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Journal of Geo-information Science >

2016 , Vol. 18 >Issue 5: 622 - 631

DOI: https://doi.org/10.3724/SP.J.1047.2016.00622

Orginal Article

Scale Parameter Estimation Based on the Spatial and Spectral Statistics in High Spatial Resolution Image Segmentation

  • MING Dongping , 1, * ,
  • ZHOU Wen 1 ,
  • WANG Min 2
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  • 1. School of Information Engineering, China University of Geosciences (Beijing), Beijing 100083, China
  • 2. Key Laboratory of Virtual Geographic Environment (Nanjing Normal University), Ministry of Education, Nanjing, Jiangsu 210023, China;;
*Corresponding author: MING Dongping, E-mail:

Received date: 2015-12-15

  Request revised date: 2016-01-23

  Online published: 2016-05-10

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Abstract

Object-Based Image Analysis (OBIA) is becoming an important technology for the information extraction from high spatial resolution images. Multi-scale image segmentation is a key and fundamental procedure of OBIA, however, the scale selection within the multi-scale image segmentation is always difficult to achieve for the high-performance OBIA. This paper firstly generalizes the commonly used segmentation scale parameters into three aspects: the spatial parameter (the spatial distance between classes), the attribute parameter (the attribute distance or spectral difference between classes) and the merging threshold (the area or pixel number of the minimum useful object). Next, this paper proposes a spatial and spectral statistics-based scale parameter estimation method for OBIA. The main concept of this proposed method is to use the average local variogram (without considering the anisotropism of spatial distribution) or the semivariogram (considering the anisotropism of spatial distribution) to pre-estimate the optimal spatial parameter. Next, the selection of the optimal attribute parameter and the selection of the merging threshold are achieved based on the local variance histogram and the simple geometric computation, respectively. Taking the mean-shift segmentation as an example, this study uses Ikonos, Quickbird and aerial panchromatic images as the experimental data to verify the validity of the proposed scale parameter estimation method. Experiments based on the quantitative multi-scale segmentation evaluation could testify the validity of this method. This pre-estimation based scale parameter selection method is practically helpful and efficient in OBIA. The idea of this method can be further extended to be integrated into other segmentation algorithms and be adaptive to other sensor data.

Key words： object-based image analysis; image segmentation; scale estimation; spatial statistics; spectral statistics

Cite this article

MING Dongping , ZHOU Wen , WANG Min . Scale Parameter Estimation Based on the Spatial and Spectral Statistics in High Spatial Resolution Image Segmentation[J]. Journal of Geo-information Science, 2016 , 18(5) : 622 -631 . DOI: 10.3724/SP.J.1047.2016.00622

1 引言

随着卫星遥感传感器技术的发展,遥感影像的空间分辨率得到了极大提高。在高空间分辨率遥感图像上,类别内的光谱异质性加剧,导致同物异谱和异物同谱现象较中低分辨率遥感影像更加明显,因此,高分辨率遥感影像像元分类不仅难以获得较高的精度,也难以保证图斑的完整性。面向对象影像分析方法（Object-Based Image Analysis,OBIA）能更有效地把空间信息和专家知识结合到遥感信息提取中,近十几年来逐渐成为高空间分辨率遥感信息提取的主流技术[1],并成为连接遥感与地理信息系统的桥梁[2]。在OBIA中,多尺度分割是将遥感影像从离散的规则像元转化为均质的影像对象基元的关键性基础工作,然而在多尺度分割过程中真正的挑战是定义合适的尺度参数[3],因为尺度参数不合适会导致过分割或者欠分割,进而会降低面向对象遥感信息提取的精度[4-5]。
虽然OBIA已经成为遥感信息提取的主流技术之一,但目前的尺度参数选择仍然大部分是基于试错法来进行。此外,有些研究以不同尺度分割结果的斑块内部的均质性和斑块之间的异质性为指标,用非监督分割评价模型辅助选择最佳分割尺度[6-8],还有一些研究采用监督法分割评价辅助选择最佳分割尺度[9-12]。文献[13]针对eCognition软件的多分辨率分割,提出利用表征分割斑块均质度的局部方差指标,从一系列不同尺度的分割结果中选择最佳尺度分割参数;文献[14]选择最佳分割尺度参数的规则是当影像对象的面积不再变化时,对应的一系列尺度参数都为最佳尺度参数。总体而言,这些方法都是基于大量分割后的评价进行尺度优选,尽管通过实验也证明了其有效性,但是这种方法的计算量比较大,而且大部分的工作都过分依赖eCognition软件的多分辨率分割算法,从尺度科学研究的角度而言,其普适性有待提高。基于遥感数据的固有特征,归纳影像分割尺度参数的一般含义,研究普适性的尺度参数估计方法,对于面向对象影像分析自动化非常重要。鉴此,本文从空间数据的空间特征和属性特征出发,提出了面向对象遥感影像分析中尺度的一般含义及尺度参数的一般内容;基于尺度的空间依赖性实质,将空间统计学和遥感光谱统计应用于面向对象遥感影像分析中的分割尺度参数估计;不依赖于具体的分割算法,提出了基于半方差和平均局部方差统计的分割前的遥感影像分割尺度参数估计方法。

