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Journal of Geo-information Science >

2016 , Vol. 18 >Issue 5: 615 - 621

DOI: https://doi.org/10.3724/SP.J.1047.2016.00615

Orginal Article

Compound Cluster Center Based Multiple Linear Regression Color Normalization Method for Remote Sensing Image

  • WU Wei , 1, * ,
  • CHENG Xi 2 ,
  • GU Guomin 1
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  • 1. College of Computer Science and Technology, Zhejiang University of Technology, Hangzhou 310023, China
  • 2. School of Geophysics, Chengdu University of Technology, Chengdu 610059, China
*Corresponding author: WU Wei, E-mail:

Received date: 2015-12-15

  Request revised date: 2016-04-12

  Online published: 2016-05-10

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《地球信息科学学报》编辑部 所有
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Abstract

Due to the impacts of phonological change, sensor distortion, variation of atmospheric conditions and a lot of other factors, the images acquired at different time points for the same area are affected by color differences, Color normalization tries to eliminate /reduce color differences between different images and obtain seamless mosaic result. However, the traditional band-by-band normalization methods ignore the correlation between different bands and corrected each band independently, which may lead to new color distortion. To solve this problem, this paper presents a compound cluster center based multiple linear regression color normalization method for remote sensing image. Firstly, the source image and the reference images are primarily normalized based on the mean and variation values for every band and a new feature vector is constructed. Then, the compound clusters, which are extracted by unsupervised compound classification, are used to model the variation relationship between the two images. Afterwards,the outliers in every cluster may induce suddencolor change between the images of different time, so the outliers is identified and excluded. Last, the mapping relationship between the source image and the reference image is established with respect to the centers of clusters andall bands of source image are corrected simultaneously. The proposed method has been applied to two datasets with different land cover and spatial resolution, and results show that the proposed method can obtain color consistency result. Compared with the result of traditional method, our method over performsin preserve color and overall precision.

Key words： color normalization; compound cluster; color preserve; multiple linear regression

Cite this article

WU Wei , CHENG Xi , GU Guomin . Compound Cluster Center Based Multiple Linear Regression Color Normalization Method for Remote Sensing Image[J]. Journal of Geo-information Science, 2016 , 18(5) : 615 -621 . DOI: 10.3724/SP.J.1047.2016.00615

1 引言

受获取时刻天气条件差异、传感器畸变和植被时相变化等因素的影响,不同影像之间存在色彩差异,使合成结果影像上不同来源的影像间存在“马赛克”现象。因而,影像无缝合成需要消除不同数据间的色彩差异。不考虑新增建设用地等地物类型突变的情况下,2期影像色彩差异有以下2种类型：（1）影像间整体的明暗程度差异;（2）植被等部分地物随时相变化的色彩差异。一般来说,变化检测[1]、复合分类[2]等应用中仅需要消除第（1）类因素影响,使各景影像具有“相同的”获取条件,以增强影像的可比性,常称为辐射归一化;而影像合成等应用中需要进一步克服植被等地物时相变化造成的色彩特征改变,以生成视觉上无缝的合成影像,常称为色彩归一化。二者常用的方法包括回归法和映射法。
回归法是从影像上提取伪不变特征（Pseudo- invariant Features,PIFs）,以此建立2期影像灰度值之间的回归模型,进而对输入影像进行相对辐射校正处理,以消除辐射差异。在PIFs选取方面,主要有主成分分析[3]、多元变化检测[4]及其改进的迭代加权多元变化检测[5]、慢特征分析[6]等方法。时相不变类别[7]及分类后回归[8]等以类别为基础的PIFs提取方法相对于像元级PIFs具有更好的鲁棒性。在回归模型方面,线性模型简单有效,在此基础上逐步发展了正交回归、TS回归[9]等改进方法。为了描述多期影像上灰度值的高阶变化,支持向量回归[10]和遗传算法[11]等非线性模型也被用于建立灰度映射关系。一般来说,回归法通过提取伪不变特征建立的灰度映射关系,能够消除第（1）类因素造成的色彩差异,处理结果具有明确物理意义,且效果易于控制,但植被、水体等地物在结果影像上仍然存在色彩差异,不能满足无缝合成的需求。
映射法是根据一定的规则直接建立影像间的灰度映射方程,并利用映射值替换输入影像灰度值。肖甫等通过线性方程将参考影像的均值和方差赋予输入影像,使处理后的输入影像具有与参考影像相同的均值和方差[12]。直方图规定化是将参考影像的直方图赋予输入影像,使处理后的影像具有与参考影像相同的直方图分布,该方法相对于仅利用均值和方差的方法具有更好的精度[13]。直方图的映射规则,主要有单映射[14]、组映射[15]、变分法[16]等。此外,影像边界包含了重要的色彩变化信息,利用边界直方图规定化能够克服2景影像上的整体灰度差异[17]。对于多波段的影像,通过定义多维空间旋转矩阵,对输入影像与参考影像在多维空间进行密度函数匹配,以消除色彩特征差异[18]。基于直方图规定化的色彩处理已被陆续用于变化检测[19]、缝隙填充[1]和影像镶嵌[12]等应用中。
上述方法在各自应用中取得了较好的效果,但这些方法大多是针对单波段发展的模型,对于多波段的影像一般是逐波段使用上述方法,成功应用的前提是各个波段之间相互独立,而实际上遥感影像的多个通道之间存在很强的相关性,如果各个波段处理结果的残差不一致,容易引起新的色彩畸变。鉴此,本文提出一种复合类别支持的多元线性回归遥感影像色彩归一化方法,旨在通过多个波段同时处理,克服逐波段处理导致的色彩畸变,提高处理结果的精度。

