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Journal of Geo-information Science >

2016 , Vol. 18 >Issue 10: 1399 - 1409

DOI: https://doi.org/10.3724/SP.J.1047.2016.01399

Orginal Article

The Remote Sensing Model for Estimating Urban Impervious Surface Percentage Based on the Cubist Model Tree

  • DAI Shu ,
  • FU Yingchun , * ,
  • ZHAO Yaolong
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  • School of Geography, South China Normal University, Guangdong Provincial Center for Smart Land Research, Guangzhou 510631, China
*Corresponding author: FU yingchun, E-mail:

Received date: 2015-09-14

  Request revised date: 2015-12-20

  Online published: 2016-10-25

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Abstract

As a typical land-cover type, impervious surface is a key indicator of urban environmental quality and urbanization scope. In comparison with the traditional remote sensing image processing methods, the assessment of impervious surface percentage (ISP) can offer the sub-pixel level exploration and acquire the fine-scale information. In this paper, the proposed method uses the Cubist model tree with both the high-resolution (Google Earth) and the medium-resolution (Landsat TM/ETM+) remote sensing data to establish an estimation model of impervious surface percentage (ISP). A base model (Base Cubist-ISP) is built integrating all the original bands from Landsat TM excluding the thermal infrared band. This paper tries to minimize the effects of noise by adopting the ensemble learning algorithm and by incorporating the median of each solar-reflective band within the adjacent temporal images. After that, the following variables are filtered to get the optimized results, including the TM thermal infrared band, the derived variables from the original bands such as Texture, and the tasseled cap transformation variables. Then the variables are simplified, and in that way, the optimized parameter of ensemble learning algorithm for Cubist tree and the well-chosen variables are used to establish an optimization estimation model (Optimal Cubist-ISP). The results of a case study for Haizhu district, which is located in Guangzhou city of Guangdong Province, show that the overall root mean square error between the estimated ISP value, which is based on the Optimal Cubist-ISP model, and the reference ISP value is 12.98%, with a determinant coefficient of 0.90. Moreover, this paper compares the Base Cubist-ISP model with the Optimal Cubist-ISP model. The accuracy of the Optimal Cubist-ISP model is better than the Base Cubist-ISP model, and the RMSE decreases by about 5.03%. It is illustrated that the Base Cubist-ISP model may over-estimate the pervious surface area and under-estimate the high density impervious surface area, which could be improved by the model optimization. In addition, the Optimal Cubist-ISP model can not only be able to well recognize the land types of soil and water, but also eliminate the influence of shadow on the high density building area to a certain extent. Thus, the proposed approach on impervious surface estimation based on the Cubist model tree as well as its optimization scheme can be applied for precisely obtaining the ISP in the urban areas.

Key words： impervious surface; Cubist model tree; ensemble learning algorithm; Optimal Cubist-ISP model

Cite this article

DAI Shu , FU Yingchun , ZHAO Yaolong . The Remote Sensing Model for Estimating Urban Impervious Surface Percentage Based on the Cubist Model Tree[J]. Journal of Geo-information Science, 2016 , 18(10) : 1399 -1409 . DOI: 10.3724/SP.J.1047.2016.01399