2 面向对象影像分析中的尺度及尺度参数

尺度是一个广泛使用的术语,在一般科学研究领域,尺度主要指研究的范围或详细程度[15]。由于面向对象遥感影像分析研究目前还处于起步阶段,故没有对面向对象影像分析中尺度的明确定义。面向对象影像分析处理的基本单元是影像对象,eCognition软件对影像对象的定义为相同属性像元组成的连通区域[16],直观上,面向对象遥感影像分析中尺度主要指影像对象的尺度,即影像对象（对象细节）在空间跨度上的大小;而从算法的角度,由于影像对象是由影像分割得到的,面向对象影像分析中的尺度选择主要对应多尺度分割算法中的尺度参数选择。本文从空间数据的空间和属性2大特征出发,将面向对象影像分析中的多尺度分割的尺度参数选择,概括为空间尺度分割参数（类别或斑块间的空间距离）、属性尺度分割参数（类别或斑块间的属性距离）和合并阈值参数（斑块大小或斑块像元数目）。
在地学尺度的一般范畴里,尺度问题的本质依旧是空间统计学的空间自相关或尺度依赖思想,合适的尺度本质上恰好能反映地物间空间相关性是否存在的一个临界点[17]。基于这个理论,明冬萍等提出了基于空间统计学计算的面向对象遥感影像分割尺度估计思想[17-18]。总体而言,遥感影像的分割尺度参数估计的实质是基于原始影像上全局或局部特征的一种统计估计,因此,空间统计学方法无论从空间统计学的科学思想基础上,还是在算法实现技术等方面,都是解决面向对象影像分析尺度参数选择问题的可行方法。

3 基于谱空间统计的高分辨率影像 分割尺度估计

对于组成一个影像场景的不同类型目标而言,绝对最优的尺度是不存在的,一个折衷的解决方案是计算理论上的最优尺度,并基于此能最大程度地保证面向对象分类的精度,以及能更好地提取信息。此外,尽管尺度参数常常依赖算法存在,但是基于空间数据的空间和属性2大基本特征,可以依据空间统计和光谱统计获得理论上最优的空间尺度分割参数、属性尺度分割参数和合并阈值参数,这些参数可以部分地或全部地应用于大多数的多尺度分割算法中。图1是基于谱空间统计的尺度分割参数估计方法流程示意图。
Fig. 1 Workflow of the pre-estimation of the optimal scale parameters based on spatial and spectral statistics

