Graphics Reference
In-Depth Information
2.2
Calculation of Fundamental Matrix
Benefitting from the feature detecting and matching of SIFT algorithm, matching
points set
M
1
={
x
1
,x
2
}between the first and third view is acquired, as well as set
M
2
={
x
2
,x
3
} between the second and third view, and set
M
={
x
1
,x
2
,x
3
}among in all of the
three views. Then the fundamental matrices
F
12
and
F
23
are estimated by RANSAC
algorithm. Calculating epipolar lines of matching points in set
M
,
l
ij
represents the
epipolar line on the
i
th
image of the
projection point on the
j
th
image and it is written
in Form of homogeneous coordinates,
y
i
is the homogeneous coordinates of points in
the
i
th
view. The next step is to acquire the intersection point of epipolar lines, and
the distance between matching point and that intersection also be calculated. Finally,
those initial matching points sets
M
1
and
M
2
are updated by new sets
M
1
'
={
x
1
,x
2
}
and
M
2
'
={
x
2
,x
3
}.
Using the new matching set, more correct result of fundamental matrix is acquired.
To obtain more precise result, M-Estimators algorithm is used after that. The basic
theory of M-estimators is to make a guarantee that the probability of being reduced is
larger than of producing error for mismatches. By this way, the precision of the
computation is improved via reducing the influence of data containing noise. The
whole process of calculating fundamental matrix is shown below as figure 4.
3
Optimization and Interpolation of 3-D Point Cloud
3.1
Reconstruction of 3-D Point Cloud
Camera intrinsic parameters could be acquired by camera self-calibration. As intrinsic
parameters known, fundamental matrix is upgraded to essential matrix. Taking
decomposition of essential matrix, the relative extrinsic parameters between adjacent
two views are obtained. What's more, the projection matrices and are recovered as
well. Form projection process, equations could be built:
x
=
PX
and
x'
=
P'X
.
X
are the
homogeneous coordinates of a 3-space point. Satisfied with equations above at the
same time, simultaneous equations could be draw as equations (1)
P
1
−
x
1
P
3
i
2
2
3
P
−
x
P
i
X
=
0
(1)
i
1
1
3
P
′
−
x
′
P
′
i
′
2
′
2
′
3
P
−
x
P
i
i
represents the
i
th
point,
x
1
is the first element of point, is the first row of matrix.
Projection matrix of the third view also could be calculated by the back calculation of
equations (1) for the points ,which have projective points in all three views.
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