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航空摄影测量中的立体模型重建
摘要本文描述的是现代航空摄影测量的操作问题和基本的技术需要。当立体模型重建时，利用航空摄影测量中的外方位元素决定摄影测量点的精度和在对应的模型点中的Y-视差分析。真正的航空摄影，在图像的比例，由1:2 500至1:6 0000，与DGPS/IMU的数据来源于各种地形，在中国由我们的POS-支持的大型区域网平差计划WuCAPS处理。实证结果证实来源于大型区域网平差的外方位元素的精度符合地形勘测规范的要求。然而，通过POS确定的外方位元素的精度不能满足地形勘测规范的要求。
关键词空中三角测量（AT）；GPS（全球定位系统）；POS（定位和定向系统）；立体模型重建；地面控制点（GCPs）；精度
导言
航空摄影测量是从空中影像获得关于地球表面的三维空间信息的科学和技术。摄影点的决定，其中通过使用图像找出地面对象，是依据识别物体的遥感。并且问题的关键是迅速和准确地确定图像的位置和行为上的即时影像。通过基于分布式地面控制点的空中三角测量满足这一目标。
随着空间定位技术的发展，遥感技术和计算机科学，以及空中三角测量的演变和发展走向没有地面控制点的数字化勘测。早在1950年，摄影科学家就开始研究如何利用各种辅助数据，以减少地面控制点的需要。然而，由于技术的局限性，方法没有变成现实。直到20世纪70年代，出现了美国的全球定位系统（GPS），在航空摄影过程中人们仅得到通过载波相位差分全球定位系统（DGPS）技术来确定曝光驻地的位置(即航摄照片的三个线性元素)，用于执行空中三角测量（简称GPS-支持AT）可以减少摄影对地面控制点的依赖，缩短测绘周期；并降低生产成本，在摄影测量的领域触发革命。然而，GPS-支持AT在空中摄影测量的操作是有利的，主要是在浩大和困难的区域，在中小型的比例尺，而不是带状区域和城市大比例尺测图。在20世纪90年代，人们开始探讨采用GPS/lNS集成系统(也称POS)获取照片的位置和姿态(即利用GPS获得曝光驻地的位置，由IMU获得图像姿态元素)，目的是照片的定向，最终目标是取代区域空中。三角
测量程序。
现代数字摄影测量学在4D产品(DEM，DOM，DLG，DRG)的自动化的生产和空间数据库的更新中将扮演一个重要角色。本文将介绍航空摄影测量学和相关的技术需要在当前的操作应用，特别是，摄影信息链的几何定位精度可从照片方向到立体模型重建获得，旨在探讨4D产品生产的可实行性。人民希望这项研究的研究结果可以在国土普查，地图测绘和基础地理信息采集方面为航空摄影测量的操作提供指导。
1 现代航空摄影测量的模式
现今，航空摄影测量主要有三种模式，即标准的航空摄影测量、GPS-支持航空摄影测量和POS-支持航空摄影测量。它们主要程序如图1所示。
从图1，我们可以了解到，区别这三种模式的方法主要是如何获取的航摄照片以及照片的方向。对于标准空中三角测量，它是通过区域空中三角测量的大量地面控制点获得模型定向点的坐标来完成图像的定向。对于GPS-支持AT，在航空照片获得的过程中，动态GPS定位是用来代替地面控制点以确定曝光中心的位置和获得该模型定向点的坐标，然后用于纠正图像的方向。对于POS-支持AT，图像和它们对应的方位元素(图像的六个外方位元素)都是已获取的，用于了解在曝光时刻几何反演摄影存储的空间位置和姿态。
2 相关技术要求
2.1 空中摄影
在现代航空摄影，为了提高获得的图像质量，除了新增飞行控制系统到空中摄影机以外(例如ASCOT，CCNS4，空中跟踪系统)，当采取GPS空中摄影和在照相机上安置POS系统进行DGPS/IMU空中摄影时，方法还包括牢固黏附与照相机的一台GPS接收器。根据空中摄影的不同的模式，我们可以制定一个负责计划如图2所示。
2.2 地面控制计划
在数字摄影测量工作站，空中三角测量进行了理论上的最严格的大型区域网平差，但为了获得照片最佳的传输点的坐标和方向的外方位元素，地面控制计划的设计应如图3所示，即不同模式的空中摄影。
2.3 数字映射
从理论上说，在得到准确的内外方位元素的图像之后，可衡量的立体模型可利用模型重建恢复，其中我们可以做地形的测绘以及物体的自动运行。然而，目
→立体像对的相对定向→单一前的四维产品的生产工艺是：单张照片的内定向
→立体模型的测绘。该方法的模型只有通过POS-支持的航空摄模型的绝对定向
影测量直接地理参考恢复。
3 实验和分析
航摄定位有两种方法。其中之一被称作区域空中三角测量，关于图像点的坐标，地面控制点的坐标和（或）图像的外方位元素加权观测值，并结合大型区域网平差来解决图像定向参数和目标点的空间坐标，来作为方向控制点的立体模型绘图和做高度精确的几何定位的应用。为不同尺度和地形类型的航空摄影测量，航摄照片办公室操作的地形图规格定义了各自空中三角测量方法，地面控制计划，以及传输点精度的具体标准。这种方法已被建立并得到了广泛的应用。另一种是所谓的直接地理参考，假定高精确的图像外方位元素是可以得到的，在立体像对中通过使用图像坐标系统的同名像点的坐标，利用空间交会计算出对应的目
