of
Andrew Bibitchev
For example, in case of edges of flat horizontal building roof height coordinate // can be considered as parameter ® ,
moreover bounds /7,.. and H,,. defineset Q: Q = [H noH nal:
min >
Thereby, the task can be reformulated as follows. It is required to find value of parameters c) from set © , for which
Sı5 D, D ; :
a"b" and a^b" are projections of one and the same 3d edge AB on “source” and “destination” images respectively.
2.2. Correlation. Obviously, for matched 2d edges a^^? and ab^ their (one-side) vicinities on images are
cognate to each other. Thus, to match a^5? and a5? ,» similarity of their (one-side) vicinities as a function of @
should be maximized on the set Q . Note that one-side vicinity usage is preferable due to existence of application noise.
As an example, in Figure 3 we can see right building wall in the “source” image and can not in the “destination” one.
Let V° =a*b*c*dS be vicinity of a°b* and VP =aPhPcPdP be appropriate vicinity of a”b”. Note that
dependence V” =v? (vs 0) should include 3d model of object facets. To construct measure of similarity, let me
introduce coordinates (A, p) presented in Figure 4, here A is a^^? length in pixels and P is vicinity width in pixels.
Then, the normalized correlation coefficient of vicinities can be introduced:
Vs y»
-1 i? s const or i? & const
corrla$ ‚65 ;0)= Op ap) (4, p) -iP (4, p) ; (11)
[e (A. p)) -Fàp | [i^a pf -Pap |
where i^ (A, psi? x 4, my a, p) is "source" image in new coordinates,
I". p= j^ (x à p:@).y PO: p. «)) is "destination" image in new coordinates, and
A P ;
SA, PIS ue! p) is mean value of a function /(A, p). For calculation intensities i? and iP at
+ FT 1=0 p=1
points with non-integer coordinates one can use bilinear interpolation.
As well known coefficient (11) has following useful properties:
(1) —1 <corr <1;
(ii) corr 212 i? (A, ny = ki” (1, p) * c, where k and c are constants;
(iii) corr is invariant for linear intensity transformations i’ = ki +c .
All these properties allow us to consider matching problem as optimization task:
©" - arg maxcorr(a? ,5?: c), (12)
weld
a? - aP (a5, 5:0 ), 5? =” (03.55: ). (13)
If corrla $ b^ 0") less than threshold value (usually 0.3) then
candidate a^ 5? should be rejected.
Example of correlation results for two candidates to the long
sides of the building roof, imaged in Figure 3, is presented in
Figure 5. It is easy to see that for both edges we obtain one and
the same value of height: H” =192m.
corr
2.2.3 Advantages and Drawbacks. Let me enumerate some Height, m
advantages of such correlation usage:
: Figure 5. Example of correlation results
e high robustness; gure 5 p t
International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B3. Amsterdam 2000. 75