图1 基于谱空间统计的尺度分割参数估计流程图

3.1 基于空间统计学的空间尺度分割参数估计方法

空间尺度分割参数（记为hs）在分割过程中对分割结果的影像常常大于属性尺度分割参数,因此该参数的估计对于面向对象影像分析尤为重要。将经典地统计学和模式识别的基本理论相结合,文献[18]提出了基于变异函数的均值漂移影像分割的空间带宽参数选择算法,这里的空间带宽参数可以上升为本文提出的空间尺度分割参数,因为二者都表明类别或斑块间的空间距离。文献[18]提出的这个算法的基本理论前提是变异函数的变程可以看做是变量间相似性量测的测度,变程的大小能预示影像中目标、现象或格局的尺寸。相似地,因为空间带宽参数对应了聚类分割过程中空间窗口的大小（记为ws且ws=2×hs+1）,文献[17]提出在不考虑各向异性的前提下,采用平均局部方差来估计最佳空间分割参数选择的大小。然而,自然界地表结构和格局错综复杂,地物空间分布在很多情况下存在各向异性。因此,本文考虑到地物分布的实际情况,将空间尺度分割参数的估计分为各向异性和不考虑各向异性2种情况。
3.1.1 不考虑地物空间分布各向异性
当地物空间分布呈现杂乱或随机性的特点时,依据文献[17]的思想,采用不考虑各向异性的平均局部方差法进行空间尺度分割参数估计。局部方差（Local Variance,LV）最早由Woodcock和Strahler在1987年提出,用于揭示遥感影像的空间结构。其通过利用一个n像元×n像元的移动窗来计算窗口内的标准差的均值（即局部方差）,在全局影像上求平均,描述方差随像元尺寸变化而变化的情况,最后形成平均局部方差曲线图,用于刻画遥感影像空间分辨率与地物尺寸之间的相互关系。本文提出采用平均局部方差方法进行空间尺度分割参数估计。实际上,某个像元位置的局部方差的计算与考虑了不同方向的半方差计算相似,因而采用平均局部方差来估计最佳空间分割参数是合理的。
如果用平均局部方差随计算窗口大小变化而产生的平均局部方差（Average Local Variance,ALV）图替代随计算间隔变化的变异函数图（Semivariogram）,与文献[18]的思想一致,平均局部方差曲线的变程对应的窗口尺寸ws所对应的hs为最佳空间尺度分割参数,这里关键问题是确定平均局部方差图的变程,其中hs=(ws-1)/2。通常函数拟合是求取变异函数变程的主要途径。然而,在很多实际应用中,空间统计特征联合分布的类型常常是未知的,造成数学函数拟合方法求取变程难于实现。此外,由于计算间隔比较小时变异函数的值对变程的影响要大于计算间隔比较大时,故本文采用简化的方法求取ALvariogram的变程。这里引入2个测度指标来辅助求取合适的hs。
ROC - ALV i = AL V i - AL V i - 1 AL V i - 1 （1）
SCROC - ALV i = ROC - ALV i - 1 - ROC - ALV i （2）
式中：ROC-ALV是平均局部方差随计算窗口尺寸变化的一阶变化率,[ROC-ALV]i是计算间隔大小为hsi时的ALV,其取值范围为[0,1]; SCROC - AL V i 是[ROC-ALV]i的变化,是其二阶变化率,其取值范围为为[0,1]。一般 [ SCROC - ALV ] i 都是很小的小数,根据经验,ROC-ALV和SCROC-ALV的阈值分别设为0.01和0.001,即随着计算间隔hs增大,第一次出现[ROC-ALV]i小于0.01且[SCROC-ALV]i小于0.001时的hs为待确定的合适的空间尺度分割参数。
3.1.2 考虑地物空间分布各向异性
当地物空间分布呈现方向规律性或各向异性时,采用考虑方向的半方差（Semivariance,SV）方法进行空间尺度分割参数估计,即分别在水平和垂直方向上,依据不同的采样计算间隔,计算影像在不同方向上的半方差,并利用半方差随计算间隔变化的变异函数曲线的变程来辅助估计空间尺度分割参数。同样,出于方法简化和实用性的考虑,本文提出采用综合半方差的变差来决定变程。某计算间隔hsi对应的综合半方差变差计算公式如式（3）、（4）所示。
Δ γ s ( h ) i = γ s ( h ) i - γ s ( h ) i = 1 （3）
Δ γ s ( h ) i = [ γ h ( h ) i + γ v ( h ) i ] 2 （4）
式中： Δ γ s ( h ) i 表示计算间隔hsi对应的综合半方差变差; γ s ( h ) i 表示计算间隔hsi对应的综合半方差,等于计算间隔hsi对应的水平方向半方差 γ h ( h ) i 与计算间隔hsi对应的垂直半方差 γ h ( h ) i 的平均值。综合半方差的平稳性较弱,取综合半方差变差 Δ γ s ( h ) i 第一次出现负值时对应的计算间隔为合适的空间尺度分割参数hs。