标点物体的空间坐标。这种方法直接地确定对象的位置，因此4D产品可以被生产。然后本文将主要讨论当利用各种方式获得图像的外方位元素时，如何定位精度可以完成立体模型的Y视差。
3.1 数据
如表1所示，来自不同领域的4个组的实际图像的实验被实施。所有的底片被扫描，其分辨率为21米，为了得到连接点，POS-支持的大型区域网平差软件WuCAPS被用于图像的测试1，测试2和测试4，自制的JX- 4数字摄影测量工作站用于图像的测试3。根据相对定向的结果与由WuCAPS去除严重错误的功能，地面控制点全部在立体镜方式下手动地被测量，并且所有图像点的统计精度(RMS)均优于±6.0米。在那以后，我们使用Applanix POS/AV系统的后处理软件POSPac做测试场校准和DGPS和IMU数据的整合，然后通过应用坐标系变换和系统误差改正每个图像的六个外方位元素，这是由POS系统规定的，可以获得。
表1 实验计划中的图像参数
测试1 测试2 测试3 测试4 时间2004.11 2005.1 2005.9 2005.10
飞机Yun-12 Yun-12 Yun-8 Aviation-Ⅱ照相机Leica RC-30 Leica RC-30 Leica RC-30 Leica RC-30 班次控制系统航空轨道航空轨道CCNS 4 CCNS 4 POS系统POS AV 510 POS AV 510 POS AV 510 POS AV 510 GPS接收机Astech Trimble 5 700 Trimble 5 700 Trimble 5 700 底片Kodak 2 444 Kodak 2 044 Kodak 2 402 Kodak 2 402 距离原则/mm 153.84 303.64 154.06 153.53
框架/cm×cm 23×23 23×23 23×23 23×23 相片比例1:2 500 1:3 000 1:32 000 1:60 000
前部重叠度/% 61 63 64 64
边缘重叠度/% 32 33 33 30
航带数量9 10 9 4
控制带 2 2 2 0
相片255 377 244 48
GCPs 73 160 34 29
密集点 3 631 5 442 2 951 712
区域/km×km 4×5 5×8 47×52 40×57
最大地带波动
/m
38.6
（平坦地区）
181.6
（山地）
729.3
（高山地区）
109.3
（低地）
GPS更新比率/s 2 0.5 1 1
GPS时间设定
/min
10 10 5 5
静态GPS/min 5 5 5 5
人工GPS/m 0.303，0.110，0.303，-0.110，-2.015，-0.030， 2.034，-0.520，
-2.029 -2.002 3.102 1.320
人工IMU/m 0.000，0.200，
-0.559 0.000，0.200，
-0.710
0.000，-0.201，
0.427
-0.006，-0.202，
0.430
3.2 外方位元素的性能
为了得到通过不同的方法分析外方位元素的性能，标准AT与边缘密集地面控制点和GPS-支持AT与四组完全地面控制点在基础领域被首先执行，可以获得每幅图像的六个外方位元素，并且它们的理论精度可以估计。然后我们假设标准的结果作为“真理”并估计通过POS提供的外方位元素的性能。结果如表2所示。
从表1我们看到的图像的测试1，测试2可用于生产规模为1:500?1:2 000的四维产品，图像的测试4可用于生产规模为1:5000?1:10 000的四维产品。在空中摄影测量办公运行的地形图规格原则中，测试1，测试2，测试3和测试4分别属于平坦的土地，山地，高山区的土地和低地。如表2的结果，一些结论可归纳如下。
表2 不同方法的外方位元素精度的确定
图像方
法
σ
/
m
μ
GCPs 控制 Pts 控制pts残差的RMS EO的理论精度
水
平
垂
直
水
平
垂
直
X Y XY Z m
X
s
/m
Y
s
/m
Z
s
/)
(/''
?)(/''
ω)
(/''
k
测试1 Std
.
5.7 23 39 49 33 0.09 0.06 0.1
04
0.0
79
0.0
28
0.0
30
0.0
19
12.1 13.1 4.4
GPS 7.0 4 4 67 67 0.10 0.09 0.1
37
0.1
05
0.0
30
0.0
34
0.0
29
9.2 11.9 5.9
POS 0.1
23
0.1
12
0.0
93
62.8 40.7 32.
4
测试2 Std
.