2 研究方法

影像 X 和 Y 是同一地区不同时间获取的2景影像,包含 b 个波段,可以表示为式（1）。
X = { X 1 , X 2 , ⋯ , X b } Y = { Y 1 , Y 2 , ⋯ , Y b } （1）
由于影像间存在着色彩差异,需要通过色彩归一化来消除。假设以影像 Y 作为参考,对影像 X 进行处理。直方图规定化是使得规定化后的影像 f ( X ) 的直方图 H ( f ( X ) ) 与影像 Y 直方图 H ( Y ) 相似程度 Sim 最高,对于第 i 个波段,传统的逐波段规定化模型 Q i 可表示为式（2）。这种方法的不足是各波段具有不同的残差,从而改变不同波段灰度值的相对关系,导致新的色彩畸变。
Q i = argmaxSim ( H ( f ( X i ) ) , H ( Y i ) ) （2）
图1（a）、（b）给出了同一地区2景影像的标准假彩色合成图,其近红外波段（ B N ）和红波段（ B R ）构成的二维直方图如图1（c）、（d）所示,颜色由红到蓝表示对应灰度值的频数逐渐降低。由此可看出：（1）影像 Y 相对于影像 X 的植被茂盛,红色更加鲜艳,即 B N 和 B R 的相差较大,在二维直方图上远离直线 y = x 分布;（2）影像 X 整体偏暗,对比度较低,在二维直方图上大量像元分布在靠近原点的区域,且灰度值分布集中;（3）2景影像二维直方图的形状具有一定的相似性。因而,将影像 X 的多维直方图整体扭曲到参考影像 Y 的直方图,实现多波段同时处理,获得更好的色彩保持特性,该问题 Q 可以表示为式（3）。
Fig. 1 The principles of multiple dimension histogram specification

图1 多维直方图规定化原理

（3）
根据上述分析可知,色彩归一化问题转化为多维直方图的规定化问题。然而,由于多维空间直方图规定化的映射方程搜索空间很大,给影像处理造成困难。对此,本文提出一种简化方法,即采用复合类别中心作为控制点,利用多元线性回归建立映射方程实现色彩归一化。具体实现过程包括复合聚类和建立色彩归一化映射方程2个步骤。

