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a single structure. Hoff and Ahuja [17] constructed a disparity map by gathering the
information of a few quadratic patches.
From the next section, we are going to briefly summarise several important es-
tablished stereo matching algorithms. The performance of these schemes will be
demonstrated in the evaluation section, where the characteristics of each algorithm
can be clearly observed. First of all, we start from a flat surface detection algorithm
[12] where an improved random sampling census algorithm is integrated for bet-
ter estimates of planar surfaces. A segment based stereo matching algorithm using
belief propagation and self adapting dissimilarity measure will be introduced [8].
Afterwards, a connectivity based stereo matching algorithm is introduced. This ap-
proach integrates the stereo correspondence with shape segmentation in order to
reach higher accuracy than the classical approaches. Finally, a wide baseline stereo
corresponding algorithm using local descriptors is presented. Evaluation of these es-
tablished algorithms will be provided before conclusions and future work are given.
2
Maximum Likelihood Estimation for Flat Surface Detection
This planar determination algorithm starts with corner feature detection using two
neighboring frames in a monocular video sequence. Given the epipolar geometry
constraint, we then build up dense matching between these two groups of points of
interest using the sum squared of differences (SSD) correlation method. Assuming
a calibrated camera (used to collect this sequence), we then compute a depth map,
based on the estimated disparity map. If there is only one single flat surface in the
scene (this constraint can only be satisfied in a small image region in many appli-
cations), we can launch a RANSAC algorithm [18] to fit a plane to the available
three-dimensional points. This RANSAC operation is iterated in an expectation-
maximisation context for seeking global minimal errors, which is the main con-
tribution of our work. The algorithmic flowchart is illustrated in Fig. 1. Note that
the proposed strategy works in the presence of motion parallax. To retrieve planes
from uncalibrated scenes, a fast multiple-view reconstruction strategy, based on the
algorithm presented here, will be explored in a future work.
2.1
Estimation of a Depth Map
Before a plane fitting scheme starts, 3-D point sets need to be generated based on
the 2-D image inputs. Of two neighboring images, we consider the later image is
the shifted one from the previous image. Given a shift (
y
) and an image point
(
x
,
y
) in a previous frame, the auto-correlation function for similarity check across
frames is defined as
c
(
x
,
y
)=
x
,
y
)]
2
,where
I
(
) denotes
the image function and (
x
i
,
y
i
) are the image points in the window
W
(Gaussian)
centred at (
x
,
y
). The shifted image can be approximated by a Taylor expansion as
follows,
I
(
x
i
+
∑
W
[
I
(
x
i
,
y
i
)
−
I
(
x
i
+
x
,
y
i
+
·
I
(
x
i
,
y
i
)+[
I
x
(
x
i
,
y
i
)
,
I
y
(
x
i
,
y
i
)]
,where
I
x
(
x
x
,
y
i
+
≈
·
y
)
) and
y
I
y
(
·
) denote the partial derivations along
x
and
y
, respectively. Eventually, we have