4.9 39 69 116 86 0.06 0.06 0.0
87
0.1
28
0.0
97
0.1
04
0.0
39
22.6 24.4 4.1 GPS 6.7 4 4 151 151 0.10 0.10 0.1
43
0.1
53
0.0
80
0.1
38
0.0
68
21.3 25.8 12.
1 POS 0.2
24
0.2
94
0.1
65
53.2 43.9 45.
1
测试3 GPS 7.6 4 4 30 30 0.74 0.76 1.0
61
0.5
03
0.2
03
0.2
40
0.2
32
9.7 10.9 9.9 POS 1.0
64
1.4
14
1.7
81
35.9 31.8 31.
9
测试4 Std
.
7.6 15 19 10 14 1.30 1.29 1.8
30
1.4
54
0.9
20
0.9
46
0.6
75
18.8 18.5 6.9 GPS 7.0 4 4 25 25 1.55 2.33 2.7
98
1.2
75
0.8
78
0.9
88
0.6
58
17.9 19.6 6.5 POS 1.3 2.8 2.861.8 57.1 67.
24 49 17 3
注：1）Std.，GPS 和POS 取于通过边缘密集GCPs 标准的方法获得的外方位元
素，各自的GPS -支持与四种正式的基础GCPs 和POS 系统（与下表相同）。 2）因为GCPs 的分配不满足标准的要求，我们不能计算出边缘密集GCPs 大
型区域网平差（与下表相同）。
3）控制点残差的RMS 计算来源于坐标平差和n 个控制点的地面测量坐标之
间的误差),,(Z Y X i i =?，即n i
i /2
∑?
=
μ；2
2,Y
X Y X μμμ+=。 4）EO 的理论精度从根据误差的增值规律计算的未知量的分散矩阵获得，
),,,,,(0k Z Y X i Q m s s s ii i ω?σ==。
1)对于测试1，密集点的水平精度和垂直精度优于0.15米，完全满足精度要求：平面精度0.25米和垂直精度0.30米的1:500地形图规格的空中摄影测量办公操作平坦土地。
2) 对于测试2，密集点的水平精度优于0.15米，垂直精度优于0.20米，完全满足精度要求：平面精度0.35米和垂直精度0.40米1:500地形图规格的空中摄影测量办公操作的山地。
3) 对于测试3，密集点的水平精度优于1.1米，垂直精度优于1.0米，完全满足精度要求:平面精度2.5米和垂直精度2.0米的1:5000地形图规格的空中摄影测量办公操作的山地。
4) 对于测试4，密集点的水平精度优于3.0米，垂直精度优于1.5米,完全满足精度要求：平面精度17.5米和垂直精度3.0米的1:50000地形图规格的空中摄影测量办公操作的高山区的土地。
从表2可以看出，在图像的不同土地类型不同规模下，从标准 AT 和GPS -支持AT 获得的致密点均满意的四维产品的需求，而且获得外方位元素的精度的这两种方法通常是相似的。相片的比例越大，我们获得的相片的线性元素的精度就越高；但是相片的角元素的精度与相片比例无关，而与相机的焦距有关，因此焦距越短，相片的角元素的精度越高。此外，通过比较表2的数据，可以发现，通过POS 系统提供的外方位元素的性能不如解析空中三角测量，也明显低于POS 的理论精度
m
m m m z y x 1.0=== ，81'
'==ω?m m ，
63'
'=k m 。
3.3 直接地理参考的精度
目前，四维产品普遍使用通过空中三角测量获得的致密点作为模型定向点取代直接从图像的外方位元素重建的立体模型。因此，外方位元素的精度要求没有定义在当前的规范。一般来说，只要我们可以获得足够的致密点满足每个模型的误差极限，通过执行绝对取向，可以重建一个可测量的模型。然后我们可以获取
令人满意空间信息。通过使用不同的外方位元素，我们分析了直接地理参考的精度，首先使用前方交会的计算方法，通过使用在上述部分得到的不同精度的六个外方位元素，计算地面坐标，并且通过比较地面坐标与多数地面控制点的地面坐标，计算目标点地面坐标的精度(详细参见表3)。
表3 直接地理参考的精度
图像获得
EQ方
法
控制
点数
量
最大差值/m 最小差值/m RMS/m
X Y XY 高
程
X Y XY 高
程
X Y XY 高
程
测试1 Std. 188 0.18 -0.25 0.2
95
-0.
276
0.00 0.00 0.0
09
0.0
00
0.08 0.07 0.1
07
0.0
81 GPS 196 -0.28 -0.28 0.3
34
0.2
54
0.00 0.00 0.0
14
-0.
001
0.13 0.08 0.1
56
0.1
00 POS 196 -0.31 0.39 0.3
90
0.3
10
0.00 0.01 0.0
55
0.0
00
0.11 0.18 0.2
10
0.1
27
测试2 Std. 412 -0.22 -0.14 0.2
22
-0.
317
0.00 0.00 0.0
07
-0.
001
0.06 0.05 0.0
83
0.1
21 GPS 419 -0.29 0.21 0.3
22
-0.