2.1 复合聚类

色彩校正需要建立2期影像之间的色彩变化关系,而复合分类（Compound Classification）是将2期影像的地表变化类型作为分类对象,根据地表辐射特征（表现为灰度值）的变化情况将其划分为不同的类别,称为复合类别。实现方法上,Demir等提出一种基于贝叶斯框架的后验期望最大化的复合分类方法[2],该方法能够获得地物类别转移矩阵,但需要同时考虑2期影像并选取大量的样本,限制了方法的实用性。
由于本文目标不是获取地表类别的转移信息,因而可以采用非监督方法将像元按照辐射特征变化聚为不同的类别,即复合聚类。某一像元pj在2期影像上灰度值可表示为一个 b × 2 的向量,如式（4）所示。
pj = x 1 j y 1 j x 2 j y 2 j ⋯ ⋯ x b j y b j （4）
式中： x i j 和 y i j ( i = 1,2 , ⋯ , b ) 分别为输入影像和参考影像在第 i 波段的灰度值;向量pj表示了2景影像上地物辐射特征的变化关系。由于不同影像的对比度差别较大,直接聚类容易导致聚类结果受对比度大的影像影响,从而失去复合聚类的意义。因此,先分别计算2景影像各个波段的均值和标准差,逐波段对各个像元进行高斯归一化,得到归一化的向量 N (pj),再对 N (pj)聚类。
k 均值聚类是通过迭代过程把数据集划分为不同的类别,使生成的每个聚类内部紧凑,而类间差异尽可能大,是一种简单而常用的聚类方法,因而本文采用 k 均值聚类以提取复合类别。聚类数目是 k 均值聚类需要确定的一个关键参数,对于1景 b 个波段的影像,多元线性回归可以表示为式（5）。
x ′ = a 0 + ∑ i = 1 b a i x i （5）
式中： x ′ 表示结果影像的灰度值; x i （i=1,2,…,b）表示输入影像原始灰度值; a i （i =0,1）为待求的参数,一共有 b + 1 个,为了进行线性方程解算,需要 b + 1 个方程。波段数目 b 一般较多,建议聚类数目设为2b。
将图1（a）、（b）所示的3个波段按照上述方法聚为6类,其结果在二维直方图上分布情况如图2（a）、（b）所示,不同颜色代表不同的复合类别。由此可看出,该方法根据辐射特征变化情况将各个像元聚为不同类别;同时灰度值相近的像元聚为一类,且各个类别在二/多维直方图上相对位置相同。因而,可以利用各个类别的中心作为控制点将图2（a）的二/多维直方图扭曲到图2（b）,从而实现色彩归一化。
Fig. 2 The result of compound classification

图2 复合聚类结果

2.2 色彩归一化映射方程建立

进一步观察图2可发现：（1）各个类别内部都存在一些其他颜色的点,这主要由噪声或地表覆被类型改变而造成;（2）图2（a）中椭圆形区域内的云,这些像元在BN和BR波段的灰度值都较大,对应于图1（c）的椭圆形区域内。由于这些像元中都不包含有效的地表辐射变化信息,因而在统计各个类别中心点时需剔除。
根据以上分析,待剔除的点包括：（1）分布分散的点。该类点比较容易剔除,对于每个类别,只考虑该类别像元在多维直方图上构成的最大联通区域;（2）远离聚类中心的点,如图1（c）椭圆形区域内的点。根据各个像元与聚类中心的距离进行迭代去除,具体方法为:（1）计算某一类别C在各个波段的聚类中心 μ 1 和标准差 σ 1 ,其中下标1表示迭代次数;（2）剔除距离聚类中心 μ 1 3倍标准差 σ 1 以外的点,然后重新计算类别中心 μ 2 和标准差 σ 2 ;（3）计算前后2次聚类中心的差值 Δμ （式（6））,如果条件 Δμ > T μ ,则重复步骤（2）、（3）,否则迭代结束,并将该类别聚类中心作为一个控制点。考虑影像的灰度值一般是整型,当灰度值变化小于1时,不能表示非整型的灰度差异,因而设置 T μ = 1 ;（4）依次将聚类得到的各个类别进行处理,得到一组控制点。图2（a）、（b）的中心点确定结果如图3所示。
Δμ = | μ 2 - μ 1 | （6）
Fig. 3 The figure indicating the mapping method of color normalization