3.2 基于局部方差直方图统计的属性尺度分割参数估计方法

属性分割参数的估计常常要结合邻域的大小引入先验知识,因此很难直接进行属性分割参数估计。然而,只要合适空间尺度分割参数能确定,在样本量足够多的情况下,可在此基础上分析局部方差的潜在分布模式,进行属性分割参数的估计。在不考虑计算效率的情况下,本文基于合适的属性尺度参数对应局部方差出现频率最多且这个合适的属性尺度参数不能过大（因为过大的属性参数常常会导致过分割）的选择原则,提出在最佳空间属性分割参数基础上,利用原始影像局部方差图像（即当计算窗口大小ws =2×hs+1时,由原始影像逐像元计算局部方差而得到的逐像元局部方差所构成的图像）的直方图的第一个峰值来辅助进行属性尺度分割参数估计的方法,其方法流程如图2所示。
Fig. 2 Workflow of the optimal bandwidth selection

图2 合适的属性分割参数估计流程图

在这个流程中,LVxy表示原始图像的在计算窗口大小为ws时的局部方差图像,d为原始图像的位深度。因为局部方差近似等于像元与其邻域差异平方和的均值,局部方差直方图统计的最小统计间隔为4,以此估计出的合适的尺度分割参数（即第一个峰值点局部方差的平方根）则大于等于2。如果影像的辐射分辨率非常高（如d=16）,则局部方差直方图统计的最小间隔可以设置成一个相对较大的数。此外,为了避免伪峰值的问题,在确定合适属性尺度分割参数之前,有必要利用曲线拟合法或内插法等进行直方图曲线平滑工作。

3.3 基于空间尺度分割参数的合并阈值参数估计

合并阈值参数M的实质是有意义的分割斑块大小或有意义斑块内的像元数目。如上所述,局部方差计算窗口的大小（或合适空间分割参数的大小）能指示空间目标的大小,因此文献[17]利用ALvariogram进行合并阈值参数M取值的粗略估计,但是该方法假设的前提是地物属性空间分布的各向同性,而通常地物属性的空间分布体现为各向异性,因此合并阈值参数M的估计需要引入以下原则和先验知识假设。估计M的一个基本原则是M的取值既不能太大也不能太小。首先,为了保证有意义的小目标不被合并到邻域斑块,M的取值不能太大;同时,为了保证分割后的斑块不能太破碎,M的取值也不能太小,那样会导致分割斑块之间的异质性较低而影响最终OBIA分析的可分性。因此,结合图3所示合并阈值参数估计示意图,以INT[ ]表示取整函数,引入如下假设和规则：
（1）当不考虑地物空间分布各向异性的情况下,M的估计采用平均局部方差方法确定的 h s 来估计。如图3(a)所示,当目标的形状比较规则或者影像覆盖的主要目标类型为人工建筑物时,采用式(5)进行M的估计;当目标的形状非规则,采用式(6)进行M的估计。
Fig. 3 Sketch map of computing the merging threshold

图3 所示合并阈值参数估计示意图

注：rh为影像水平方向半方差函数的变程,rv影像垂直方向半方差函数的变程

M = INT [ ( h s 2 ) / 2 ] （5）
M = INT [ ( h s 2 ) / 4 ] （6）
（2）考虑地物空间分布各向异性的情况下,M的估计采用水平和垂直方向的半方差进行计算。如图3(b)所示,当目标的形状比较规则时,采用式(7)进行M的估计;如图3(c)所示,当目标的形状非规则,采用式(8)进行M的估计。
M = INT [ ( r h × r v ) / 2 ] （7）
M = INT [ ( r h × r v ) / 4 ] （8）
（3）如果不引入任何先验知识而且也不考虑目标性状的破碎性,M的计算公式如式（9）所示。
M = INT [ ( r h × r v ) / 4 ] （9）