428
0.00 0.00 0.0
06
0.0
00
0.11 0.06 0.1
31
0.1
66 POS 419 0.26 -0.49 0.4
97
0.4
87
0.00 0.00 0.0
03
0.0
01
0.09 0.24 0.2
57
0.1
82
测试3 GPS 68 2.34 1.92 2.5
40
-2.
660
0.02 0.02 0.1
46
-0.
030
1.00 0.83 1.2
99
1.3
25 POS 64 -2.95 -2.43 3.3
99
2.3
30
-0.0
3
0.04 0.2
98
0.0
82
1.20 0.78 1.4
35
1.0
51
测试4 Std. 46 -3.63 3.01 3.8
84
4.3
74
-0.0
3
0.05 0.1
74
0.0
28
1.40 1.33 1.9
30
1.8
80 GPS 46 4.43 4.75 4.8
32
4.3
59
0.00 0.02 0.1
08
0.0
33
1.45 1.50
2.2
15
1.9
12 POS 46 5.29 4.47 5.4
47
5.9
47
-0.1
4
-0.0
2
0.5
84
-0.
058
2.55 1.79
3.1
15
3.7
11 从表3，这样的结论可归纳如下：
1) 对于测试1，直接地理参考的水平精度优于0.25米，垂直精度优于0.15
米，这也符合要求指明的1:500的平坦的土地的地形测绘标准：平面0.3米，海拔0.2米。
2) 对于测试2，直接地理参考的水平精度优于0.3米，垂直精度优于0.2米，这也符合要求指明的1:500山区地形测绘标准：平面0.4米，海拔0.5米。
3) 对于测试3，直接地理参考的水平精度和垂直精度均优于1.5米，这也符合要求指明的1:5000地形测绘标准：平面3.75米，海拔2.5米。
4) 对于测试4，直接地理参考的水平精度优于3.15米，垂直精度优于3.75米，这也符合要求指明的1:50000的丘陵地形测绘标准：平面25.0米，海拔4.0
米。
从表3可以了解到，当直接地理参考应用到图像的不同土地类型和规模时，空中三角测量的方法优于利用POS获得的外方位元素。这个结果表明将通过空中三角测量的方法取得的外方位元素运用到直接地理参考中可以得到满意的地形测量的精度标准。因此可以推断出，只要空中三角测量符合精度标准，来源于此的外方位元素的内容绝对可以用于生产四维产品。
3.4 重建立体模型中的Y-视差
在摄影测量工作中，我们应该注意的另一问题是利用外方位元素直接重建地形测绘的立体模型的可行性，即模型点的Y-视差不超过20米。因此描述不同地形类型的三个立体像对利用得到的外方位元素从四个重建立体模型测试中分别获得，表4是Y-视差在立体模型中的对应点。
从表4可以看出，当使用空中三角测量的方法得到的外方位元素重建立体模型时，无论何种类型的地形和应用多大的比例，该模型点的最大Y-视差位于一个像素，精度的最大Y-视差低于半个像素，每个模型的能满足精度要求的地形测量垂直视差的有效值不应该超过20米。但是，当我们使用POS提供的外方位元素时，每个模型点的垂直视差都偏大，较小比例的相片，较大的垂直视差，完全不符合要求。
表4 利用外方位元素的立体模型重构的Y-视差
图像模型Pts 最大高
程不同
/m
Y-视差/m
最大值最小值RMS
规定GPS POS 规定GPS POS 规定GPS POS
测试1 282/281 23 0.57 14.2 16.2 17.7 0.3 0.3 0.0 8.0 8.8 12.9 274/273 32 17.87 11.2 14.5 28.6 0.2 0.3 0.2 5.8 6.7 12.9 343/344 27 36.38 13.1 15.7 38.1 0.2 1.3 0.3 6.8 7.3 18.0
测试2
14/13 26 26.41 15.0 11.7 31.2 0.1 0.1 1.6 5.9 5.7 18.1 29/28 47 68.27 10.9 17.8 19.6 0.0 0.2 0.2 4.0 7.2 10.3 275/274 34 105.74 14.3 16.1 24.5 0.3 0.7 0.8 6.4 10.0 12.8
测试3 1017/1018 31 26.00 18.7 44.9 1.0 4.8 10.0 22.9 1013/1014 22 91.60 17.5 35.6 0.2 2.5 7.9 17.8 234/233 54 192.90 18.0 36.2 0.5 0.9 8.2 12.9 238/237 23 375. 76 17.0 49.2 0.1 0.0 8.1 17.7
测试4
1076/1075 32 7.48 18.7 19.1 36.8 0.4 1.8 0.6 12.3 12.9 21.3 1115/1114 28 17.45 14.8 17.2 39.0 0.2 0.2 1.3 6.9 7.3 22.0 1105/1104 28 109.55 11.6 12.9 25.2 0.1 0.6 1.0 6.5 6.3 14.0
4 结论
从实验可以看出，如果从空中三角测量获得的外方位元素符合精度标准，它
们可以直接用于图像的定向和立体模型重建。然而，由于存在POS外方位元素
的系统误差，当前很难符合摄影测量的标准，特别是当提取三维空间信息时。发现，在数字摄影测量时期，工作可以由计算机自动地完成，对地面控制点的信任逐渐减少，从而简化了摄影测量的操作。从总体上看，标准，是获取图像定向参数最确定的和广泛使用的方法，仍然是摄影测量的主体；GPS-支持AT是易于操作和低成本的方法，相应的标准已经被起草：POS直接地理参考在摄影测量中是一个重要的尖端技术。基本空间信息采集应利用这一点，设计良好的计划获得最大的经济利益。我们建议，对于交通状况良好的平坦地区的大比例测图，应该主要采用标准空中三角测量；对于困难区域，非指明的地区或领域无法访问，没有地面控制点的GPS-支持AT可以为国民生产的基础地图获取基本的空间信息；POS摄影测量可用于在小区域生产正射影像和更新四维产品。然而，POS在大比例的城市测图，LIDAR，数字航空摄影测量的领域中是有前景的。我们应该通过开展大规模的实验推动POS系统的整合技术及其传感器，从而为经济和迅速聚集的地理空间信息提供技术支持。
鸣谢
数据收集的实验由遥感应用中国科学院，中非通用航空有限公司，辽宁经纬测绘科技有限公司，大连市测绘设计研究院，四维航空遥感有限公司，西安全国测绘航空遥感有限公司等支持。对这些支持表示感谢。作者希望对参与部分实验的付建宏，谢筹，季顺平和杨明表现出他热诚的谢意。作者要感谢杨明和张井雄教授为他们润饰英语。
参考文献
[1] 李徳仁，单杰（1989）导航数据大型区域网平差的质量分析[J]。工程摄影测量与遥感，55（12）：1743-1746
[2] Ackermann F（1994) Practical experience with GPS-supported aerial triangulation [J]．Photogrammetric Record, 16(84):861-874
