63 
STUDY ON THE HEIGHT MEASUREMENT OF CULTURAL FEATURE 
BASED ON THE SINGLE AERIAL PHOTO 
Li Ersen * , Zhang Baoming, Guo Haitao, LuJun, Zhao Yong, Chen Ke 
Zhengzhou Institute of Surveying and Mapping,-Henan, 450052 
lixiaosen01784@sohu.com 
Commission IV, WG IV/1 
KEYWORDS: Photogrammetry, Projection Error, Radicalization Distance, Monoposition 
ABSTRACT: 
As an important property information, the height information of buildings possesses quite high utilizing value in the civil fields. The 
traditional method to get the heights of artificial buildings is to carry on the measurement on stereopairs, This method acquires work 
departments to have stereometers and professional workers, further more, it calls for advanced software and hardware, so it disagreed 
with those non-professional surveying and mapping departments. This paper studied how to ensure the height information of 
buildings by the projection error on single aerial cartographic photography. The technology could not need costly software and 
hardware to measure on stereopairs, depressed the speciality ability of workers, and make the technology approach to obtain the 
height information of buildings more broadly. Further more, the projection error on images is corresponding to the vertical edge of 
culture features which passes photo nadir points, it’s easy to carry on automatic extraction to the vertical edge, so this method owns 
very large potential to the direction of robotization. This paper has implemented experiments and precision analysis to the method 
and proved that its feasibility and high precision. 
1. INTRODUCTION 
Along with the continuous development of the city construction, 
the amount of the high buildings and large mansions grows day 
by day, so the high buildings’ height information becomes to be 
an necessary parameter in the activity of city planning, 
economic decision-making. The traditional method to get the 
heights of artificial buildings is to carry on the measurement on 
stereopairs. This method acquires work departments to have 
stereometers and professional workers, further more, it calls for 
advanced software and hardware, so it disagreed with those 
non-professional surveying and mapping departments. This 
paper studied how to ensure the height information of buildings 
by the projection error on single aerial cartographic photography. 
The technology could not need costly software and hardware to 
measure on stereopairs, depressed the speciality ability of 
workers, and make the technology approach to obtain the height 
information of buildings more broadly. 
2. THE BASIC PRINCIPLE OF THE HEIGHT 
INFORMATION EXTRACTION METHOD BASED ON 
THE SINGLE AERIAL PHOTO 
In photogrammetry, the projection error is an important 
conception. It is caused by the terrain relief and is on the radial 
line. Based on the traditional photogrammetric theory, the 
rigorous formula of the projection error is: 
r 
1 — sin® sin 2a 
y~ (1) 
Ah . 
1 r sin (o sm la 
2 Hf " 
Based on the above formula, we can get the formula to compute 
the height information as follows: 
In Photogrammetry, there are three main methods to get the 
height information of the buildings: the height information 
extraction based on the single aerial photo, the height 
information extraction based on the stereopairs and the height 
information extraction based on the multi-source data. In our 
country the researchers have made great study on the method 
based on the stereopairs, these years, people begin to study the 
height extraction method based on the laser radar data, there is 
little study on the height information extraction based on the 
projection error, besides, there is great potential to extract the 
height information automatically(On the aerial photos, the 
projection error of an image point corresponds with the vertical 
line of the building, the photo nadir point is on the vertical line, 
so it is relatively easy to extract the vertical line). So, study on 
the method of height information extraction based on the single 
aerial photo has great significance. 
Ah = ■ 
2JH 
(2) 
r n (If - r n sin (p sin 2o)/5h a + r n sin (psin 2a 
For tilt imagery, approximate altitude difference formula: 
Sh„ 
Ah = 
H 
(3) 
r n ( 1—— sin (p sin 2a) 
For plane imagery, altitude difference formula: 
a 7 Sh 
Ah = —H 
r 
(4) 
In the above formulas V n , §h a ,H, Ah , f, a , (p separately 
represents radicalization distance of photo nadir point ,