5. Istanbul 2004
ated set.
rm ree ren
real errors
2000 3000
ited set.
3000 3000
ited set.
Smm
2.7576 pix
2.0554 pix
1 7.1805 pix
ed by different
4. STITCHING
There are two ways to combine the image sequence taken from
one point to a panoramic image mosaic. The single images can
be stitched together directly based on the two dimensional
projective transformation
a, X, + ary +03
asx) +asy t dg
X5 = "ae
V2 (1)
3X t agy; tl a7x; + agy, +1
or the rotations between the images can be solved and the
images projected to a common surface.
The transformation parameters a;,..., a; and ag in Equation | can
be solved if the image coordinates of at least four corresponding
points are known on both planes and if no three points lie on
the same line. Instead of using a set of points, the whole
overlapping area can be utilized to determine the transformation
parameters. The initial transformation parameters can be solved
using the coordinates of four corresponding points and then
adjusted using least squares so that the sum of squared grey
level differences in corresponding points will be minimized
(Szeliski, 1996; Póntinen, 1999).
In the other method the rotations of the images are solved based
on image correspondences. Also in this case it is possible to use
either single points or the whole overlap area. The mathematical
model is
| @)
where a and b are the corresponding image vectors and R is the
unknown rotation matrix. Using least squares principle the
optimal rotation matrix, which minimizes the squared sum of
grey values in corresponding points can be found. After the
rotations have been solved, the relatively oriented images can
be projected to a chosen surface. If the amount of the images is
small, the chosen surface can be a plane, but the more there are
images the better is to use a cylinder or a sphere.
According to common sense the more images have overlap the
more reliable is the joint. But on the other hand the more
images are needed to cover a certain object and the stitching
process is slower. Because the image sequence usually is not
exactly concentric and the camera calibration parameters are not
exactly correct, also the stitching order has some impact to the
deformations. As an example the image shown in Figure 3 was
created two more times so that in both two cases the stitching
order was different than in the first case. Again the 19
checkpoints were measured on all images. The movements
relative to the first image mosaic are shown in Figures 7 and 8.
Both new images had the middle image of the set as a starting
image and in the case presented in Figure 7 the rest eight
images were combined clockwise starting from the middle left
image. Figure 8 shows the deformation caused by the
anticlockwise stitching order starting from the middle right
image. The statistics of the deformations are presented in Table
2. It can be seen the deformation is pushed to the corners of the
image mosaics. Surprisingly the stitching order causes stronger
deformations than the non-concentricity. Based on authors own
experiences the best way to avoid the accumulation of errors to
à certain part of image is to do the combining symmetrically.
For example, the middle left and middle right images are
International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B5. Istanbul 2004
combined to the middle image, then the middle top and middle
bottom images to the previous mosaic and finally the corner
images. And if there are differences in the overlaps the images
with the biggest overlaps should be combined first to make the
structure of the mosaic stronger.
stitching order: $-4-1-2-3-6-9-8-7
T T
T
2000 D 4
© e ?
5004 4
-500i- E
4A
-1000r 4
-1500 ? E
72000 reer errmsg perta A v i 1 end
73000 -2000 -1000 0 1000 2000 3000 4000
Figure 7. Clockwise stitching order causes strongest
deformations to the top right part of the image mosaic (error
scale 50:1).
stitching order: 5-6-3-2-1-4-7-8-9
2500 T m T T
= E
2009 & +
; 5
D
A
1500H E
1000 P &
« Q ©
500} X \ |
I © ©
or S E
-500+ J
©
[2]
-1000F- 4
©
5
-1500 of ^v
-2000 NUR ——— i ILI = +
-3000 -2000 -1000 0 1000 2000 3000
Figure 8. Anticlockwise stitching order causes strongest
deformations to the top left part of the image mosaic (error scale
50:1).
set clockwise anticlockwise
mean 4.1688 pix 3.3928 pix
std. 5.2864 pix 4.1973 pix
max. 21.9940 16.8583
Table 2. Statistics of the deformations caused by different
stitching order.
5. SMALL PANORAMIC BLOCK
To obtain some numerical values for achieved accuracies of
panoramic image measurements a small panoramic block was
calculated. Three panoramic images of a facade shown in
Figures 9, 10 and 11 were created. Images in Figures 9 and 10