4 实验与分析

如图4所示,本实验采用4幅大小均为800像元×800像元高空间分辨率影像作为实验数据。building_1为覆盖建筑区的IKONOS全色影像,空间分辨率1 m;building_2为覆盖建筑区的航空全色影像,空间分辨率1 m;farmland_1和farmland_2为覆盖农田区的IKONOS全色影像和Quickbird全色影像,空间分辨率分别是1 m 和0.6 m。为了进行方法对比,数据building_2和farmland_2采用了和文献[17]相同的实验数据。
Fig. 4 Experimental panchromatic high spatial resolution images

图4 高空间分辨率全色实验影像

4.1 基于谱空间统计的高分辨率影像分割尺度参数估计

依据上文提出的方法并根据先验知识,building_1和building_2的空间尺度参数估计不考虑各向异性,采用本文提出的平均局部方差方法,其ALV和SCROC-ALV的计算结果分别如图5(a)和5(b)所示,估计出building_1和building_2的适合空间尺度参数分别为19和15。farmland_1和farmland_2的空间尺度参数估计考虑各向异性,采用本文提出的半方差方法,其半方差及综合半方差变差计算结果分别如图6(a)和6(b)所示,估计出farmland_1和farmland_2的适合空间尺度参数分别为18和22（文献[17]对farmland_2影像数据采用局部方差方法估计出的空间尺度参数是20,说明2种方的估计结果存在一些差别）。 基于合适空间尺度分割参数的结果,绘制合适空间尺度参数的LV图像及其直方图（图7）,根据LV直方图确定出各实验数据相对适合的属性分割参数分别为6、8、5和5。结合图6(a)的水平和垂直半方差计算结果,估计出各实验数据相对适合的合并阈值参数分别为181、113、162和242。
Fig. 5 ALvariogram and SCROC-ALV of building_1 and building_2

图5 建筑区平均局部方差及变化率计算结果图

Fig. 6 Semivariogram and the change of synthetic semivariance of farmland_1 and farmland_2

图6 农田区半方差及综合半方差变差计算结果图

Fig. 7 Images and histograms of LV with window size of hs for different features

图7 LV影像及直方图（窗口大小为hs估计参数）

4.2 实验验证和分析

以均值漂移分割算法为例,采用分割后评价方法对本文提出的分割尺度参数估计方法的有效性进行了验证。均值漂移分割算法的基本原理详见文献[19]。综合评价模型采用的指标包括分割斑块内部的均质性（记为F(U)）和分割斑块间的异质性（记为F(V)）,这2个指标的计算及综合评价（综合评价分值记为Fs）计算的原理和公式,详见文献[20]和[18],综合评价时F(U)和F(V)的权重按照文献[18]分别取0.4和0.6。
验证hs和hr的有效性时,为了降低合并阈值参数M对分割结果的影响,M统一取10。此外,由于在面向对象影像分类中,F(U)和F(V)都不能过低,因此,合适的分割尺度参数应该满足2个要求：(1)估计出的合适尺度分割参数对应的Fs值应该在分割评价曲线（综合评价分值随尺度参数变化的曲线）的峰值区间,这里的峰值区间指Fs在整个计算结果中处于高位且F(U)和F(V)均不小于0.3的参数取值区间;（2）估计出的合适尺度分割参数对应的Fs值应尽量接近峰值点。
4.2.1 基于固定hr和M的空间尺度分割参数的验证
系列尺度参数取值分别为：hs∈[3,30],步长间隔为3。为了便于比较,hr统一使用估计结果值,M统一取为10。系列尺度分割评价结果如图8所示。
Fig. 8 Changes of segmentation evaluations with respect to different hs values

图8 空间尺度参数hs变化时的分割评价结果

根据图8的分割评价曲线走势,结合本文方法的尺度参数估计结果,得到表1的结果对比。表1表明尽管本文估计得到的合适空间尺度参数hs不一定是绝对的最优值或峰值点,但其基本上都在分割评价的峰值区间内,证明了本文提出的基于谱空间统计的空间尺度参数估计方法的有效性。
Tab. 1 Peak ranges and peak point in the verifications of hs

表1 hs验证实验中的分割评价峰值范围和峰值点

影像 building_1 building_2 farmland_1 farmland_2
峰值范围 (hs) 18~24 15~21 18~24 18~24
峰值点 (hs) 24 21 24 21
本文方法的估计合适参数 19 15 18 22
4.2.2 基于固定hs和M的属性尺度分割参数的验证
系列尺度参数取值分别为：hr∈[1,10],步长间隔为1。为了便于比较,hs统一使用了估计结果值,M统一取为10。系列尺度分割评价结果如图9所示。
Fig. 9 Changes of segmentation evaluations with respect to different hr values

