PE&RS July 2016 Public - page 560

is less than two pixels. In these experiments, the top eight
nearest neighbors are retained for each feature point. Only
approximately 60 percent correct matches appear in the first
nearest neighbor. Figure 1 shows the experiment result. To
find additional correct matches, considering multiple nearest
neighbors is valuable during the matching process (retain-
ing the top four nearest neighbors is an appropriate choice),
especially for images that are difficult to match.
Additional algorithms have been proposed in literature
et al.
, 2014), most of which employ the geometrical
consistency between features. Relaxing labeling (Joglekar
, 2014; Kittler, 1997; Zhang
et al.
, 1995) is one of the effec-
tive methods to reject incompatible matches. To some extent,
it is similar to the Hough transform method (Kittler, 2000) in
two ways. First, they both choose geometrical consistency
criterions. Then, matches with extra support are selected as
correct matches by finding support from neighbors. However,
relaxing labeling is performed iteratively, whereas Hough
transform is not.
In the image retrieval field, methods based on geometri-
cal consistency have been proposed in recent years, such
as geometric coding (Zhou
et al.
, 2013) and weak geometric
consistency (Jegou
et al.
, 2008). Geometric coding encodes
the spatial relationships of local feature points and itera-
tively removes matches that cause the largest inconsistency
in the geometry structure. The assumption of weak geometric
consistency suggests that the matched features should have
similar scale and rotation changes. In those methods, the scale
and orientation information should be provided by the feature
extraction and description algorithms, such as
In this paper, a candidate match filter based on Hough
transform (Hough, 1962) is proposed, namely, the geometric
consistency voting strategy. Hough transform has been widely
used in many applications for many years (Ballard, 1981;
Illingworth and Kittler, 1988; Razavi
et al.
, 2012; Woodford
et al.
, 2014). This paper provides a detailed description of
the application of Hough transform in filtering initial candi-
date matches. Only two parameters, namely, the scale and
the rotation between images, are used to form the parameter
space in Hough transform. Thus, it works better when dealing
with a low ratio of inliers. The method can handle multiple
nearest neighbors. Furthermore, the criteria to decide whether
a match is an inlier or not are straightforward. It is not a
replacement of the
-like method because our method
is unsuitable for working with the rigorous transformation
model between images (the epipolar geometry constraint). It
is suitable to be used as a preprocessing step of other outlier
removal methods. Good matching results can be obtained
even when the ratio of inliers is less than 10 percent when
combining our method and the
-like method.
The paper is organized as follows: The basic mechanism
of Hough transform is introduced first. Then, the process in-
volved in using Hough transform to remove incorrect matches
is described. Experiments and conclusions are presented in
the final section.
Basic Mechanism of Hough Transform
Hough transform uses the internal relationship between
two subjects (e.g., feature locations and the transformation
parameters) to construct a voting mechanism. Useful informa-
tion can be revealed through an analysis of the peaks of votes.
Taking the classic problem of finding straight lines as an
example, Hough transform can find the existence of straight
lines from a given distribution pattern of feature points. Sup-
pose that a straight line can be expressed by
y = ax + b
. All
feature points (
x, y
) on this line share the same parameters (
). From another perspective, a point (
x, y
) in feature space
can determine a straight line,
b = -xa + y,
in the parameter
space. Considering that these feature points share the same
parameters, straight lines determined by these feature points
will intersect into one point (
a, b
) in the parameter space, as
illustrated in Figure 2.
The parameter space is discretized into a two-dimensional
accumulate array by intervals. Then, the voting process can
be performed as follows. The accumulate array bins are ini-
tialized to zero. Then, for each feature point, the votes of bins
which are passed through by the straight line determined by
this feature point are increased. Consequently, array bins near
position (
a, b
) will have most of the votes, thereby forming a
Figure 1. Proportion of the first eight nearest neighbors in total
correct matches.
Figure 2. Hough transform uses the relationship between features and parameters to detect straight lines.
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