figure 17 the circular Gaussian spot
A contour of constant gray level P is a circle of radius
(19)
Such a contour encloses an area
(20)
The area function of Eq(20) may now be differentiated to yield the histogram [1]
(21)
Shown in Figure 18 Notice that the point of zero slope at the origin is not powerful enough to produce a spike at As it did in the onedimensional case
For more complex images the histogram may be derived by first partitioning the imageinto disjoint regions over which the area function may be determined The histogram of the complete image is then the sum of the histograms of all the disjoint regions
Figure 18 histogram of the circular Gaussian spot
14 SUMMARY OF IMPORTANT POINTS
6 The graylevel histogram is the negative of the derivative of the threshold area function
7 The histogram shows how many pixels occur at each gray level
8 Inspection of the histogram points out improper digitization
9 The area and IOD of a simple object can be computed from the histogram of its image
10 The histogram of an image of specified functional from can be derived with the aid of the area function
REFERENCES
1 RJWallAKlingerand KRCastlemanAnalysis of Image HistogramsProcSecond IntCongon Pattern RecognitionCopenhagen1974
2 CLNovak and SAShaferAnatomy of a Color HistogramProceedings of the 1992 IEEE Computer Society Conference on Computer Vision and Pattern Recognnition599—605IEEE Computer Society PressLos AlamitosCA1992
3 JPrewitt and MMendelsohnThe Analysis of Cell Images Annals of the New York Academy of Sciences1281035—1053January 1966
4 MMendelsohnBMayallJPrewittRBostromand RHolcombDigital Transformation and Computer Analysisi of Microscope Imagesin RBarer and VCossletedsAdvances in Optical and Electron Microscopy 2 Academic Press London 1968
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