Stephan Scholze
By requiring chromatic similarity on at least on side, the set of geometrically possible match candidates {1’} gets reduced
substantially. For all geometrically and chromatically possible pairs we now compute the 3D reconstruction of the (finite)
3D line segment, stemming from the common part of both involved 2D line segments. In the next section, we will
investigate these remaining candidates in more detail.
3.4 Restricting the initial match hypotheses
A line segment l' in the second view can only be the line segment corresponding to a given line segment l in the first view
provided l/ and 1 have similar chromatic properties at least on one side. The chromatic similarity is only demanded for one
(corresponding) side of the flanking regions, since the line segment might be an occluding edge for one of its neighboring
3D patches. We now investigate this initial set of match candidates in more detail by computing the normalized cross-
correlation in the a*-b*-bands. In Figure (4, a) a possible configuration of two line segments (1, l^) and their corresponding
3D line reconstruction is depicted. The epipolar relation generates a point-wise one-to-one correspondence between the
corresponding lines 1 and l' in the two views; provided 1’ is not an epipolar line in the second view. Explicitly, a point p
‘on line 1 corresponds to the point p’ on 1’ in the second image, which is the intersection of 1’ with the epipolar line L prof
p in the second image.
(a)
(b)
. 3D line reconstruction
Figure 4: (a): Possible configuration when computing the 3D information for a candidate pair (1,1). To compute the
cross-correlation measure, the extent of the reconstructed 3D line segment is chosen to be the common part of the back-
projections of 1 and l'. Note the length of the common pieces in the two views can differ, due to perspective foreshortening.
(b): Detail of the two-sided image area A = { A;, A, } used for correlation and the two-sided correlation window W =
{W1, W,}-.
To be meaningful, the cross-correlation has to be computed over corresponding image regions. For each line segment pair
(1,1) forming a possible match, we therefore first determine the corresponding (two-sided) i image areas A, A’ in each
view. For example, the outline of the right image area A, in image one, belonging to line segment 1 is given by: the
backprojection b of the common part of the 3D line reconstruction onto 1, the line segment b,. parallel to b, and the two
line segments c; ,. and c» ,. on the epipolar lines through the endpoints of b.
Choosing the orientation of the sides c, ; /r and c»,;, to be given by the epipolar lines turns out to be a reasonable
approximation for restricting the image areas in the different views to one corresponding roof patch in the 3D scene.
See below for cases, where the angle between the line segment and the epipolar lines from the second view is too small.
If we further assume that the epipolar lines determining c, ; /r and c5, / are parallel to each other, which is a good
approximation in the given framework, then the extraced image areas A, A’ become parallelograms.
The length ¢;/, = |c;, ir | = |c2,1/,| is variable. During the examination of a putative pair, the length c;,,. of one of the
two image areas A, A’ is changed over a given interval to handle possible foreshortenings occurring to planar surfaces
under projective perspective.
We obtain the pixels in the image areas A, A” by first transforming the left and right neighborhoods of 1 and 1’ in an axis
aligned coordinate system, the same way as described in Section (3.2.1). Again, we ensure the area is not overlapping
neighboring contours. During the affine transformation we additionally introduce a length scaling, taking into account
the different length of the common pieces b and b' of the projected 3D line segment in the two images. The scaling
is adjusted to map the transformed regions onto rectangles of the same length. Thus we make the implicit one-to-one
correspondence induced from epipolar geometry directly accessible.
820 International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B3. Amsterdam 2000.
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