In: Paparoditis N., Pierrot-Deseilligny M.. Mallet C... Tournaire O. (Eds), IAPRS. Vol. XXXVIII. Part ЗА - Saint-Mandé, France. September 1-3, 2010 
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(as optional choice). Its interest points are matched with a 
multi-image geometrically constrained LSM (Grim and 
Baltsavias, 1988) based on the collinearity principle and the 
orientation parameters previously computed with SIFT or 
SURF features. Table 3 shows the accuracy improvement using 
the developed approach. 
2.4 Correspondence reduction and uniform distribution 
High resolution images picturing objects with a good texture 
could generate a huge number of image correspondences, which 
are very often not uniformly distributed in the images. 
Therefore, each image can be divided into rectangular cells 
where only the features with the largest multiplicity are held. 
This method demonstrated a significant reduction of the 
correspondences (even more than 100 times), preserving the 
accuracy of the final product. Secondly, as the features are 
generally random-distributed in the images without a uniform 
distribution (Figure 3), the method improves the geometric 
distribution of tie points. The quality of the final results is 
increased in terms of geometric distribution of tie points and in 
a drop of the processing time and computational cost. 
Figure 3. Random and non-uniform distribution of the features 
extracted with SIFT (above) and derived uniform distribution 
with the proposed approach (below). 
2.5 Extension to spherical images 
ATiPE can be also used to extract reliable correspondences 
from spherical images (or panoramas), i.e. a mosaic of 
separated images acquired with a rotating head and stitched 
together. The derivation of metric information from spherical 
images for interactive exploration and realistic 3D modeling is 
indeed receiving great attention due to their high-resolution 
contents, large image field of view, low cost, easiness, rapidity, 
and completeness (Fangi, 2007). But spherical images, if 
unwrapped on a plane, feature different resolutions (width and 
height), scale changes and the impossibility to use a classical 
bundle solution in Cartesian coordinates. In fact, while a 
pinhole image is described by its camera calibration parameters, 
a generic spherical image is only described with its 
circumference C, which corresponds to the image width (in 
pixels) under an angle of 2n. In fact, a spherical image can be 
intended as a unitary sphere S around the perspective centre and 
3D point coordinates x can be expressed in terms of longitude A 
and co-latitude ig as: 
x = [x y z] r = [sin^cosA sin ^ sin A cos^] r (1) 
The relation between a point onto the sphere and its 
corresponding 3D coordinates is x = X / || X ||. Homogenous 
image coordinates m can be mapped onto the sphere by using 
the equi-rectangular projection: 
m = [m ] m 2 l] r =[/?/l Rig l] r (2) 
where R=CI(2n) is the radius of the sphere. 
Given a spherical image, we developed a matching strategy to 
unwrap the sphere onto a local plane. First of all, the median of 
the longitudes p(A) is subtracted from A, obtaining new 
longitudes A* =A - p(A). This allows the projection of the points 
of the sphere onto the plane x = 1 as: 
p = [l p, p y ] T = [l tgA* coty/7cosA*] r (3) 
Here, p 2 and p 3 can be intended as the inhomogeneous image 
coordinates of a new pinhole image. Moreover, the centre of the 
spherical images is also the projection centre of the new pinhole 
image, with the advantage that given two spherical images S 
and S', an outlier can be removed by robustly estimating a 
fundamental matrix. Obviously, this procedure cannot cope 
with large longitude variations. However, the partitioning of the 
spherical images into 4 zones (lad2 <A< (¿+1)7t/2, k = 0,..., 3) 
produces 4 local pinhole images that can be independently 
processed. In addition, this method allows the combined 
matching of spherical and pinhole images. 
The extracted image correspondences are then processed with a 
bundle solution in spherical coordinates to derive the camera 
poses and a sparse 3D geometry of the analyzed scene. 
3. EXPERIMENTS 
3.1 Ordered image sequences 
Figure 4a shows the recovered poses for a sequence matched 
with the SIFT operator and the kd-tree search for comparing its 
descriptors. It took roughly 30’ to orient 33 images (used at 
their original size) acquired with a 10 Megapixel calibrated 
camera. The robust estimation of the epipolar geometry was 
necessary to remove mismatches (e.g. moving objects such as 
people and pigeons). The orientation procedure was carried out 
starting with a relative orientation between the first image pair, 
then progressive resections alternated to triangulations have 
been used to provide approximations for the final and robust 
photogrammetric bundle adjustment. Figure 4b shows the poses 
of 28 images recovered with the SURF operator in 15’, deriving 
a final sparse point cloud of ca 12,000 3D tie points. 
Figure 5 shows the results from the ISPRS Comm. 3 dataset 
“Fountain-K6”. The 25 images have been automatically 
oriented with the SIFT operator in approximately 20’. The 
adjustment with all the extracted features (more than 96,000 
image points) gave a final RMS of 3.6 pm, while the 
application of the point reduction described in subsection 2.4 
(ca 6,000 image points) ended with a RMS of 3.3 pm. 
3.2 Sparse image block 
ATiPE has been also tested on large image blocks acquired with 
an UAV system. Figure 6 shows the orientation results for a 
block of 70 images taken with a calibrated 12 Megapixel 
camera. The global number of image combination is 2,415, 
while the pre- analysis with the visibility map found 507 image 
combinations.