In: Wagner W., Szekely, B. (eds.): ISPRS TC VII Symposium - 100 Years ISPRS, Vienna, Austria, July 5-7, 2010, IAPRS, Vol. XXXVIII, Part 7B
Reference image Target image
Figure 2: a) Two images of the coastal city of the Rincón de la Victoria (Málaga-Spain). b) Digital terrain model (DTM) of the region
of interest, c) Quadtree decomposition of the DTM. Each parcel will contain a CP for posterior image registration.
25 pixels of side (i. e. s = 25), it is rejected. This means that the
smallest cell size, for this example, will be bigger than 25 pixels
and smaller than 50.
Algorithm 1 Quadtree decomposition of the DTM.
1: II Rq contains the coordinates of the regions to be analyzed
2: R 0 <= (coord(DTM)} // Rq is initialized with the
3: // coordinates of the DTM
4: // R will contain the coordinates of the final regions
5: f?4=0
6: for all r € Rq do
7: v <= DTM(r) Hr — {x, y, width, height}
8: if size(r) > s and (max(u) — min(u)) > t then
9: // quad divides r into 4 equal pieces and returns
10: // their coordinates
11: Ro 4= {R 0 U quad(r)}
12: else
13: Hr is not divided and it is stored in R
14: i?4={f?Ur)
15: end if
16: Hr is removed from Ro
17: Ro -<= {Ro — r}
18: end for
Finally, the selection of the final CP set is accomplished as fo
llows: for each parcel of the decomposition, we check the num
ber of detected CP pairs and, if this number is greater than one,
we select the CP pair that exhibits the best score in the matching
process, that is, the CP pair with the minor SSD value.
3. EXPERIMENTAL RESULTS
The benefits of the proposed method has been successfully veri
fied by elastically registering a number of panchromatic (Ortho
ready) QuickBird image pairs (0.6 m./pixel), as the one shown
in figure 2-a. The multitemporal series considered in our tests
present significant relative geometric distortions induced by the
off-nadir observation of no-planar regions as well as radiometric
changes. The reader can found more details on satellite posi
tioning data and the acquisition dates in (Arevalo and Gonzalez,
2008).
The registration process is accomplished by means of radial ba
sis functions (RBF). Radial basis functions are scattered data in
terpolation methods where the spatial transformation is a linear
combination of radially symmetric basis functions (second term
of (3)), each of them centered on a particular CP, typically com
bined with a global affine transformation (first term of (3)). Mat
hematically
m j n
x = ( x 'Y~ k {y) k + ^2 A i 9 (rj)
;=o fc =o i=i (3)
m j n
y = ¿ ¿ b jk (;x'Y~ k (y') k + J2 fa)
j=0 fc=0 j=1
where
f‘j = \\(x,y) - (xj,Vj)\\ (4)
being Xj <—> x'j the refined CPs.