图9 属性尺度参数hr变化时的分割评价结果

根据图9的分割评价曲线走势,结合本文方法的尺度参数估计结果,得到表2的结果对比。表2表明,除了building_2以外,其他hr的估计结果都在分割评价的分值区间,可证明本文提出的基于谱空间统计的属性尺度参数能保证得到较好的分割效果。
Tab. 2 Peak ranges and peak point in the verifications of hr

表2 hr验证实验中的分割评价峰值范围和峰值点

影像 building_1 building_2 farmland_1 farmland_2
峰值范围 (hr) 6~8 3~6 1~2,5~6 5,7~9
峰值点 (hr) 7 6 1, 2, 5 7
本文方法的估计合适参数 6 8 5 5
4.2.3 基于固定hs和hr的阈值合并参数的验证
系列尺度参数取值分别为：M∈[50,500],步长间隔为50,hs和hr使用统一的估计值。系列尺度分割评价结果如图10所示。
Fig. 10 Changes of segmentation evaluations with respect to different M values

图10 合并阈值参数M变化时的分割评价结果

根据图10的分割评价曲线走势,结合本文方法的尺度参数估计结果,得到表3的对比结果。表3表明,根据本文方法估计出的合适的合并阈值参数不仅在峰值区间内,也非常接近于峰值点,该结果证明了本文提出的基于地物几何形状先验假设的合并阈值参数估计方法可行、有效。
Tab. 3 Peak ranges and peak point in the verifications of M

表3 M验证实验中的分割评价峰值范围和峰值点

影像 building_1 building_2 farmland_1 farmland_2
峰值范围 (M) 150~200 100~200 150~200 100~200
峰值点 (M) 200 150 150 250
本文方法的估计合适参数 181 113 162 242

5 结论

分割尺度参数的选择和预估计对于高分辨率的遥感应用至关重要,本文在文献[17]和[18]的研究基础上,首先从理论上将面向对象影像分析中的多尺度分割的尺度参数概括为空间尺度分割参数、属性尺度分割参数和合并阈值参数;接着,进一步细化了基于影像光谱空间统计的分割尺度参数估计的理论基础;最后,针对影像的不同特征,将基于影像光谱空间统计进行面向对象影像分割的尺度参数估计分为考虑地物空间分布各向异性和不考虑地物空间分布各向异性2种情况,并分别提出了具体的分割尺度参数估计策略和方法。实验结果表明,尽管本文方法估计出的合适空间尺度参数不一定是应用上绝对的最优值,但其基本上都在分割评价的峰值区间内,证明了本文提出的基于谱空间统计的空间尺度参数估计方法具有可行性和有效性。
本文以均值漂移分割为例进行了实验验证,取得较好效果。但需要说明的是,本文提出的基于影像光谱空间统计进行面向对象影像分割的尺度参数估计方法实质上体现了一种尺度估计的思路,是不依赖于具体分割算法的。理论上,本文提出的方法可全部或部分地应用于绝大部分的多尺度分割算法的尺度参数估计问题。此外,从遥感影像分割的尺度优选问题研究进展来看,除了大量尺度序列分割后评价的方法,目前还没有其他途径能做到分割前的尺度参数的估计和优选,而谱空间统计方法理论上具有合理性、方法上具有可行性、应用上具有有效性。
作为一种探索性研究,本文的技术路线仍存在不足：综合评价时斑块内部的均质性和分割斑块间的异质性的权重按照文献[18]分别取0.4和0.6的客观性和合理性还有待进一步研究,这2个指标的权重分配会对评价结果和尺度参数选择有一定的影响;在面向对象影像分析中,斑块内部的均质性和分割斑块间的异质性通常是一对互为矛盾的指标,如何定量地研究二者的关系及其对面向对象信息提取精度的影响,是今后研究的一个重要内容,该研究也将一定程度上促进面向对象影像分割尺度参数选择和尺度规律认知。

The authors have declared that no competing interests exist.

References

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