XXXIX-B3, 2012 
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International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Volume XXXIX-B3, 2012 
XXII ISPRS Congress, 25 August — 01 September 2012, Melbourne, Australia 
imagery as the multi-constraint conditions, and presents an 
improved line matching algorithm based on the improved 
homograph matrix constraint condition. This algorithm firstly 
obtains the homologous points by feature matching, and for 
each line to be matched, it calculates the homograph matrix 
with the homologous points in the neighbourhood of this line. 
And then it projects the line to be matched line in target image 
to the search image by the homograph matrix, and determines 
the candidate lines according to the distance between the central 
points of lines and the distance between two lines; In these 
candidate lines, this algorithm further determines the possible 
homologous lines according to the similarity constraints of the 
line angles, the distance from the origin of image to the lines, 
and the overlap of lines; Finally, the epipolar constraint is 
adopted to find out the overlap segments between homologous 
lines, and the real homologous line will be determined by the 
gray similarity constraint. 
2. PRINCIPLES 
21 The Flowchart of Line Matching Based on Multi- 
Constraint Conditions 
Stereo Image Pair | 
Edge detection by Canny edge detector 
  
  
  
  
Extracting lines using a modified 
Hough Transformation 
: : 
Determine the neighborhood points of 
line to be matched 
: 
Computation of the Homograph 
Matrix. 
; 
Line Mapping | 
| 
Constrain candidates for the line | 
? 
Similarity Constraints | 
' 
Epipolar Constraint | 
Y 
| Brightness Contrast Constraint | 
| Matched homologous lines 
Figure 1. The flowchart of line matching based on multi- 
  
  
| | Matched homologous points 
  
  
  
  
  
  
  
  
  
  
constraint conditions 
22 Homograph Matrix 
22.1 The Principle of Homograph Matrix 
Homograph matrix is a mathematical concept, it defines the 
relationship between two images that any point in one image 
can befindthe corresponding point in another image, and 
the corresponding point is unique, and vice versa (Wu 
Fuchao,2002). The homograph matrix can determine the 
correspondence relationship between images, and transfer the 
features from one image to the other. Through the location 
constraint of two line segments sets, the homograph matrix can 
realize the collection of matching lines. 
Leturzx, yy as the homogeneous coordinates of the point 
on the left image, and b — (x ,y',l)' as the homogeneous 
coordinates of the point on the right image. Then the transform 
from point Q to point D by homograph matrix H will be 
described as b — Ha , where H is a matrix of 3x3 size, 
and defines the one by one relationship between the points of 
two image points Æ is defined as following (Lou 
Anying,2010) : 
hh ih; y" 
H- hy,h5,h5 |- hy (D 
h.n h.l 
— 
h 
32233 
Where hr (17 1,2,3) is the vector (hh, , ha). By the 
matrix H, the corresponding point of point @ in the right image 
can be expressed as: 
  
  
„ha 
X m 
h; a 
: Q) 
feat 0 
* h/a 
In fact, the point a is corresponding with the point b in the 
right image, and b= Ly. IY . Then the following 
equation can be drawn: 
h'a—x'(h"a)=0 
h'a-y'(h"a)=0 
All of the homologous points in the stereopair will obtain the 
above equations, and merges all the equations into a matrix 
expressing: 
(3) 
LH =0 (4) 
Where: 
a’,0,—xa’ 
T p T 
Qa .- Vid, h, 
L = H = h, 
T. ! T 
ao rd, h, 
T tT. 
0,4, 7 Y d, 
7 is the group number of corresponding points. To ensure that 
the equations have a solution, there must be at least 5 groups 
corresponding points, and then using the least square algorithm 
to calculate the image transformation matrix having minimum 
error, i.e., the homograph matrix H.