1 引言

不透水面是城市区域中一种典型的土地覆盖类型,指难以被水穿透的地表,主要由人造地物构成,如屋顶、停车场、广场、公路、街道和人行道等[1]。作为一种典型的人工地貌特征,不透水面是衡量城市环境质量和城市化水平的重要标志之一[2]。与传统的基于像元级的遥感研究方法相比,不透水面百分比（Impervious Surfaces Percent,ISP）的估算可以进入像元内部,获得更准确的城市信息。而土地利用类型为植被的像元中,同样有可能分布少量不透水面,只有在亚像元尺度下量化估算不透水面百分比,才能更准确地分析城市化与城市生态的影响及两者的联系[3]。
近年来,基于亚像元的不透水面百分比估算方法一般包括多元回归法[4-5]、线性光谱混合分析法[6-7]、人工神经网络法[8-9]、决策树法[10-11]。Weng[3]认为多元回归法最大的不足在于易受季节影响,落叶季节低估植被覆盖度,生长季节高估植被覆盖度,进而影响不透水面百分比的估算;而线性光谱混合分析法问题在于不透水面的光谱容易与其他某些地物混淆,使得不透水面呈小块分散分布的区域的估测结果往往被高估,而不透水面集中分布的区域被低估。人工神经网络法与上述2种方法不同,具有解决非线性问题的能力,得到的结果也更精确。然而,人工神经网络法也存在一定的局限性[12]：在选择拓扑结构时常缺乏充分的理论依据,以及网络连接权值的物理意义不明确,因此人们通常难以理解其推理过程,可信度较差;此外,人工神经网络算法将信息处理都归结为数值运算,对知识的表达、存储和推理是隐式的,因此,存在依赖学习样本数量和质量的好坏,以及在学习上收敛速度慢、网络记忆不够稳定等方面的不足。在决策树法中,较为广泛使用的是分类回归树（CART）算法。CART算法继承了一般决策树具备的所有优点,既可以用于分类研究,又能进行连续变量的预测和回归,且实现简单,运算效率高,成为研究不透水面的热点。Cubist模型树也是一种决策树,相对于CART算法,Cubist模型树与其最大的区别在于模型树的叶子节点上是一个线性回归模型,而回归树的叶子节点上只是一个具体的值。因此,Cubist模型树比回归树建模更灵活,且精度更高[13]。2001年,美国地质调查局EROS数据中心选择使用Cubist模型树估算不透水面百分比和植被覆盖度,并将获得的数据加入到国家土地覆盖数据库中。此后,Cubist模型树越来越多的结合Landsat数据用于反演不透水面百分比,高志宏等[14]以山东省泰安市为例,基于TM影像除了热红外波段外的6个波段反射率变量运用Cubist软件进行城市不透水面百分比（ISP）遥感估算,基于ISP制图结果对城市土地利用变化进行检测。除Landsat原始波段以外,相关研究引入了更多的变量组合建模,如缨帽变换的分量组合、归一化差值植被指数（NDVI）、归一化建筑指数（NDBI）和建筑指数（BU）[15-17],并针对山谷区域不透水面百分比提取增加了坡度变量[16]。Walton[18]用Landsat ETM+数据的7个波段变量和缨帽变换三分量共10个变量分别基于Cubist模型树、随机森林法和支持向量回归3种方法估算城市的植被覆盖度和不透水面百分比,且估算结果表明Cubist模型树估算不透水面百分比的效果最好。
Cubist模型树节点上的回归方程建模比较灵活,可以针对不同区域构建合适的应用模型。但Cubist模型树也是一种学习算法,在对不透水面信息进行估算时,对数据噪声敏感。当训练样本存在大量噪声时,会降低Cubist模型树的学习能力,估算精度也会相应降低。因此,原始波段和变量的选择在模型树建模中显得非常重要。对于异质性很强的城市地表不透水面百分比估算的应用,增加有用的变量将有助于提高估算精度,而删除冗余变量则可以减少数据容量并提高计算效率。但上述研究没有讨论遥感影像波段及相关变量的适用性及在Cubist模型树中变量优选的方法,故本文拟在应用Landsat提取城市不透水面百分比的研究案例中,从波段和变量优选角度探讨Cubist模型树建立和优化的方法,以提高运算效率和估算精度。

2 研究区与数据源

本文选取广东省广州市海珠区作为研究区。海珠区是广州市的老四区之一,位于广州市中部,珠江南面,由珠江水系广州河段前后航道所环绕,总面积92.11 km2,是四面环水的天然良壤。研究区不透水面较集中,是城市化的典型区域,同时异质地表相嵌复杂多样,主要地物类型包括建筑物、道路、空地、湿地、林地、农田和河流等。

2.1 遥感影像数据

如图1(a)所示,研究区遥感影像目标数据选用2004年12月6日采集的Landsat TM图像,条带行列号为122/44,全景影像含有8%的云,黄色线所示区域为广州市,红色线所示区域即是本研究区。研究区（图1(b)）图像质量较好,清晰无云。本文选取了研究区部分区域分辨率为1.1 m的Google Earth影像（图2）,采集时间为2005年1月6日,总面积10.8 km2,用以获得ISP估算的训练样本和测试样本。对Google earth 影像和TM影像进行了精确的几何配准,将Google earth影像配准到TM影像上,经投影和坐标转换后统一到UTM/WGS84投影坐标系。
Fig.1 The study area

图1 研究区

Fig.2 Google Earth image of the sample area

图2 样本区Google Earth影像

同时,为了提高模型的估算精度,本文还选取了部分辅助数据,包括目标数据相邻的冬季多时相Landsat影像和夏季多时相Landsat影像。其中,相邻的冬季多时相Landsat影像包括2004年11月20日的TM影像和2004年12月14日的ETM+影像;相邻的夏季多时相Landsat影像包括2004年6月13日、2004年6月29日、2004年10月19日和2005年7月18日这4个时相的TM影像。本文所有Landsat影像数据均来源于USGS(美国地质调查局)官方网站中的CDR（Climate Data Record）产品[19]。该产品为地表反射率产品,使用由美国航空航天局研发的陆地卫星生态系统干扰自适应处理系统（Landsat Ecosystem Disturbance Adaptive Processing System,LEDAPS）,经过几何校正、辐射定标、大气校正和Fmask云掩膜处理得到。LEDAPS 大气校正基于6S 辐射传输模型,获得有效的气溶胶分布数据,开展适用于TM/ETM+数据可见光、近红外及短波红外波段反射率的反演[20]。

2.2 ISP 训练数据和测试数据获取

应用面向对象分类法,将配准后的Google Earth影像分为不透水面（主要由建筑物、道路和水泥面空地等组成）、植被、耕地、裸地、水体和阴影。其中,为了防止样本区透水面所占比例过高,有2块植被区域（图2红线所示的区域）被排除在样本区之外。对分类后的结果进行排查、修改,以便精确提取最终的不透水面区域,并叠加到TM影像的像元网格,获得30 m尺度下ISP统计结果,即不透水面亚像元分布的参考值。考虑到很多阴影区的实际地物类型无法确定,含有阴影且无法确定实际地物类型的像元网格不参与ISP的统计。因此,在实验区随机选取4000个符合条件的样本点,其中3200个作为训练样本,剩下800个作为测试样本,训练样本和测试样本是相互独立的。

