Juliang Shao
The nearest compatible neighbours in a local region R are counted for the contributions to O, for the current segment.
The above formula only illustrates the compatibilities among neighbours in the same image. For a clique constructed in
the initial or extended matching, any change in the rejection and acceptation of one or more candidates in any iteration
will have an impact on other nodes of the clique. The probabilistic expression for this impact is defined by
Joe jeta re RON = C
Qo z0 Nz2
where Q^» stands for the contributions from other points in the clique; P», P5, ..., Py are the previous probabilities of the
candidates in the images 2, 3, ..., N, provided that the current point is in Image 1. If the previous probability of that
candidate is zero (ie that candidate was rejected), no contribution is made, whereas if it is 1 (accepted), then most
contribution is assigned. When only two image points remain on the clique (ie. N = 2), no contribution will be provided.
As a result, the current candidate will fail. By this means there is global consideration for all images, instead of just two
images.
4.3 The Relaxation Process
The essence of relaxation labelling is that compatible neighbours reinforce each other, whereas incompatible neighbours
decrease their mutual support, regardless of the similarity functions used. The following section details the relaxation
functions utilised for the present investigation. With the two types of contributions from the same image and between
images, an iterative computation is performed:
p** z px BxQixQs) (6)
where 4 and B are coefficients that control convergence speed, and & and &--/are the iteration numbers. A multi-image
clique is accepted if all probabilities P; (4, J eN, 1# jwith N representing the number of overlapped images of the
clique) related to the points on this clique reach a given threshold.
Fig. 7 shows the matching results using unrestricted epipolar geometric constraint prior to relaxation processing, while
Fig. 8 displays the outcome of this process. Segment 2 in Fig. 7 are rejected through the relaxation process.
b
Fig. 7: Corresponding segments before the relaxation processing.
b
Fig. 8: Corresponding segments after the relaxation processing.
5 EXPERIMENTAL APPLICATION
The segment matching process developed has to date been evaluated on four sets of images, including both aerial and
close-range image configurations of three overlapping images. One of these experimental applications is reported here
842 International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B3. Amsterdam 2000.
to
to
dis
of
m
pr
ini
27
che
sh
wh
col
