PHD Thesis - Institute for Computer Graphics and Vision - Graz ...

4.2. Representation of the detections 46
point-to-point (region-to-region) correspondences between the reference image I 1 and I i and the
smaller number of points (regions) detected in one of the images. Only points (regions) located
in the part of the scene present in both images are taken into account. It is given in Eq. (4.1).
r i = r 1i =
|C 1i |
min(|R 1 |, |R i |)
(4.1)
R i is the set of all detected regions in image I i and |.| denotes the cardinality of a set. C ij is the
set containing all true region correspondences between the images I i and I j . C ij contains only
single correspondences, i.e. no element of R i corresponds to more than one element in R j .
4.1.2 Matching score
The matching score m i is the ratio of correct matches and the smaller number of regions detected
in one of the images. It is depicted in Eq. (4.2).
m i = m 1i =
|M 1i |
min(|R 1 |, |R i |)
(4.2)
M ij is the set containing all detected true region matches between the images I i and I j . In
addition we define m i as the matching score related to the number of possible matches |C ij | (see
Eq. 4.3).
m i = m 1i = |M 1i|
(4.3)
|C 1i |
4.1.3 Complementary score
The complementary score c n i is the number of correctly matched non-overlapping regions between
two different viewpoints. The measure is given relative to the sum of all matching detections.
It is given in Eq. (4.4).
c n i = |M i 1 ∪ M i 2 ∪ ... ∪ M i n|
|Mi 1| + |M i 2| + ... + |M i n| (4.4)
M j i
is the set of correctly matched correspondences for detector type j between images I 1 and I i
and n is the number of combined detectors. The complementary score is defined between 0..1. A
complementary score of 0 means that there are no non-overlapping regions, the detectors produce
the same regions. A complementary score of 1 states that the detections of both detectors are
completely different. Thus a high or close to 1 complementary score will reveal good detector
combinations.
4.2 Representation of the detections
The variety of local detectors is vast and their results may differ substantial. However, most
of the detectors represent their results in a similar manner. In most cases the detectors return
a center location and a measurement area around the center. Most of the difference lies in
the representation of the measurement area. In the case of simple interest point detectors
only a location is returned for a detection. Scale invariant detectors commonly return a center
location and a circular measurement region based on the center location. Most of the affine
invariant detectors return a center location and an elliptical measurement region based on the