An Effective Rigidity Constraint for Improving RANSAC in Homography Estimation - Advanced Concepts for Intelligent Vision Systems - page 206

a) Two sets of correspondences
sorted out using RANSAC
(plain lines: best random sample,
dashed lines: other correspondences)

b) Correct registration
obtained from the orange
set of correspondences

c) Wrong registration
obtained from the yellow
set of correspondences

Fig. 1. Two different results of RANSAC in a dicult image registration task

when RANSAC — yet known to be very robust — is used, dealing with images
with little overlapping leads to diculties in some image registration tasks. The
kind of issues encountered is illustrated in figure 1 where the image registration
was done following an approach similar to the one in [4,5]. In this example, the
overlap is of about thirty per cent, which is usually enough for a fairly good
registration. In this case, however, the situation is more dicult, as many point
correspondences are detected in the sea area which is different in both images.
This introduces a lot of outliers and reduces the number of possible inliers in
the overlapping region, so that the total amount of inliers is finally estimated at
eight only. In the best case, it is possible to get the result of figure 1‌b‌). How-
ever, depending on the random sample selection, the result of figure 1‌c‌)was
also obtained. This less glorious result suggests that some kinds of degenerated
samples led to an absurd homography for which eight bad point correspondences
were unfortunately consistent. Anyway, in this case the wrong solutions compete
with the good one and the result is somewhat uncertain, which justifies a further
investigation.

3 A Rigidity Constraint for Improving RANSAC

3.1 Analysis of the Invalid Homographies Obtained with RANSAC

When analyzing the cases where RANSAC fails to give a good result, it appears
that most often, the resulting homographies do not reflect a rigid-body trans-
formation. Figure 2 illustrates quite well the kind of homographies which can
occur in dicult situations where the number of outliers is high with respect to
the number of inliers. The homographies of figure 2 were obtained by artificially
imposing a geometrical rectification on the original image of figure 2‌a‌)inaway
which has nothing in common with a rigid-body transformation. In these exam-
ples, the top-left, top-right, bottom-left and bottom-right corners were shifted