[3] 袁修孝（2001）GPS-支持空中三角测量的原理及应用[M]。北京：测绘出版社（中文）
[4] Cannon M E, Sun H (1996) Experimental assessment of a non-dedicate GPS receiver system for airborne attitude determination [J]．ISPRS Journal of Photogrammetry & Remote Sensing, 51(2): 99-108
[5] Cramer M, Stallmann D, Haala N (2000) Direct georeferencing using GPS/Inertial exterior orientations for photogrammetric applications [C]. International Archives of Photogrammetry and Remote Sensing, 33(B3):198-205
[6] Gruen A, Baer S (2001）Aerial mobile mapping-georeferencing without GPS/INS [C]．The 3rd Intemational Symposium on Mobile Mapping Technology,
[7] Jacobsen K (2002) Calibration aspects in direct georeferencing of frame imagery [C]．Pecora 15/Land Satellite Information, ISPRS Commission I/IV
[8] Mostafa M R (2002) Camera/IMU boresight calibration:new advances and performance analysis [C].The ASPRS Annual Meeting, Washington D.C.
[9] 袁修孝，谢筹，王书亘(2004)通过与固定图像组合的大型区域网平差进行图像定向[J]。摄影测量与遥感的国际文件，35(B2)：34-38
[10]Applanix产品概述[OL]。https://www.doczj.com/doc/2c15214516.html,/products/ pospac_airborne_index.php
[11] 国家统计局的标准（1998）1:500，1:1000，1:2000空中摄影测量办公操作的地形图规格[S]。北京：中国标准报(中文)
[12] 国家统计局技术监督（1993）1:5000，1:10000航摄相片办公操作的地形图规格[S]。北京：中国标准报(中文)
[13] 国家统计局技术监督（1991）1：25000，1:50000，1:100 000航摄相片办公操作的地形图规格[S]。北京：中国标准报(中文)
[14] 王之卓（1990）摄影测量原理（遥感）[M]。武汉：武汉测绘学院学报；北京：测绘出版社
[15] 袁修孝，付建宏，阎佩利等(2007)通过使用从定位和定向系统获得的外方位元素分析立体模型重建的垂直视差[J]。武汉大学测绘和信息科学，32（6）：489-493
On Stereo Model Reconstitution in Aerial Photogrammetry
YUAN Xiuxiao
Abstract This paper describes the operational issues and basic technical requirements of modern aerial photogrammetry.The accuracy of photogrammetric point determination and the y-parallax at corresponding model points is analyzed when stereo models are reconstituted by using the exterior orientation elements of aerial images. Real aerial photographs, at image scales from 1:2 500 to 1:6 0000，with DGPS/IMU data taken from various topographies in China were processed by our POS-supported bundle block adjustment program WuCAPS. The empirical results verified that the accuracy of the exterior orientation elements from bundle block adjustment meets the requirements of the specifications of topographic mapping.However, the accuracy of the exterior orientation elements determined by POS fails to meet the requirements of the specifications of topographic mapping. Keywords aerial triangulation (AT); GPS (global positioning system）；POS （position and orientation system）；stereo model reconstitution；ground control points (GCPs)；accuracy
Introduction
Aerial photogrammetry is the science and technology for obtaining 3-dimensional spatial information about the Earth's surface from aerial images．Photogrammetric point determination, which locates ground objects by using images, is the basis for object recognition in remote sensing. And the key point of this issue is the rapid and accurate determination of an image's position and behavior at the instant of imaging. This goal was met by aerial triangulation based on well distributed GCPs.
