立体视觉结构恢复：Dhond 1989年综述
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"Dhond的经典SfM（结构来自立体）文献回顾-1989年，主要讨论了从立体图像中提取三维结构的技术进展。"
这篇文章是IEEE Transactions on Systems, Man, and Cybernetics在1989年11月/12月发表的一篇综述性文章，由Umesh R. Dhond（学生会员，IEEE）和J.K. Aggarwal（院士，IEEE）共同撰写。文章的主题是“结构来自立体：一个回顾”，主要关注的是立体视觉中的对应关系建立，以提取场景的三维结构。
立体视觉（Stereo Vision），或称为结构来自运动（Structure from Motion，SfM），是一种通过分析两幅或多幅图像来恢复场景三维信息的技术。在这篇文章中，作者回顾了当时的主要发展，将立体算法分为不同的类别，这些类别基于图像几何差异、匹配基本元素以及所使用的计算结构。
文章讨论了以下核心概念：
1. **图像几何**：研究了不同算法如何处理图像间的几何关系，例如视差、基线和相机参数等。
2. **匹配原理**：分析了用于寻找对应点的不同策略，如特征匹配、像素级比较和模板匹配等方法。
3. **计算结构**：探讨了各种算法的计算复杂性和实现结构，包括分治法、动态规划和优化方法等。
4. **性能评估**：对这些立体技术在不同类型测试图像上的表现进行了评价，可能包括图像质量、匹配精度和计算效率等方面。
5. **未来研究方向**：指出了可能的研究趋势，可能涉及到更高效的匹配算法、鲁棒性增强、实时处理能力和对复杂环境的适应性等。
在1989年的背景下，这篇文章为立体视觉领域提供了一个重要的里程碑，总结了当时的最佳实践，并为后来的研究者提供了参考框架。由于计算机视觉领域的快速发展，尽管这篇文章较早，但它仍然是理解早期立体匹配和三维重建技术发展的重要资源。随着深度学习和人工智能的兴起，现代SfM方法已经远远超出了这个时代的范畴，但Dhond和Aggarwal的工作为后续的研究奠定了基础。
DHOND
AND
AGGARWAL: STRUCTURE
FROM
STEREO-A
REVIEW
1493
the filtered images are found by scanning them along lines
perpendicular to the orientation of the mask.
3)
For each
mask size, matching takes place between the zero-crossing
segments extracted from each filtered image output that
are of the same sign and roughly the same orientation.
Local matching ambiguities are resolved by considering
the disparity sign of nearby unambiguous matches.
4) Matches obtained from wider masks control vergence
movements aiding matches among output of smaller masks;
5)
The correspondence results are stored in a dynamic
buffer called the 2.5-D sketch.
Marr and Poggio [41] formulate two basic rules for
matching left- and right-image descriptions. Each item in
an image can be assigned to one and only one disparity
value (uniqueness). Secondly, matter is cohesive. Hence
disparity varies smoothly almost everywhere, except where
depth discontinuities occur at surface boundaries (continu-
ity).
B.
Grimson’s Implementation
Grimson
[
191 implemented the computational theory of
Marr and Poggio [41] and addressed certain implementa-
tion details that were not covered earlier by the Marr-
Poggio theory.
1)
Feature Extraction:
Marr and Hildreth [39] have
shown theoretically that, provided two simple conditions
on the image intensity function in the neighborhood of an
edge are satisfied, intensity changes occurring at a particu-
lar scale may be detected by locating the zero-crossings in
the output of the
v2G
(Laplacian of Gaussian) filter.
Instead of convolving each image with
12
directional
DOG
operators, each of which yield an approximation to
the second directional derivative, Grimson
[
191 used the
Laplacian of Gaussian
(v2G)
operator and grouped the
zero-crossing points in 12 directional bins. The precise
form of the operator is given in polar coordinates
(r,
0)
by
where
U
is the Gaussian space-constant. This is a rotation-
ally symmetric function shaped like an inverted Mexican
hat (Fig.
3).
The width of the central negative region is
given by
w2-D
=
2au. Grimson used three [20] or four
[19] different sizes
of
filters for his images.
2)
Matching:
The algorithm begins with images filtered
by the largest filters because the reduced density of zero-
crossings makes matching easier. The overall matching
strategy of Grimson [19] uses a coarse-to-fine iterative
approach with disparities found at coarser resolutions used
to guide match-point search at finer resolutions. Marr [38],
[41] studied the probability distribution of the interval
between adjacent zero-crossings of the same sign obtained
from the convolution of random dot stereograms with the
Laplacian of Gaussian filter. The results indicated that
if
the disparity between the images is less than
+(w/2),
a
search for matches within the range
,(w/2)
will yield
only the correct match with probability
0.95.
However the
Fig.
3.
2-D
Laplacian
of
Gaussian.
alternate strategy of using a search space with range
f
o
is
used by Grimson [19] since it allows one to search for
matches over a larger disparity range and yet get unam-
biguous and correct matches with probability
0.5.
In
Grimson’s implementation [19] for each zero crossing
PL(x, y)
in the left image, possible candidate matches
P;(x’,
y)
are searched for along the epipolar line in the
right image such that,
x
+
d,
-
<
x’<
x
+
d,
+
(2)
as shown in Fig. 4(a), where
d,
is the estimated disparity
and
w
(
=
2au) is the width of the
LOG
filter. Zero-cross-
ings in the left and right images having the same contrast
sign and approximately the same orientation (within
k
30’)
are matched. If only one match is found within the
+w
region, then that match is accepted as unambiguous, and
the disparity is recorded.
3)
Disambiguation
of
multiple matches:
If more than one
match is found within the
+
w
region, then the one having
disparity of the same type (convergent, divergent, or zero)
as the dominant disparity in the neighborhood is accepted.
Otherwise the match at that point is left ambiguous. This
can be regarded as the pulling effect which is described in
the psychophysical experiments of Julesz and Chang [32].
Each 2-D array of matched results is scanned and if the
percentage of matched points is
<
0.7 then all matches in
that region are discarded.
C. Grimson’s Modified Implementation
of
Marr
-
Poggio Theory
Grimson’s earlier implementation [19] of the Marr-
Poggio theory [41] imposes a regional continuity check on
disparity. Later, Grimson
[20]
highlights some of the prob-
lems associated with the earlier implementation of the
Marr-Poggio theory and presents a modified implementa-
tion.
1)
Figural Continuity:
Grimson’s implementation
[
191 of
the Marr-Poggio theory [41] used a regional continuity
check on disparity in order to validate the matches.
Grimson
[20]
observed that this caused difficulties in prop-
agation of disparity at occluding boundaries between ob-
jects and along thin elongated surfaces. Elsewhere the
matched feature points tended to form extended contours.
Hence the figural continuity constraint of Mayhew and
Frisby [44] that required continuity of disparity along
contours was deemed more appropriate.
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