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.