3 研究方法

本文基于Cubist模型树,通过基于模型树的集成学习算法[21]对TM影像原始波段变量（除热红外波段）进行降噪处理,增选有用变量并精简其相关属性对模型进行优化。在提供Cubist模型树优化评价方法的同时,建立城市不透水面百分比的估算模型。具体技术路线如图3所示。
Fig.3 Flow chart of the research

图3 技术路线图

3.1 基于Cubist 模型树的ISP 估算模型

3.1.1 Cubist 模型树
Cubist模型树是由RuleQuest公司开发的决策树算法,来源于Quinlan的M5'模型树算法[13]。模型树是一种在叶子节点采用线性回归函数的决策树,表示一种分段式多元线性函数通过一系列的独立变量（称为属性）来预测一个变量的值。对给定的数据集,模型树将样本空间分为边缘相互平行的长方形区域（图4(a)）,对每个分区确定一个相应的回归模型,使所建立的模型更为直观、清晰。如图4(b)所示,在模型树的每一层,选择最有识别力的属性作为子树的根节点,并以此将节点样本划分成若干子集。模型树持续划分,停止生长的条件有：(1)结点的样本数少于一定数量;(2)结点的样本目标属性标准差与总体样本目标属性标准差的比例小于某个限定值。模型树建立后,还需要对树进行剪枝,即是对某些子树进行归并后以叶子节点取代,以提高模型树的简洁性和效率。剪枝后,还需要使用平滑过程来补偿叶子节点的不连续性,平滑的方法需要考虑叶子结点的父结点,将子结点与父结点拟合方程合为一个新的线性方程。
Fig.4 Illustrative diagrams of the Cubist model tree

图4 Cubist模型树示意图

模型树算法用一系列组合起来的分段线性模型,很好地解决了非线性问题。它与单纯的线性回归的区别在于,对输入空间的分割是由算法自动进行的,训练规则简单、有效,训练时间短,可以处理高维属性的问题。这种方法在估算不透水面上很好地结合了回归树和多元线性回归法,在预测连续值方面很成功。此外,该方法还根据样本信息将相关性不强的输入变量剔除,因此除了预测功能外,该方法还具有变量的重要性分析功能。本文采用R软件中的Cubist程序包。
3.1.2 基于Cubist 模型树的ISP估算模型
3.1.2.1 ISP估算基础模型（Basic Cubist-ISP）
首先,以目标数据除热红外波段以外的6个波段的光谱反射率作为估算模型的独立变量,将从高分辨率影像得到的30 m分辨率ISP 参考数据作为目标变量。运用Cubist模型树对上述样本进行学习,建立对应于该时相遥感影像的ISP回归估算模型,并将此估算模型称为ISP估算基础模型,简称Basic Cubist-ISP。其中,模型树的结构可以表示成一系列if-then形式的决策规则：
Rule 1: [234 cases, mean 0.0072628, range 0 to 0.57196, est err 0.0114008]
if
BAND1 <= 0.092
BAND4 > 0.1659
then
ISP = -0.0530795+2.7 BAND6 - 1.67 BAND5-1.4 BAND3 + 1.6 BAND1+ 0.4 BAND2
Rule 2: [246 cases, mean 0.0208308, range 0 to 0.450773, est err 0.0301795]
if
BAND1 <= 0.1001
BAND4 > 0.2054
then
ISP = -0.0091819 + 1.58 BAND6 - 1.6 BAND3 + 1.6 BAND2 - 0.4 BAND4- 0.29 BAND5
Rule 3: [152 cases, mean 0.0333124, range 0 to 0.810607, est err 0.0501680]
if
BAND6 <= 0.0588
then
ISP = -0.1893327 + 0.84 BAND6 + 1.7 BAND2 - 0.6 BAND4 + 1.3 BAND1-0.22BAND5 + 0.2 BAND3
Rule ······
本文利用高分辨率影像提取的不透水面得到的ISP参考值来评估ISP估算模型的质量,即评价ISP参考值和ISP估算值的差异大小,所用的评价指标包括平均偏移误差（Mean-Bias-Error,MBE）、平均绝对误差（Mean-Absolute-Error,MAE）和均方根误差（Root-Mean-Square Error, RMSE）。各指标的计算公式如式（1）-（3）所示。
MBE = 1 N ∑ i = 1 N ( f ^ i - f i ) (1)
MAE = 1 N ∑ i = 1 N | f ^ i - f i | (2)
RMSE = 1 N ∑ i = 1 N ( f ^ i - f i ) 2 (3)
3.1.2.2 优化的ISP估算模型（Optimal Cubist-ISP）
（1）基于模型树的集成学习优化
Cubist模型选用了一种叫基于模型树的集成学习算法,该方法类似于boosting算法。当第一棵模型树遵循M5'模型树规则建立后,接下来的模型树是训练集结果的调整版本：如果模型高估某一目标值,那么下一个模型的响应为向下调整,以此类推。最终的估算值为每棵树的模型计算值的平均值。该优化方法可以降低模型树对数据噪声和训练样本误差的敏感性,提高估算精度。特别是在输入变量过多有大量属性冗余的情况下,基于模型树的集成学习算法可以提取有效信息,大大提高模型树的精度。而树的个数即参数committees的值需要设定,当committees的值足够大（≥10）时,估算结果及模型精度稳定,本文暂时设定committees为最大值100。表1为使用集成学习算法的优化方法前后的对比精度评价,从表中可知,使用集成学习算法的优化方法后,3个精度指标都有一定的提升。
Tab.1 The comparison of accuracy before and after the optimization through ensemble learning algorithm based on the model trees

