> XXXIX-B3, 2012
projected edges and the
nall, as either the model
ation parameters are
ted Pixels
x 9 Vz)
.
‘® e
x)
A
(ls and buffer
king for is the projected
building edges in the
presents a discrepancy
sponding edge line v;v;,
re, the objective of the
res sum of dj. Suppose
f the projected vertices
an edge pixel Ty (x,
ance dj, from the point
lated as the following
+ On — Ya) (1)
NY y
nage
v;2(X;2, V;2) are functions
nparatively the exterior-
own. Therefore, dj; will
Taking a box model for
| h, a, dX, dY, and dZ,
ng rarely has a tilt angle
uares solution for the
S:
^dZ] min (2)
rd to the unknowns, SO
solve for the unknowns.
ed with respect to the
tion with regard to the
| of the function Pj
ns of the unknown
parameters. Given a set of unknown approximations, the least-
squares solution for the unknown increments can be obtained,
and the approximations are updated by the increments.
Repeating this calculation, the unknown parameters can be
solved iteratively. Eq.(2) and Eq.(3) are used for geometric
model reconstruction. As for image orientation determination,
they are modified as Eq.(4) and Eq.(5). The unknowns turn to
the increments of the image orientation parameters.
xdg - X[Fg(e, 9, k,X0, YO, ZO — min. (4)
d = Fo Aan- OF, Ant oF Pn
e a 0 2p 0 ok 0 (5)
eJ A (5 n (a) x
0
aX, 0 oY, E oZ, i
The linearized equations can be expressed as a matrix form:
V-AX-L, where A is the matrix of partial derivatives; X is the
vector of the increments; L is the vector of approximations; and
Vis the vector of residuals. The objective function actually can
be expressed as q-V^V— min. For each iteration, X can be
solved by the matrix operation: X-(AT Ay A'L. The iteration
normally will converge to the correct answer. However,
inadequate relevant image features, affected by irrelevant
features or noise, or given bad initial approximations may lead
the computation to a wrong answer.
4. CONCLUSIONS
Photo-realistic 3D building models are the basic geospatial
information infrastructure for many applications. This paper
proposed a concept toward automated texture generation based
on least-squares model-image fitting algorithm to overcome the
bottleneck. Instead of using the precise and expensive mobile
mapping instruments, the personal mobile computing devices
are used to collect facade images of the buildings. Benefit from
the built-in GPS receiver and G-sensors, the approximate image
orientation parameters are directly recorded as the picture was
taken. Then the orientation is refined by fitting model to image
iteratively. Some experiments are still undergoing, so the
results will be presented in the conference in an interactive way.
ACKNOWLEDGEMENT
The author deeply appreciates the research grant sponsored by
the National Science Council of Republic of China. (NSC 100-
2221-E-003 -025)
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