Shoichi Horiguchi
includes errors since it is based on DEM data,
which tends to be noisy. Therefore, we need to
calculate an approximate line that suppresses the
errors. We approximate the lines by applying the
MDL principle.
2.4 Reconstructing Road surface model using
MDL principle
The models created by the above processes tend A
to be impractical because the amount of data DD
used to form a model, its description length, is =<) .
extremely large. Obviously there is a tradeoff La all TENA
between description length and error, the (a) Orthographic
discrepancy between the actual object and its
model. The bottom image in Figure 4 shows the
cross section of road surface models of interval
intersection C and D. In this case, road
elevations Ei (I=1,2,...,n) are given even if the El E2
road is perfectly flat as the data set includes à #
noise. de > dde > »
The following shows our approach to WI W2
approximating aroad surface as a polynomial.
The cross section data of DEM take the form Z; (b) Cross section
(i=1,2,...,n), where n is the number of data
points. If Z; contains noise that has normal Ewe Eve
distribution with mean 0, and variance s , then 4
the information source model
Pi P2
y |
ba
XS") = {Pim Ines (m = L2, tty M) i 3 A A
(1) |
is expressed by the follows equation.
1 1 n Su
p^. (z") = ———CCKP es - S: (z, xs)
s (42ps, )" | 28; 5
(2)
) ); )k, 1
fi za Ha (3)
(c) Road model
S50 ={d™ = @™,a{™, ai) 1a” 20} (4)
Figure 4. Reconstructing Road surface model
Equation (2) means probability distribution,
normal distribution. Equation (3), (4) are
polynomiak of degree m. if k,=m, M>>n then the code word length is expressed as follows.
m n n n Kon
Ig" (z") 2 -logy Dio (^) * —-logy n*logy M
rr ] ^m.
=nlog x (/2ps,) + 2 YG- f ) *—log, n*log, M (5)
i=l
28. i 2
o
In equation (5) first and third functions are constant. Therefore the cost function related to the degree of the model is as
follows.
416 International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B3. Amsterdam 2000.