表1 基于模型树的集成学习算法优化前后精度对比

committees MBE/(%) MAE/(%) RMSE/(%)
1 -0.47 12.51 18.01
100 -0.25 12.19 17.50
（2）波段合成中值与热红外波段选择
Landsat影像经过辐射定标和大气校正后,由于阴影、云和雾霾等因素影响,仍然存在残余的噪声。为了减小噪声的影响,本文增加目标数据附近的冬季多时相Landsat影像。通常,多时相影像的合成取值可以最大限度地填补缺失数据和消除各种残余的噪声[22]。由于残余噪声的影响,影像数据中会出现过大或过小的异常值,显然,取多时相数据的均值是不合适的,而中值合成可以很好地解决这一问题[23]。利用目标数据和目标数据相邻的冬季影像共3个时相（2004年11月20日,2004年12月6日和2004年12月14日）的Landsat影像各波段反射率的中值代替原始波段反射率（表2实验1和2）,RMSE降低了1.3%,模型估算精度明显提高。
Landsat TM影像数据包括6个波段反射率和1个热红外波段,相关研究在自变量中加了热红外波段[15-16,18]。根据表2的实验1和实验3对比证明,加入热红外波段数据可以提高估算精度,但提高得很少。研究表明,不透水面百分比与地表温度呈正相关关系[24]。热红外波段具有温度信息,有助于区分透水面与不透水面。本文尝试引入当年夏季（2004年6月29日）的TM影像的热红外波段,依据样本点的数据,把夏季和冬季的热红外波段分别与不透水面百分比做相关性分析。分析结果显示,夏季的相关系数为0.65,冬季的相关系数为0.41,表明夏季的热红外波段与不透水面百分比的相关度更高,能更好地区分透水面与不透水面。所以,本文用夏季的TM影像热红外波段代替冬季热红外波段。表2的实验1和实验4对比表明,加入夏季热红外波段可以有效地提高估算精度,RMSE也降低了约1.3%。遥感影像原始波段变量组合的实验表明,多时相中值和夏季热红外波段的加入有助于提高研究区不透水面百分比的估算精度。
Tab.2 Estimation of MAE and RMSE using various combinations of the independent variables from the original bands

表2 各种原始波段自变量的组合的MAE和RMSE

实验 MAE/(%) RMSE/(%) 输入的自变量
1 12.19 17.50 b1-6
2 10.92 16.20 b1-6_med
3 12.26 17.45 b1-6,b7
4 11.26 16.21 b1-6,su_b7

注：b1-6为2005年12月6日的TM1~TM5和TM7;b1-6_med为目标数据附近的冬季多时相中值合成的TM1~TM5和TM7;b7为2005年12月6日的TM6波段;su_b7为夏季（2004年6月29日）TM影像的热红外波段

（3）衍生变量的增选及属性精简
在植被-不透水面-土壤模型中,不透水面主要与建筑用地有关,并区别于土壤和覆盖在上面的植被。由原始波段反射率变换得到的3类衍生变量,较好的突出了这3种地表覆盖组分的特征,分别是：①指数变量,即归一化差值植被指数（Normalized Difference Vegetation Index,NDVI）[25],归一化建筑指数（Normalized Difference Built-up Index,NDBI）[26]和归一化裸土指数（Normalized Difference Bareness Index,NDBaI）[27];②缨帽变换分量,能区分土壤地表平面与植被平面特征,包括绿度、亮度和湿度[28],跟植被和土壤有密切的关系;③纹理特征值,能重点突出地表成分空间结构关系。基于此,本文尝试加入指数变量、缨帽变换三分量和纹理特征值,实现多源信息辅助下ISP估算模型的建立。同时,对比各指标变量对ISP估算模型的影响(表3),得出以下2点结论：
①表3中实验1-3为研究NDVI相关变量的有效性。从实验1、2可以看出,加入NDVI后精度变化不明显,主要是因为NDVI容易受到物候的影响。因此,本文将单时相的NDVI换成目标数据相邻夏季多时相Landsat影像的NDVI最大合成值,即NDVI_max。从表3的实验1和实验3可知,加入NDVI_max后,精度有明显的提高。NDVI夏季最大值合成可以更好地区分植被和非植被区域,特别是某些只有在夏季覆盖植被的土壤,最大值合成便可以有效地区分土壤和不透水面。
Tab.3 Estimation of MAE and RMSE using various combinations of the derived variables