With the development of spatial positioning technology, remote sensing technology, and computer science, aerial triangulation evolved and progressed towards digital mapping without GCPs．In the early 1950's, photogrammetric scientists began studying how to utilize various auxiliary data to reduce the number of GCPs required. However, the methods haven't become practical due to technological
limitations]1[．Until 1970's, with the emergence of American Global Positioning System (GPS), people got to adopt carrier phase differential GPS（DGPS）technology to determine an exposure station's positions(that is three linear elements of aerial photos) during aerial photographic process, which was used to perform aerial
triangulation (called CJPS-supported AT for short) that can decrease photogrammetric reliance on GCPs, shorten the mapping cycle; and reduce production costs, triggering
the revolution in the field of photogrammetry]2[.Nevertheless, GPS-supported AT is advantageous for aerial photogrammetric operation primarily over vast and difficult areas, at small and medium mapping scales, not for strip-like zone and urban large-scale mapping]3[．In the 1990s,people started to investigate employing GPS/lNS integrated system (also called POS) to acquire a photo's position and attitude (i.e.，to obtain exposure station's position by GPS，and images’attitude elements by IMU), for the purpose of photo orientation, and the final goal is to replace block aero triangulation procedure]94[ ．
Modern digital photogrammetry will play an important role in automated productions of 4D products(DEM, DOM, DLQ DRG) and updating of spatial databases. This paper will introduce current operational applications of aerial photogrammetry and related technical requirements, in particular, geometric positioning accuracy obtainable in the photogrammetric information chain from photo orientation to stereo-model reconstitution, aiming to investigate their practicability for 4D products production. It is hoped that findings from this study will provide guidance for operational aerial photogrammetry in the context of national, land surveying, mapping, and fundamental geographic information acquisition.
1 Current patterns of the modern aerial photogrammetry
Nowadays, there are primarily three patterns for aerial photogrammetry, namely, standard aerial photogrammetry GPS-supported aerial photogrammetry and POS-supported aerial photogrammetry. Their main procedures are shown as Fig. l.
From Fig.l，we can learn that the main difference between these three patterns lies in the ways of aerial photo acquisition and photo orientation. For standard AT, it is through block aerotriangulation with a large number of GCPs to get a model
orientation points’ coordinates to complete image orientation. For GPS-supported AT, in aerial photo acquisition process,dynamic GPS positioning is used instead of GCPs to determine the positions of exposure center and meanwhile obtain the model's orientation points’coordinates, which are then used to rectify the image's orientation. For POS-supported AT, images and their corresponding orientation elements (six exterior orientation elements of images) are both acquired, in order to realize geometric inversion of photography by storing their spatial positions and attitude at the moment of exposure．
2 Related technologic requirements
2 .1 Aerial photography
In modern aerial photography, in order to improve the quality of obtained images, besides adding flight control systems to aerial camera (such as ASCOT,CCNS4, Aerial TRACKER system), the methods include sticking a GPS receiver with the camera firmly when adopting GPS aerial photography and mounting POS system on the camera in DGPS/IMU aerial photography. According to the different patterns of aerial photography, we can formulate an answerable plan as shown in Fig.2.
2.2 Ground control plan
In digital photogrammetry workstations, aerotriangulation is carried out by the most theoretically rigorous procedure of bundle block adjustment, but for the sake of obtaining the best pass points' coordinates and the exterior orientation elements of photos,ground control plan should be designed, as shown in Fig.3，for different patterns of aerial photogrammetry.
2.3 Digital mapping
Theoretically, after getting the accurate exterior orientation elements of images, measurable stereo models can be reconstructed using model restoration,by which we can do surveying and mapping of terrain and objects automatically. However, the current process of producing 4D product is：single photo interior orientation→relative orientation of stereo pair→single model absolute orientation→surveying and mapping on stereo models．The method of model restoration is only adopted in the direct georeferencing of POS-supported aerial photogrammetry.
