PHOTOGRAMMETRIC FEATURE INTERSECTION 
Riadh Munjy 
Professor of Civil and Surveying Engineering 
California State University, Fresno 
Karen Schuckman 
Graduate Student 
California State University, Fresno 
U.S.A. 
Commission III 
ABSTRACT: 
Photogrammetric space intersection requires image coordinates of a point in space to be digitized 
on two or more photos. In digital photogrammetry or in single photo digitizing, it is difficult 
to locate the matching image of poorly defined points on different photos. A mathematical technique 
has been developed that requires only that lines or features be digitized on different photos 
without the need to digitize the same image points to perform the intersection. This method is very 
useful in single photo digitizing and 3D robot vision. 
KEY WORDS: Aerotriangulation, Algorithm, Photogrammetry, Robot Vision, 3D 
y; FY; (X ,Y ,2) 
1. INTRODUCTION where: 
XY; photo coordinates of the point on 
In digital photogrammetry, edge detection photo j 
algorithms result in discrete points. In Xp rYy principal point coordinates of 
digital stereopairs, the discrete points of an photo j 
edge on one image do not match the same C; principal distance of photo j 
discrete points of the other stereopair. This X Y; £5 object space coordinates of photo 
prohibits using traditional photogrammetric j 
space intersection of a point in space which fj «sy orthogonal orientation matrix 
requires at least two photos of known interior à elements for photo j 
and exterior orientation and the image X, ŸY, Z object space coordinates of the 
coordinates of the same point on all the point. 
photos. This problem is obvious in single 
photo digitizing of feature lines on multiple 
photographs. Equation 1, is a non-linear equation with 3 
unknowns (X, Y, 2Z). For n photos, the 
collinearity equation will result in 2n 
equations. Obviously a minimum of two photos 
In this paper a modified photogrammetric space 
intersection technique will be presented that 
does not require the same point to be will be required to solve for the object space 
digitized on multiple photos. The new approach coordinates of the point. The linearized 
requires only that the feature lines be observation equation for Eq. 1 for one photo 
digitized on multiple photos (minimum two is: 
photos). 
In the next section, the reader will be 
presented with some background on V+BA=f 
photogrammetric space intersection. In the 
third section the new modified model of 
photogrammetric space intersection of feature where: 
lines will be presented. Finally a report 
about results obtained with this method is 
  
presented, followed by conclusions. Vv, 
V = 
Vy 
2. BACKGROUND 
; 5X 
The mathematical relationship between an image (2) 
point, the camera orientation (exterior and A=[öY 
interior), and the object space coordinates of 82 
a point can be expressed using the 
collinearity equation: dfx Ofx Ofx 
Be 0X oy oz 
Ofy Ofy Ofy 
Xm Xa147€C m,(X-X,)) * m,,(Y-Yj)) * m,(Z-Z,) ax ay 67 
ym Wnud X) :msYY) 5g) 
My 5 (X=X;) * m;,(Y-Yj) * m4,(Z-Z,) The normal equation is: 
  
= ze 
Yi pj Tm (X-X) + M2; (Y-Y;) + m3; (Z-Z;) 
(BTWB) À = BTwf 
(1) (3) 
where W is a weight matrix. 
or Equation 1 can be reformulated to produce a 
linear model in the following form: 
X = PX (X,Y ,%) 
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