表3 各种衍生自变量组合的精度评价指标MAE和RMSE

实验 MAE/(%) RMSE/(%) 输入的自变量（opt_b7：b1-6_med,su_b7）
1 10.41 15.39 opt_b7
2 10.34 15.42 opt_b7,NDVI
3 9.82 14.45 opt_b7,NDVI_max
4 8.77 12.67 opt_b7,NDVI_max,NDBI,NDBaI,TC,Texture
5 9.04 13.21 opt_b7,NDBI,NDBaI,TC,Texture
6 8.74 12.67 opt_b7,NDVI_max,NDBaI,TC,Texture
7 8.76 12.82 opt_b7,NDVI_max,NDBI,TC,Texture
8 8.84 12.72 opt_b7,NDVI_max,NDBI,NDBaI,Texture
9 9.38 13.83 opt_b7,NDVI_max,NDBI,NDBaI,TC

注：opt_b7为b1-6_med和su_b7合成的7个变量;NDVI：为目标数据的归一化植被指数;NDVI_max为2004年12月6日（TM）附近夏季NDVI最大合成值;NDBI为目标数据的归一化建筑指数;NDBaI为目标数据的归一化裸土指数;TC为缨帽变换三分量;Texture为TM图像主成分变换生成的第一主成分衍生出的8个纹理特征值,即均值(mean)、方差(var)、协同性(homog)、对比度(contr)、非相似度(diss)、熵(entropy)、角二阶矩(sec_mom)和相关度(correl)

Tab.4 Evaluation of the accuracy before and after the simplification on attributes

表4 属性精简前后精度评价

实验 b1-6_med MNF1-4_med su_b7 NDVI_max Texture MAE(%) RMSE(%)
1 √ √ √ √ 8.84 12.86
2 √ √ √ √ 8.94 13.09

注：“√”表示被选择

②表3中实验4-9为测试每一个添加变量的有效性,设计了通过逐一去除变量测试变量影响的实验方案。其中,实验4为将所有考虑到的衍生变量均加入模型中,实验5-9分别为去除某一变量得到的结果,由表3可看出,去除了NDVI_max或Texture,精度均有明显的降低;而去除了TC、NDBI和NDBaI中的某一变量,精度差别不大。
因此,本文增加的衍生属性包括NDVI_max和Texture（8个纹理特征值）,既保留有用的变量、删除了冗余变量,又达到了预期的精度。
增选衍生变量后,还需要对现有的变量做属性精简。对6个波段中值进行最小噪声分离,最小噪声分离得到的前4个主分量波段涵盖了主要的信息,取前4个波段主分量,表示为MNF1-4_med。由表4可知,用MNF1-4_med代替b1-6_med,ISP的估算精度相差不大,所以,基于属性精简原则,本文用MNF1-4_med代替b1-6_med建模,并进行重要性分析。以Cubist模型树每个变量的重要度为指标,综合衡量以上增选后每个属性在各个Cubist模型树节点和多元线性回归模型中的贡献（表5）。在各变量的贡献中,最大是最小噪声分离变量的第二波段（79）,最小为纹理特征的熵变量（0）,本文通过实验选择重要度排在前面的10个属性,即MNF1-4_med、SU_TM6、NDVI_max和4个纹理特征值（均值、方差、对比度和非相似性）作为最终的自变量,建立估算不透水面百分比模型。上述可知,基于模型树的集成学习算法的参数committees暂时设为100,还需要设定优化参数。如图5所示,以10为间隔设置参数committees,选取优化的效果最佳,即RMSE最小时committees的值。
Tab.5 Importance analysis of the attribute variables

表5 属性变量重要性分析

属性变量 MNF2_med NDVI_max MNF1_med SU_TM6 var MNF3_med mean
重要度 79 64 59 55.5 47.5 47 46
属性变量 MNF4_med diss contr homog correl sec_mom entropy
重要度 38 30 28.5 19 6.5 1 0
Fig.5 The diagram showing the relationship between committees and RMSE

图5 参数Committees与RMSE关系图

综上所述,本文以MNF1-4_med、SU_TM6、NDVI_max和4个纹理特征值（均值、方差、对比度和非相似性）作为自变量,设定参数committees=60,建立最终的估算不透水面百分比的优化模型,简称Optimal Cubist-ISP。

4 结果与讨论

4.1 ISP估算结果与Optimal Cubist-ISP模型评估

为了节省计算时间,本文基于改进的归一化差异水体指数（MNDWI）[29],选用合适的阈值,既能够掩膜掉大部分水体,又避免误将城区的阴影掩膜。水体掩膜后,基于Optimal Cubist-ISP模型的海珠区的不透水面百分比估算结果如图6所示。统计可得,海珠区不透水面总面积39.92 km2,占海珠区总面积43.34%。从图6可以看出,ISP估算结果图可以识别主要的公路,如广州大道南、广州环城高速和华南快速等。整体上,由于海珠区东部有大片的湿地和植被,东部的ISP平均水平要低于西部。
Tab.6 Overall and hierarchy evaluation of the accuracy of Optimal Cubist-ISP model

