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2433e-06 
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0700e-07 
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3290e-07 
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Dolo on 
5. Istanbul 2004 
GENERALIZED POINT PHOTOGRAMMETRY AND ITS APPLICATION 
Zuxun Zhang*, Jianqing Zhang 
School of Remote Sensing and Information Engineering, Wuhan University, Wuhan, China, 430079 
(zxzhang, jqzhang)@supresoft.com.cn 
Commission V, WG V/1 
KEY WORDS: Photogrammetry, Digital, Theory, Industry, Calibration, Orientation, Reconstruction, Inspection 
ABSTRACT: 
Point based co-linearity is an essential conception in Photogrammetry. But point in photogrammetry means only physical or visible 
points, such as dots, cross points and corner point etc. Especially in the stage of either analogue or analytical, even digital 
photogrammetry, the main primitive feature, which can be measured by human operator, is physical point. It can be referred to as 
Point Photogrammetry contrary to Line photogrammetry, which is proposed and used only in the past about 20 years. 
For a straight line a coplanar equation is used, where the line on the image lies on the plane, passing through corresponding spatial 
straight line and the photographing centre in line photogrammetry. All straight lines and curves are normally referred to linear 
feature rather than point feature in line photogrammetry. The co-planarity can be normally explain as Sa-(SPxSQ)=0, which means 
the image point a must lie on the plane composed by perspective centre S and two end point P and Q of the 3D line. 
However, in mathematics all lines or curves are consists of points, which is expressed as gencralized point in this paper. Collinear 
equation could be used to linear features similar as the visible point, and all kinds of features existing in photogrammetry can be 
concentrated on "point" — called as Generalized Point Photogrammetry. According to this philosophy the adjustment form would be 
consistent, simpler and more convenient comparing with line photogrammetry. 
In the Generalized point photogrammetry the only difference between physical points and feature line point is that two collinear 
equations of both x and y are used for the physical point and only one collinear equation of x or y depending on the local direction of 
the line segment is used for feature line point. The collinear equation, used for feature line point, includes the parameters of feature 
line. For example, the coordinates of point in a straight line or circle can be expressed by their parameters, and be substituted to the 
collinear equation, and the parameters can be computed in the same time. 
Besides physical point and feature line point, the invisible point — infinity is also included in generalized point scope, and collinear 
equations are used for them too. 
After the theory of the generalized point photogrammetry is introduced, its applications are presented, including extraction of vanish 
points, determination of interior parameters of the image, and sheet-metal part inspection and measurement. Corresponding 
experiments and results are demonstrated with the conclusion. 
1. INTRODUCTION 
The co-linear equation is the core of photogrammetry (Wang, 
1990), because it is source from foreword and backwards 
intersection for point measurement in the surveying. The co- 
linearity of points is the basic concept of the photogrammetry. 
The points concern the dot, the intersection, the corner and so 
on. Whether analogue or analyse even digital photogrammetry, 
the basic feature point, which can be measured by manual way, 
is physical or visual. Then the photogrammetry can be called as 
point photogrammetry. 
However, There are a lot of straight lines in extraction of 
buildings, architecture photogrammetry ‘and industry part 
measurement. Line based photogrammetry (based on co-planar 
equation) was studied and applied (F.A.Van.den Heuvel, 1999). 
In line photogrammetry, co-planar equation can be used for 
straight line, where the line on the image passed through the 
plane determined by photographic centre and corresponding 
spatial line. In line photogrammetry all lines and curves are 
considered as line features instead of point feature. The co- 
planar equation expressed as Sa-«(SPxSQ)- 0, where image 
  
Corresponding author. 
point a is within the plane determined by photographic centre .S 
and two points P and Q of a spatial line. 
In the real world, there are large number of curves, such as 
roads, rivers and lakes on the ground, circles, arcs and curves in 
architecture photogrammetry and industry measurement. In 
addition, the corresponding points between old map and new 
image are selected as control points in the map update, which is 
a quite difficult job. Usually, there are few distinct points, such 
as dot point and corner point, and their matching is not precisc. 
Therefore, if a mount of lines in the map and image could be 
applied as control information for the matching, it would be 
significative in both theory and practise. 
In mathematics, all line and curve consist of points. Same as 
visual point, co-linear equation can be used to the points in line 
feature, and all feature points can come down to the point in 
order to fit the co-linear equation----that is so called as 
generalized point photogrammetry. According to the principle, 
the form of the adjustment is consistent, and simpler and more 
convenient than line photogrammetry. The only different 
between feature point and physical point is that the latter is 
fitting two co-linear equations relative to x and y respectively,