3 Experiments and analysis
There are two ways of aerial photogrammetric positioning. One is called block aerotriangulation, regarding image points’coordinates, GCPs’coordinates and/or the exterior orientation elements of images as weighted observed values, and combined bun dle block adjustment is performed to solve the images’ orientation parameters and target points’spatial coordinates, so as to supply orientation control points for stereo model mapping and do highly accurate geometric positioning. For aerial photogrammetry of different scales and topographic types, topographic maps specifications for aerophotogrammetric office operation has defined respective aerotriangulation method, ground control plan, and also concrete standards for pass point accuracy. This method is established and widely used. The other is called direct georeferencing, under the supposition that highly accurate image elements of exterior orientation were available, space intersection is carried out to calculate corresponding object point's object space coordinates by using photo coordinate system's coordinates of conjugative image points in stereo pairs. This approach directly determines the object's position, so 4D products can be produced. Then the paper will mainly discuss how well the positioning accuracy can be achieved and the stereo model Y-parallax when using image exterior orientation elements obtained in various ways.
3.1 Data
Experiments were implemented on 4 groups of actual images from different areas as shown in Table 1.All negatives were scanned with a resolution of 21 m, and in order to get the tie points, POS-supported bundle block adjustment software WuCAPS was used for images of test 1，test 2 and test 4, and homemade JX-4 digital photogrammetry workstation was used for images of test 3．The GCPs are all measured manually in the stereoscopic mode, and the accuracy (RMS) of all image points is statistically better than 16.0 m according to the results of relative orientation modual with the function of gross error elimination by WuCAPS．After that, we use
Applanix POS/A V system's postprocess software POSPac
]
10[ to do test field
calibration and the integrated process of DGPS and IMU data, then by applying coordinate system transformation and system error rectification,six exterior orientation elements of each image,which were provided by the POS system, can be obtained.
3.2 Performance of exterior orientation elements
In order to analyze the performance of exterior orientation elements obtained by different methods,standard AT with dense GCPs on the border and GPS-supported AT with four full GCPs in corners were firstly implemented, the six exterior orientation elements of each image can be obtianed, and their theoretic accuracy can be estimated. Then we assumed the results of standard AT as the "truth" and estimated the performance of exterior orientation elements provided by POS ．The results are shown in Table 2．
From Table 1，we see that the images of test 1，test 2 can be used for producing 4D product at the scale of 1:500~1:2 000, and images of test 4 for that at the scale of 1:5000~1:10 000. In the principle of Topographic Maps Specifications for Aerophotogrammetric Office Operation
]
1311[ ,test 1，test 2, test 3，and test 4 belong to
flat land, mountain land, high mountain land, and lowland, respectively. From the
results in Table 2, some conclusions can be summed up as follows.
1）For test 1，densified points’horizontal accuracy and vertical accuracy are better than 0.15 meter, totally meeting the accuracy requirement: 0.25 meter in planimetry
and 0.30 meter in height]11[of 1:500 Topographic Maps Specifications for Aerophotogrammetric Office Operation for flat land.
2) For test 2, densified points’horizontal accuracy is better than0.15 meter and vertical accuracy better than 0.20 meter, totally meeting the accuracy requirement:
0.35 meter in planimetry and 0.40 meter in height]11[of 1:500 Topographic Maps Specifications for Aerophotogrammetric Office Operation for mountain land.
3) For test 3, densified points’horizontal accuracy is better than 1 ．1 meters and vertical accuracy better than 1.0 meter, totally meeting the accuracy requirement: 2.5
meters in planimetry and 2.0 meters in height]12[of 1:5 000 Topographic Maps Specifications for Aerophotogrammetric Office Operation for mountain land.
4) For test 4, densified points’horizontal accuracy is better than 3.0 meters and vertical accuracy better than 1.5 meters, totally meeting the accuracy requirement:
17.5 meters in planimetry and 3.0 meters in height]13[of 1:50000 Topographic Maps Specifications for Aerophotogrammetric Office Operation for high mountain land.
It can be seen from Table 2 that for the images of different land types at different scales, the densified points obtained from standard AT and GPS-support AT both satisfied the requirement of 4D product, and that the accuracy of exterior orientation
elements obtained by these two methods are generally similar.The larger the photo scale is, the higher the accuracy of the photo's linear elements we can get; but the accuracy of the photo's angular elements has nothing to do with the photo scale but is related to the focal length of the camera, so the shorter the focal length is,the higher the photo's angular elements accuracy is.Additionally, by comparing the data in Table 2, it can be found that the exterior orientation elements provided by POS system perform are worse than that of analytic aerotriangulation, and also obviously worse than the POS nominal accuracy
m m m m z y x 1.0===，81''==ω?m m ，
63''=k m .
3.3 Accuracy of direct georeferencing
Currently, 4D product commonly uses the densified points acquired by aerotriangulation as the model orientation points instead of reconstructing the stereo model directly from the image exterior orientation elements ．So the accuracy requirement of exterior orientation elements is not defined in the current norm. Generally speaking, so long as enough densification points meet the error threshold limit for each model can we get; by performing absolute orientation,a measurable model which can be reconstructed.Then we can acquire satisfying spatial information. We analyzed the accuracy of direct georeferencing by using different exterior orientation elements, which is calculated by the approach that firstly employ forward intersection
]
14[, by using the six exterior orientation elements with different accuracy
obtained in the above section, to compute the ground coordinates, and calculate the RMS of ground coordinates of object points (seeing Table 3 for detail) by comparing the ground coordinates with those of most GCPs.
