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
2.2.2 Constraint of Candidate Lines Based on the
Modified Homograph Matrix
In the field of computer vision, the homograph matrix only be
applied to transfer the features between two images. This paper
introduces the principle of homograph matrix in the line
matching algorithm, and realizes the effective location
constraint for the line segments sets of the left and right images.
For aerial images, according to the complex surface relief
especially in the urban areas, if only adopt one homograph
matrix in the matching process, the offset of homologous lines
will be very large after the projection of homograph matrix. In
order to avoid this situation, this paper modifies the homograph
matrix algorithm. For each line to be matched, it utilizes the
homologous points in the neighbourhood of line to calculate the
homograph matrix.
Firstly, it determines the existing homologous points in the
neighbourhood of line to be matched, and calculates the
homograph matrix with them. Then, it projects the line to be
matched to the right image based on the homograph matrix, and
determines the possible candidate lines in the right image
according to the distance between the central points of lines and
the distance from central point to other lines. The principle is
shown as Figure 2:
L
pjid
middle point = >
vertical point
Figure 2. Constraint of candidate lines based on the modified
homograph matrix
2.3 Gray Similarity Constraint
Taking the fitted two line sets A and B as the references, and
comprehensively considering the following three kinds of
similarity constraints:
(1) Similarity constraint of line angle
The slope À of the extracted line can be calculated by
the coordinates of the two end points, and then the inclination
6 of this line also can be solved.
60 = arctan k (5)
An sim(m,,m,) — cos(8, —O,) (6)
Where 0, is the inclination of target line 772, , and 9, is the
inclination of searching line 772 b:
(2) Similarity constraint of distance from the origin of image to
the line the polar equation of line is:
p=x-cos@+y-sinf,0<0<r (7)
Where pO is the distance from the origin of image to the line in
the polar space, i.e., the vertical distance from the origin to the
line.
Rho sim(m,,m,) ^ abs(p, — p,) (8)
Where pO, is the distance from the origin of target image to the
target line M, , and JO, is the distance from the origin of target
image to the searching line 771, .
(3) Similarity constraint of overlap between lines
Lap sim(m,,m,) — overlap(m,, m,)
(9)
Where overlap(m,,m,) expresses the overlap length of
line 772, and line 7, , length(m, ) is the length of line L, 4» and
length(m,) is the length of line 77, .
2.4 Epipolar Constraint
If a pair of matching lines satisfies all the above similarity
constraints, then the epipolar constraint will be used to find out
the corresponding overlap segments between the two lines (Wu
Bo, 2012). For example, for a pair of matching lines AC and
BD in Fig. 3(a) and (b), the epipolar lines of the end points of
AC and BD can be derived as illustrated using dashed lines in
Fig. 3. By intersecting these epipolar lines with the lines AC
and BD, the overlap segments between these two lines can be
obtained, which is AD’ and A’D.
(a) Left image (b) Right image
Figure 3. Using epipolar constraint to find corresponding
overlap segments for line matching
2.5 Brightness Contrast Constraint
After the epipolar constraint, it obtains the overlap segments of
homologous lines. The brightness contrast in a local buffering
region along both sides of the matching lines can be used to
further disambiguate the line matching.
(left) the supporting region of linear feature
(right) the decomposition of supporting region
Figure 4. Linear feature supporting region and decomposition
Firstly, it needs to introduce the concept of linear feature
supporting region. As shown in Figure 4 (a), L is a straight
line segment which length is M in the discrete 1mage surface.
Then limits a rectangular area with the central axis is L and
~~ TTT
min(/ength(m,), length(m,))
Intern
the width is
linear featu
4 (b), the s
parallel lin
segments al
also L and
linear featu
in the line
of (r+1)x#
as a matri>
linear fe:
Simultaneo
supporting
be-matchec
values will
values with
the final
coefficients
calculated.
A
Where NC
the left and
This paper
digital aer
matching.
3.1 Exper
The experi
imaged by
are 512 X5
is the searc
(I) Comput
In this ste
feature po
stereopair |
matched pi
coefficient
solves the
Decomposi
H =
(2) Line ext
This paper
the edge c
image. Th
image us
setting th
for lon
short stra
Fig. 5(d) a
H it pro
System def