ı Figure 2 it is
nds to actual
ch is mapped
on departures
fitting and the
urther restrict
image.
surfaces may
'Z data.
itred system.
| points.
y).
h the analyti-
hole object.
> projection.
developing is
3, Ypi = Yi, in
med by each
AL IMAGES
ides the final
based on the
lly equivalent
| orthoimages
nerally, how-
d surfaces of
not fully meet
5, and for de-
'apping of the
le. Evidently,
ns cannot be
her on 'DDMs'
(Xp, Yo) grids
)zikis, 1979).
This procedure of digital ‘photo-unwrapping’ is realized in
following phases which are also illustrated in Figure 3.
1. For each image the area of development is fixed by its
left (X,Y)L and right (X,Y)Rr points, and YmiN, YMAX.
2. Next, the system Xb,Yp of development is established
with known correspondences (XYZ) — (Xp, Yo).
The pixel size in developed object space is chosen.
Hence, the size MxN of the unwrapped image is fixed.
For each elementary patch i,j of the unwrapped image
the object space coordinate (X,Y,Z)i is found.
6. Back projection through the collinearity condition
leads to the corresponding point (x,y)i on the film
plane.
7. The corresponding position io,jo on the scanned image
is established with affine transformation.
8. Alternatively, the last two steps are fused into one by
a direct linear transformation between scanned image
and object space.
9. From io,jo the grey value of pixel i,j of the unwrapped
image is interpolated.
10. Finally, resampled images are adapted radiometrically
and combined into a single mosaic to provide a raster
end product of surface development.
e io
Figure 4 Two images of the water-tower.
5. APPLICATION
5.1 Test object and data acquisition
A late 19"-century railroad water-tower (right circular cy-
linder of R 2 1.25 m, height 2.5 m; cap radius 1.35 m)
was fully covered with 6 images of negative scale 1:120,
taken with an amateur 35 mm camera (f = 70 mm); they
were enlarged x4 and scanned at 350 dpi (two images
are in Figure 4). To the total of 24 control points (o = 1.4
cm) a circle on the XZ-plane was fitted (centre: oxz = 0.5
cm; or = 0.4 cm). Digital images and object space were
related to each other directly via a DLT-approach through
7-9 control points per image (Theodoropoulou, 1996).
Figure 5 Perpsective and developed part of an image.
5.2 Vector development
Manual digitization of all scanned images was performed
within the Autocad 12 environment with the RASTEREX
RxAutolcon-P software. Exported DXF files containing all
perspective vector information were then used to trans-
form digitzed image data to corresponding 3D polygons
on the cylinder surface; these were subsequently deve-
loped. The cap was separately transformed with its own
radius.
Figure 5 shows the original perspectively distorted data
from an image and the developed vector product. All se-
parate unwindings were finally merged to generate — after
some editing — the full development of the water-tower as
seen in Figure 6. The RMS differences in the final position
of the control points was equal to their intitial precision.
5.3 Raster development
All digital images were unwrapped in the described proce-
dure using a pixel size of 5 mm in the ‘developed’ XoYp
object space. The cylinder cap was unwrapped separately
and inserted into the images at its known height. Image
resampling succeeded with a nearest-neighbour interpo-
lation. Figure 7 contrasts an unwrapping with its corres-
ponding orthoimage. Radiometric averaging and mo-
saicking of the new images were performed using a
commercial software (ADOBE Photoshop 2.5). The full
mosaic is shown in Figure 8.
Bm e erm
E E e E
ol edhe Lada L Sl AU rd
TTD or ra TE TY TY
JERS SR ra dam ar NU OU CEUEETERNET
e M ed 3 MT rr T = T in
LEE ta | ea
ti wi wl i ET EE eu
re tede re die E yes [ Y
eA du d ool Erb
ep usque Fey emere emer
Figure 6 Full view of merged vector data after development.
293
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B5. Vienna 1996