表6 Optimal Cubist-ISP模型整体与分密度精度评价

评价指标 整体 高密度 中密度 低密度 透水面
MBE/(%) -0.38 -5.76 1.84 6.42 5.91
MAE/(%) 8.88 7.46 13.24 14.83 6.31
RMSE/(%) 12.98 11.14 16.46 18.85 10.43
表6为模型的整体和分ISP高密度（70%~100%）、中密度（40%~70%）、低密度（10%~40%）和透水面（0%~10%）的精度评价,可以看出：(1)模型整体的RMSE为12.98%,MAE为8.88%,RMSE与MAE相差较大,主要是由于测试数据中异常值（离群值）的影响;(2)高密度不透水面和透水面精度较高,中、低密度不透水面精度较低;(3)高密度不透水面被低估,中、低密度不透水面和透水面被高估,其中高密度不透水面和透水面的MBE的绝对值和MAE相差不大,表明大部分高密度不透水面都处于被低估的状态,而大部分透水面都处于被高估的状态。
对比表3中实验4和筛选有效的变量并进行属性精简后的建模时间,在参数committees相同（均设为100）的情况下,前者建模时间为38.70 s,后者的建模时间为21.80 s,在精度相差不大的情况下,建模效率大幅提升,提高了77.52%。
Fig.6 Result of the ISP estimation over Haizhu district

图6 海珠区ISP估算结果

Fig.7 Scatter plots between the estimated and reference ISP

图7 ISP估算值与参考值散点图

Fig.8 Google Earth image of special pixels

图8 特殊像元点Google Earth影像图

4.2 优化前后模型对比

如表7所示,相比基础模型（Base Cubist-ISP）,优化后的模型MAE降低3.63%,RMSE降低5.03%。并且,RMSE在高、中、低密度和透水面均有降低,特别是透水面,降低7.06%,精度有大幅提升。
Tab.7 The comparison of overall and hierarchy evaluation accuracy before and after the model optimization

表7 模型优化前后整体与分密度评估精度对比

MAE/(%) RMSE/(%)
整体 高密度 中密度 低密度 透水面
Base Cubist-ISP 12.51 18.01 15.88 21.86 21.77 17.49
Optimal Cubist-ISP 8.88 12.98 11.14 16.46 18.85 10.43
图7为基础模型（Base Cubist-ISP）与优化后的模型（Optimal Cubist-ISP）的ISP估算值与参考值散点图。对比散点图可以看出,优化后,异常点显著减少,特别是在透水面区域。R2从0.80提高到0.90,斜率从0.79提高到0.87,ISP在透水面区域（图7中红圈所包含的点）被高估和高密度不透水面区域（图7中黄圈所包含的点）被低估均得到改善。
如图8所示,选取了A、B、C、D、E、F 6个像元点。像元A、B、C分别为含有裸土的透水面像元、含有水的透水面像元和含有裸土和水的透水面像元,像元D、E、F分别为含有裸土的高密度不透水面像元、含有水的中密度不透水面像元和含有裸土和水的低密度不透水面像元。由于水体与城市里的阴影、透水的裸土或空地与不透水的人工地物存在光谱混淆,A、B、C、D、E、F的ISP值均被高估,优化后的模型能较好地识别裸土和水体,很好地改善了低值高估的现象（表8）。
Tab.8 The comparison of the ISP estimations of special pixels before and after the model optimization

表8 模型优化前后特殊像元点ISP估算值对比

像元点 ISP参考值/（%） Base Cubist-ISP模型估算值/（%） Optimal Cubist-ISP模型估算值/（%）
A 0.00 43.70 4.15
B 4.08 55.49 14.00
C 0.00 35.04 5.94
D 75.28 92.69 75.41
E 51.84 88.43 46.61
F 26.16 71.34 12.00
图9为优化前后海珠区ISP估算结果分级图。从图9可以看出,优化前本是大片高密度建筑区出现了很多破碎的高密度不透水面斑块,这主要是因为阴影的穿插使原本连续的高密度区域变得很破碎,而优化后在一定程度上消除了阴影对于高密度建筑区的影响。由优化前后的图中均可以看出,林地周围的植被较多,不透水面百分比降低,但却受不透水面地物的阻隔,斑块呈现小而破碎状。林地构成了大部分透水面,优化前后的ISP估算结果分级图中林地的分布差别不大。
Fig.9 The classification map of the ISP estimation for Haizhu district before and after the model optimization

图9 模型优化前后海珠区ISP估算结果分级图

5 结论

本文基于Cubist模型树增加有用属性和删除冗余属性的重要性以及对数据噪声敏感这一现象,通过集成学习的优化算法、对TM原始波段变量通过辅助数据进行中值合成、加入有用的变量以及属性精简对基础模型进行优化,得到最终的自变量,建立优化的ISP估算模型（Optimal Cubist-ISP）。
（1）辅助的冬季数据可以一定程度上消除残余噪声,利用辅助的夏季数据可以得到夏季热红外波段和夏季NDVI最大值。增加2种数据变量均可以有效地提高模型的精度。
（2）Optimal Cubist-ISP模型整体的RMSE为12.98%,MAE为8.88%。其中,高密度不透水面和透水面精度较高,中、低密度不透水面精度较低;高密度不透水面被低估,中、低密度不透水面和透水面被高估。在Cubist模型树的集成学习算法的参数committees相同（均设为100）的情况下,筛选有效的变量并进行属性精简,建模效率大幅提升,提高了77.52%。
（3）基于模型树的集成学习的优化算法和中值合成等可以最大程度地消除噪声的影响,再通过加入有用的变量和属性精简后得到的Optimal Cubist-ISP模型精度明显优于基础模型（Base Cubist-ISP）,均方根误差降低5.03%,R2提高了0.10,异常点显著减少,ISP透水面区域被高估和高密度不透水面区域被低估的现象得到改善,适用于城市区ISP的提取。
（4）水体与城区里的阴影存在光谱混淆,透水的裸土或空地与不透水的人工地物（如停车场等）也存在光谱混淆,造成含有水体、裸土或空地的像元被高估。优化后的模型能较好地识别裸土和水体,很好地改善低值高估的现象。此外,优化后的模型可以一定程度上消除阴影对于高密度建筑区的影响,从而避免高密度建筑区斑块破碎化的现象。

The authors have declared that no competing interests exist.