图3 色彩归一化方程建立方法示意图

在此基础上,将影像 X 和 Y 上各个类别的中心点作为控制点,根据最小二乘法,建立影像 X 灰度值到影像 Y 灰度值的线性映射方程,得到校正矩阵,可表示为式（7）。
( x ′ 1 , x ′ 2 , ⋯ , x ′ b ) = k 10 k 11 ⋯ k 1 b k 20 k 21 ⋯ k 2 b ⋯ ⋯ ⋯ ⋯ k b 0 k b 1 ⋯ k bb ( 1 , x 1 , ⋯ , x b ) T （7）
式中： k ij ( i , j = 1,2 , ⋯ , b ) 表示校正系数; x ′ b ) 表示色彩校正后的灰度值。该方法考虑了多个波段同时处理,从而避免多个波段色彩残差不一致导致的色彩差异。

3 试验结果与分析

3.1 数据与试验方法

本文选取2组影像进行试验,分别记为试验1和试验2。
3.1.1 试验1
试验1选取一组Landsat TM5影像,裁剪其中600像元×600像元的子区域进行试验。研究区位于浙江省临安市,土地覆被类型包括林地、湖泊以及居民点等。2期影像获取时间分别为2000年7月15日（第197天）和12月22日（第357天）,其灰度差异与色彩特征包括：（1）水体、居民区、植被在近红外波段的灰度值依次升高,且交织在一起。尤其是12月22日影像整体偏暗,地物灰度级压缩,使得3种地物的灰度值交织现象更加严重;（2）随着时间变化,植被叶绿素降低,湖泊中水草和泥沙含量改变,造成影像上相应地物色彩改变。
将影像聚为6类,然后同时处理上述3个波段和同时进行色彩归一化处理,结果如图4（a）所示。整体上看,处理后的影像与参考影像整体灰度分布与对比度相似,不存在明显的色彩差异,与目视具有较高的一致性。具体观察水体、城市以及植被等地物可看出,处理后的影像与参考影像色彩逼真,具有较好的色彩保持能力。
Fig. 4 The result of experiment 1

图4 试验1处理结果

由于实验1中2期影像间的植被存在较大的色彩差异,回归方法根据选取的PIFs进行校正,仅能消除城市的色彩差异,而植被等仍然存在较大色彩残差。因而,试验1选用多维概率密度匹配[18]作为对比方法,即在多维概率密度空间建立映射方程,对输入影像进行校正。由图4（b）的对比方法处理结果可看出,水体与城市的色彩保持能力与本文方法相当,而植被的色彩校正效果不如本文方法,存在新的色彩畸变。
3.1.2 试验2
试验2为新疆伊犁地区的SPOT 5多光谱影像,获取时间分别为2004年9月11日和2008年8月1日。影像空间分辨率10 m,影像上细节信息丰富,标准假彩色合成如图5（a）、（b）所示。2期影像的获取时相相近,植被色彩差异相对较小;但由于影像获取时间相隔较长,城市扩张、农田中种植的作物改变、河流改道,造成较大的色彩差异,且变化幅度和方向各不相同,给色彩归一化带来困难。
Fig. 5 The original image and result of experiment 2