From Table 3，such conclusions can be summed up as follows ：
1）For test 1，the horizontal accuracy of direct georeferencing is better than 0.25 meter and vertical accuracy better than 0.15 meter, which well meet the requirement specified in 1:500 flat land terrain mapping standards ：0.3 meter in plane and 0.2 meter in elevation
]
11[.
2) For test 2, the horizontal accuracy of direct georeferencing is better than 0.3 meter and vertical accuracy better than 0.2 meter, which well meet the requirement specified in 1:500 mountain terrain mapping standards ：0.4 meter in plane and 0.5 meter in elevation
]
11[.
3) For test 3，the horizontal and vertical accuracy of direct georeferencing are both better than 1.5 meters, which well meet the requirement specified in 1:5000 terrain mapping standards ：3.75 meters in plane and 2.5 meters in elevation
]
12[.
4) For test 4, the horizontal accuracy of direct georeferencing is better than 3.15 meters and vertical accuracy better than 3.75 meters, which well meet the requirement specified in 1:50 000 downland terrain mapping standards ：25.0 meters in plane and 4.0 meters in elevation
]
13[.
It can be learned from Table 3 that the aerotriangulation approach performs better than POS in obtaining exterior orientation elements when direct georeferencing is applied to images with different land types and scales.This result indicates that using the exterior orientation elements acquired by the aerotriangulation method to perform direct georeferencing can satisfy the accuracy standards of topographic surveying. So it can be deduced that so long as aerotriangulation meets the accuracy standards, the exterior orientation elements derived from that can be used absolutely for producing 4D product.
3.4 Y-Parallaxes in reconstituted stereo models
In the work of photogrammetry, another issue we should pay attention to is the feasibility of directly reconstructing the stereo model for terrain mapping with exterior orientation elements used, that is Y-parallax of model point is not beyond 20 m
]
1311[ . So three stereo pairs depicting different terrain types are chosen from four
tests respectively to reconstruct stereo model using the obtained exterior orientation elements
]
15[, and Table 4 is the Y -parallax on stereo model's corresponding points.
From Table 4, it can be seen that when using the exterior orientation elements
obtained by the method of aerotriangulation to reconstruct stereo model, no matter what type of terrain is applied and how much t he scale is, the model points’maximum Y-parallax lies in one pixel and the RMS of that is below half a pixel, which satisfies the accuracy requirement of terrain mapping that vertical parallax's RMS of each model should not be beyond 20 m. But when we use the exterior orientation elements provided by POS, the vertical parallaxes of each model point are all slightly larger, and the smaller the photo scale, the larger the vertical parallax, completely not meeting the requirement.
4 Conclusion
It can be shown from the experiment that, if the elements of the exterior orientation obtained from aerotriangulation meet the accuracy standards, they can be used directly for image orientation and stereo model reconstitution. However, because of systematic errors in POS exterior orientation elements, it is currently difficult to meet the standards of photogrammetry, especially when extracting 3D spatial information. It was found that, in the time of digital photogrammetry, much work can be done automatically by computers, with the reliance on GCPs lessened gradually, thus simplifying operational photogrammetry. On the whole，standard AT, which is the most established and widely-used approach to obtain image orientation parameters, is still the main body of photogrammetry; GPS-supported AT is the easy-to- operate and low- cost method and corresponding standards have been drafted for it; POS direct georeferencing is one of the important cutting-edge techniques in photogrammetry. The basic spatial information acquisition should take advantage of this, and design good plans to gain maximum financial benefits. We propose that, for large-scale
mapping of flat areas with good transportation, standard AT should be employed primarily; for difficult areas, non-charted areas or areas that are not accessible, GPS-support AT without GCPs can be adopted to acquire the basic spatial information for producing national base maps; POS photogrammetry can be used for the production of orthophotos and update of 4D products in small regions．However, POS has a promising prospect in the field of large-scale urban mapping, LIDAR, and digital aerial photogrammetry. We should promote the integration technology of POS system and other sensors by undertaking large- scale experiments, thus providing technical support for economical and rapid gathering of geospatial information. Acknowledgement
The experiment data acquisition are supported by Institute of Remote Sensing Applications Chinese Academy of Sciences, Zhong Fei General Aviation Company, Liaoning Jingwei Surveying & Mapping Technology INC, Dalian Urban Surveying Design Institute, Siwei Aviation Remote Sensing Co. Ltd., Xi'an National surveying＆Mapping Aviation Remote Sensing Co. Ltd and so on. These supports are gratefully acknowledged. The author would like to express his hearty gratitude to Fu Jianhong, Xie Chou, Ji Shunping and Yang Ming for participating in partial experiments. The author would like to thank Yang Ming and professor Zhang jingxiong for their polishing in English.
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