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高志宏,张路,李新延,等.城市土地利用变化的不透水面覆盖度检测方法[J].遥感学报,2010,14(3):593-606.通过分析城市中不透水面数量和分布的变化与城市土地利用变化之间的对应关系,综合中、高分辨率遥感数据各自的优势,运用CART算法进行城市不透水面覆盖度(ISP)遥感估算,基于ISP制图结果对城市土地利用变化进行检测.以山东省泰安市为例开展实验研究,结果表明,与传统的变化检测方法相比,基于ISP的变化检测方法,不仅能够反映土地利用类型转换的潜在信息,而且可以灵活地量化定义和解释城市用地变化情况.这种方法为城市土地利用变化信息的提取和分析提供了一种新的思路,可以作为现有变化检测方法的有益补充.

[ Gao Z, Zhang L, Li X, et al.Detection and analysis of urban land use changes through multi-temporal impervious surface mapping[J]. Journal of Remote Sensing, 2010,14(3):593-606. ]

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Yang L, Huang C Q, Wylie B K, et al.An approach for mapping large-area impervious surfaces: synergistic use of Landsat-7 ETM+ and high spatial resolution imagery[J]. Canadian Journal of Remote Sensing, 2003,29(2):230-240.Not Available

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Xian G.Mapping impervious surfaces using classification and regression tree algorithm[A]. In: Weng Q. Remote sensing of impervious surfaces[M]. Boca Rotan, FL: CRC Press, 2008:39-58.

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Im J, Lu Z Y, Rhee J, et al.Impervious surface quantification using a synthesis of artificial immune networks and decision/regression trees from multi-sensor data[J]. Remote Sensing of Environment, 2012,117:102-113.Impervious surface quantification is important for many planning and management applications because of the impacts that impervious surfaces have on a range of environmental resources such as groundwater. This research proposes an integrated method to quantify impervious surfaces at multiple spatial scales via a synthesis of several machine learning approaches. In this study, we 1) proposed a hierarchical classification method to detect impervious surfaces through a fusion of optimized artificial immune networks (OPTINC) and decision trees at high spatial resolution, 2) evaluated the method using multi-sensor data (i.e., high spatial resolution WorldView-2 and LiDAR data) to map impervious surfaces, 3) tested the applicability of the binary impervious surface maps to quantify sub-pixel imperviousness from Landsat TM data of a larger region using regression trees at moderate spatial resolution, and 4) examined the model sensitivity of regression trees to training sample size for impervious surface quantification. OPTINC and decision trees successfully identified impervious surfaces at high resolution (overall accuracy>90%). The regression tree predicted imperviousness from the TM data with a moderate success (R-2=0.64 and MAE=14.2%). Although the regression tree appeared robust when training sample size was sufficiently large, it was not stable with small sample size (e.g., <100). (C) 2011 Elsevier Inc. All rights reserved.

DOI

[18]
Walton J T.Subpixel urban land cover estimation: comparing Cubist, random forests, and support vector regression[J]. Photogrammetric Engineering & Remote Sensing, 2008,74:1213-1222.Three machine learning subpixel estimation methods (Cubist, Random Forests, and support vector regression) were applied to estimate urban cover. Urban forest canopy cover and impervious surface cover were estimated from Landsat-7 ETM+ imagery using a higher resolution cover map resampled to 30 m as training and reference data. Three different band combinations (reflectance, tasseled cap, and both reflectance and tasseled cap plus thermal) were compared for their effectiveness with each of the methods. Thirty different training site number and size combinations were also tested. Support vector regression on the tasseled cap bands was found to be the best estimator for urban forest canopy cover, while Cubist performed best using the reflectance plus tasseled cap band combination when predicting impervious surface cover. More training data partitioned in many small training sites generally produces better estimation results.

DOI

[19]
USGS. Landsat higher level science data products[ER/OL]. .

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Schmidt G, Jenkerson C, Masek J, et al.Landsat ecosystem disturbance adaptive processing system (LEDAPS) algorithm description (No. 2013-1057)[R]. US Geological Survey, 2013.

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Quinlan J R.Combining instance-based and model-based learning[C]. Machine Learning Proceedings, 1993:236-243.

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Txomin H, Michael A W, Joanne C W, et al.An integrated Landsat time series protocol for change detection and generation of annual gap-free surface reflectance composites[J]. Remote Sensing of Environment, 2015,158:220-234.