图5 试验2原始影像及其处理结果

试验2将影像聚为6类,同时利用图中3个波段进行色彩归一化。参考影像与本文方法结果的卷帘显示如图5（c）所示。可以看出,本文方法处理结果与参考影像的色彩相似程度较高,卷帘线两侧的整体色彩基本一致,没有明显的接缝线,说明本文方法能够分别校正城市、河流和植被不同类型地物的色彩变化。图5（e）给出了图5（c）中局部区域A的放大显示,除地物发生变化处外,卷帘线两侧的河流与植被基本不存在色彩差异。
试验2色彩差异主要是由地物变化引起的整体色彩差异,地物变化造成直方图畸变,若采用概率密度匹配将会引入新的误差。因而试验2采用回归法作为对比方法。首先利用迭代多元变化检测方法[5]选取PIFs,然后通过正交最小二乘法建立回归方程,进而对输入影像进行校正。参考影像与对比方法结果卷帘显示如图5（d）所示,由于选取的样本主要是城市中的建筑物、道路等,居民区色彩差异消除与本文方法相当或者略好于本文方法,但河流仍然存在明显的色彩校正残差（图5（f））。同时,影像整体偏红,如图5（d）中B区域的裸地表现出淡红色,产生了新的色彩畸变。

3.2 试验结果及评价

对于校正后的影像,采用辐射分辨率 SR （式（8））、均方根误差 R （式（9））和线性相关性 C （式（10））3个指标进行定量评价。
SR = V ( f ( X ) ) （8）
R = 1 n ∑ j = 1 n f ( x j ) - y j 2 （9）
C = ∑ j = 1 n ( f ( x j ) - μ f ( x ) ) ( y j - μ y ) ∑ j = 1 n ( f ( x j ) - μ f ( x ) ) 2 ) ∑ j = 1 n ( y j - μ y ) 2 ) （10）
式中： f ( X ) 和 Y 表示色彩归一化的结果影像和参考影像; V 表示频数不为0的灰度级数目; f ( x j ) 和 y j 分别表示 f ( X ) 和 Y 的某一像元 j 的灰度值; μ f ( x ) 和 μ y 分别表示 f ( X ) 和 Y 灰度均值; n 表示影像区域的像元数目; SR 表示有效的辐射分辨率; R 表示结果影像与参考影像间的整体相似程度;线性相似性 C 表示结果影像与参考影像的线性相关性,即色彩的相似程度。
表1为本文及其对比方法在近红外（ B N ）、红（ B R ）、绿（ B G ）3个通道的上述指标值。由表1可看出：（1）本文方法 R 值较小,说明本文结果影像与参考影像整体偏差更小;（2）本文方法 C 值较大,说明本文方法相对于对比方法具有更好的线性相关性,色彩一致性更高;（3）本文方法的 SR 大于对比方法,说明本文方法具有更多的有效灰度值,更好地保持了辐射分辨率。综上,试验中本文方法在整体精度、色彩保持方面相对于对比方法具有一定的优势。
Tab. 1 The comparison of experiment results

表1 试验结果比较

SR R C
BN BR BG BN BR BG BN BR BG
试验1 本文方法 129 110 82 7.9 6.9 9.5 0.95 0.91 0.89
对比方法 109 85 63 10.5 9.6 11.6 0.75 0.77 0.84
试验2 本文方法 160 141 127 11.3 13.1 12.5 0.82 0.85 0.84
对比方法 128 115 105 14.6 13.5 0.80 0.79

4 结论

本文提出了一种复合类别支持的多元线性回归的遥感影像色彩归一化方法。该方法利用所有像元进行处理,回避伪不变特征的选取;同时,对所有波段进行归一化处理,克服逐波段处理导致的色彩畸变。试验结果表明：本文方法较传统的多维密度匹配和线性回归方法具有良好的色彩匹配特征;同时,能更好地保持处理结果影像的辐射分辨率,避免了逐波段处理造成的色彩畸变。
此外,本文研究存在2点不足：（1）复合分类及其类别中心确定对于校正效果具有较大影响,而这2个方法也存在较大的不确定性,需要从方法设计上增加一些措施,以增强算法的鲁棒性;（2）依据控制点建立的映射方程可能不是最优解,即结果影像与参考影像的多维直方图相似性不一定最高,更理想的方式是直接建立多波段灰度映射方程,但由于建立多维空间灰度映射方程的搜索空间很大,给影像处理造成困难,需进一步研究加以克服。

The authors have declared that no competing interests exist.

References

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Nikolova M, Wen Y W, Chan R.Exact histogram specification for digital images using a variational approach[J]. Journal of Mathematical Imaging and Vision, 2012,46(3):309-325.We consider the problem of exact histogram specification for digital (quantized) images. The goal is to transform the input digital image into an output (also digital) image that follows a prescribed histogram. Classical histogram modification methods are designed for real-valued images where all pixels have different values, so exact histogram specification is straightforward. Digital images typically have numerous pixels which share the same value. If one imposes the prescribed histogram to a digital image, usually there are numerous ways of assigning the prescribed values to the quantized values of the image. Therefore, exact histogram specification for digital images is an ill-posed problem. In order to guarantee that any prescribed histogram will be satisfied exactly, all pixels of the input digital image must be rearranged in a strictly ordered way. Further, the obtained strict ordering must faithfully account for the specific features of the input digital image. Such a task can be realized if we are able to extract additional representative information (called auxiliary attributes ) from the input digital image. This is a real challenge in exact histogram specification for digital images. We propose a new method that efficiently provides a strict and faithful ordering for all pixel values. It is based on a well designed variational approach. Noticing that the input digital image contains quantization noise, we minimize a specialized objective function whose solution is a real-valued image with slightly reduced quantization noise, which remains very close to the input digital image. We show that all the pixels of this real-valued image can be ordered in a strict way with a very high probability. Then transforming the latter image into another digital image satisfying a specified histogram is an easy task. Numerical results show that our method outperforms by far the existing competing methods.

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[18]
Inamdar S, Bovolo F, Bruzzone L, et al.Multidimensional probability density function matching for preprocessing of multitemporal remote sensing images[J]. IEEE Transactions on Geoscience and Remote Sensing, 2008,46(4):1243-1252.This paper addresses the problem of matching the statistical properties of the distributions of two (or more) multi-spectral remote sensing images acquired on the same geographical area at different times. An N-D probability density function (pdf) matching technique for the preprocessing of multitemporal images is introduced in the remote sensing domain by defining and analyzing three important application scenarios: 1) supervised classification; 2) partially supervised classification; and 3) change detection. Unlike other methods adopted in remote sensing applications, the procedure considered performs the matching process by properly taking into account the correlation among spectral channels, thus retaining the data correlation structure after the pdf matching. Experimental results obtained on real multitemporal remote sensing data sets confirm the validity of the presented technique in all the considered scenarios.

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[19]
Mas J F.Monitoring land-cover changes: a comparison of change detection techniques[J]. International Journal of Remote Sensing, 1999,20(1):139-152.Six change detection procedures were tested using Landsat MultiSpectral Scanner (MSS) images for detecting areas of changes in the region of the Terminos Lagoon, a coastal zone of the State of Campeche, Mexico. The change detection techniques considered were image differencing, vegetative index differencing, selective principal components analysis (SPCA), direct multi-date unsupervised classification, post-classification change differencing and a combination of image enhancement and post-classification comparison. The accuracy of the results obtained by each technique was evaluated by comparison with aerial photographs through Kappa coefficient calculation. Post-classification comparison was found to be the most accurate procedure and presented the advantage of indicating the nature of the changes. Poor performances obtained by image enhancement procedures were attributed to the spectral variation due to differences in soil moisture and in vegetation phenology between both scenes. Methods based on classif...

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[20]
Helmer E H, Ruefenacht B.Cloud-free satellite image mosaics with regression trees and histogram matching[J]. Photogrammetric Engineering & Remote Sensing, 2005,71(9):1079-1089.This study's objective is to test whether a new strategy foe developing cloud free imagery over a project area can yield image mosaics that permit simple change detection. The strategy proposed first uses regression tree models to predict band values of cloudy pixels in a reference scene from other scene dates. It secondly matches adjacent scenes with histogram matching based only on image overlap areas. Results of the study indicate that the regression tree prediction offers an effective tool for overcoming persistent cloud cover in Landsat imagery. In addition, histogram matching based on image overlap areas permits seamless mosaicing of scenes that have undergone cloud removal with regression tree prediction. The results also show that mosaics resulting from this new strategy can support change detection in persistently cloudy regions.

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