[23]
Neil F.Seasonal composite Landsat TM/ETM+ images using the medoid (a multi-dimensional median)[J]. Remote Sensing, 2013,5(12):6481-6500.Multi-temporal satellite imagery can be composited over a season (or other time period) to produce imagery which is representative of that period, using techniques which will reduce contamination by cloud and other problems. For the purposes of vegetation monitoring, a commonly used technique is the Maximum NDVI Composite, used in conjunction with variety of other constraints. The current paper proposes an alternative based on the medoid (in reflectance space) over the time period (the medoid is a multi-dimensional analogue of the median), which is robust against extreme values, and appears to be better at producing imagery which is representative of the time period. For each pixel, the medoid is always selected from the available dates, so the result is always a single observation for that pixel, thus preserving relationships between bands. The method is applied to Landsat TM/ETM+ imagery to create seasonal reflectance images (four per year), with the aim being a regular time series of reflectance values which captures the variability at seasonal time scales. Analysis of the seasonal reflectance values suggests that resulting temporal image composites are more representative of the time series than the maximum NDVI seasonal composite.

DOI

[24]
Weng Q.A remote sensing-GIS evaluation of urban expansion and its impact on surface temperature in the Zhujiang Delta, China[J]. International Journal of Remote Sensing, 2001,22(10):1999-2014.The Zhujiang Delta of South China has experienced a rapid urban expansion over the past two decades due to accelerated economic growth. This paper reports an investigation into the application of the integration of remote sensing and geographic information systems (GIS) for detecting urban growth and assessing its impact on surface temperature in the region. Remote sensing techniques were used to carry out land use/cover change detection by using multitemporal Landsat Thematic Mapper data. Urban growth patterns were analysed by using a GIS-based modelling approach. The integration of remote sensing and GIS was further applied to examine the impact of urban growth on surface temperatures. The results revealed a notable and uneven urban growth in the study area. This urban development had raised surface radiant temperature by 13.01 K in the urbanized area. The integration of remote sensing and GIS was found to be effective in monitoring and analysing urban growth patterns, and in evaluating urbanization impact on surface temperature.

DOI

[25]
Price J C.Using spatial context in satellite data to infer regional scale evapotranspiration[J]. IEEE Transactions on Geoscience & Remote Sensing, 1990,28(5):940-948.Several methods have been used to estimate regional scale evapotranspiration from satellite thermal infrared measurements. These procedures assume knowledge of surface properties such as surface roughness, albedo, vegetation characteristics, etc. In many areas of the earth these parameters are not accurately known due to the rapidity of change of vegetation, lack of adequate geographical data b...

DOI

[26]
Zha Y, Gao J, Ni S.Use of normalized difference built-up index in automatically mapping urban areas from TM imagery[J]. International Journal of Remote Sensing, 2003,24(3):583-594.Remotely sensed imagery is ideally used to monitor and detect land cover changes that occur frequently in urban and peri-urban areas as a consequence of incessant urbanization. It is a lengthy process to convert satellite imagery into land cover map using the existing methods of manual interpretation and parametric image classification digitally. In this paper we propose a new method based on Normalized Difference Built-up Index (NDBI) to automate the process of mapping built-up areas. It takes advantage of the unique spectral response of built-up areas and other land covers. Built-up areas are effectively mapped through arithmetic manipulation of re-coded Normalized Difference Vegetation Index (NDVI) and NDBI images derived from TM imagery. The devised NDBI method was applied to map urban land in the city of Nanjing, eastern China. The mapped results at an accuracy of 92.6% indicate that it can be used to fulfil the mapping objective reliably. Compared with the maximum likelihood classification method, the proposed NDBI is able to serve as a worthwhile alternative for quickly and objectively mapping built-up areas.

DOI

[27]
Zhao H M, Chen X L.Use of normalized difference bareness index in quickly mapping bare areas from TM/ETM+[J]. Geoscience & Remote Sensing Symposium Proceedings, 2005,3:1666-1668.Borland ED.

DOI

[28]
Crist E P.A TM tasseled cap equivalent transformation for reflectance factor data[J]. Remote Sensing of Environment, 1985,17(85):301-306.A transformation of TM waveband reflectance factor data is presented which produces features analogous to TM Tasseled Cap brightness, greenness, and wetness. The approach to adjusting the transformation matrix to other types of reflectance factor data (different instrument or band response) is described in general terms.

DOI

[29]
徐涵秋. 利用改进的归一化差异水体指数(MNDWI)提取水体信息的研究[J]. 遥感学报,2005,9(5):589-595.在对M cfeeters提出的归一化差异水体指数(NDWI)分析的基础上,对构成该指数的波长组合进行了修改,提出了改进的归一化差异水体指数MNDWI(M odified NDWI),并分别将该指数在含不同水体类型的遥感影像进行了实验,大部分获得了比NDWI好的效果,特别是提取城镇范围内的水体。NDWI指数影像因往往混有城镇建筑用地信息而使得提取的水体范围和面积有所扩大。实验还发现MNDWI比NDWI更能够揭示水体微细特征,如悬浮沉积物的分布、水质的变化。另外,MNDWI可以很容易地区分阴影和水体,解决了水体提取中难于消除阴影的难题。

DOI

[ Xu H Q.A study on iInformation extraction of water body with the modified normalized difference water Index(MNDWI)[J]. Journal of Remote Sensing,2005,9(5):589-595. ]

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