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Keywords
(7)
Cost Function
Dynamic Programming Algorithm
Feature Extraction
Fixed Cost
Normal Distribution
Relative Position
Maximum Likelihood
Related Publications
(71)
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A Maximum Likelihood Stereo Algorithm
A Maximum Likelihood Stereo Algorithm,10.1006/cviu.1996.0040,Computer Vision and Image Understanding,Ingemar J. Cox,Sunita L. Hingorani,Satish B. Rao,
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A Maximum Likelihood Stereo Algorithm
(
Citations: 314
)
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Ingemar J. Cox
,
Sunita L. Hingorani
,
Satish B. Rao
,
Bruce M. Maggs
A stereo algorithm is presented that optimizes a
maximum likelihood
cost function. The
maximum likelihood
cost function
assumes that corresponding features in the left and right images are normally distributed about a common true value and consists of a weighted squared error term if two features are matched or a (fixed) cost if a feature is determined to be occluded. The stereo algorithm finds the set of correspondences that maximize the
cost function
subject to ordering and uniqueness constraints. The stereo algorithm is independent of the matching primitives. However, for the experiments described in this paper, matching is performed on the $cf4$individual pixel intensities.$cf3$ Contrary to popular belief, the pixelbased stereo appears to be robust for a variety of images. It also has the advantages of (i) providing adensedisparity map, (ii) requiringnofeature extraction, and (iii)avoidingthe adaptive windowing problem of areabased correlation methods. Because
feature extraction
and windowing are unnecessary, a very fast implementation is possible. Experimental results reveal that good stereo correspondences can be found using only ordering and uniqueness constraints, i.e., withoutlocalsmoothness constraints. However, it is shown that the original
maximum likelihood
stereo algorithm exhibits multiple global minima. The
dynamic programming algorithm
is guaranteed to find one, but not necessarily the same one for each epipolar scanline, causing erroneous correspondences which are visible as small local differences between neighboring scanlines. Traditionally, regularization, which modifies the original cost function, has been applied to the problem of multiple global minima. We developed several variants of the algorithm that avoid classical regularization while imposing several global cohesiveness constraints. We believe this is a novel approach that has the advantage of guaranteeing that solutions minimize the original
cost function
and preserve discontinuities. The constraints are based on minimizing the total number of horizontal and/or vertical discontinuities along and/or between adjacent epipolar lines, and local smoothing is avoided. Experiments reveal that minimizing the sum of the horizontal and vertical discontinuities provides the most accurate results. A high percentage of correct matches and very little smearing of depth discontinuities are obtained. An alternative to imposing cohesiveness constraints to reduce the correspondence ambiguities is to use more than two cameras. We therefore extend the two camera
maximum likelihood
toNcameras. TheNcamera stereo algorithm determines the “best” set of correspondences between a given pair of cameras, referred to as the principal cameras. Knowledge of the relative positions of the cameras allows the 3D point hypothesized by an assumed correspondence of two features in the principal pair to be projected onto the image plane of the remainingN− 2 cameras. TheseN− 2 points are then used to verify proposed matches. Not only does the algorithm explicitly model occlusion between features of the principal pair, but the possibility of occlusions in theN− 2 additional views is also modeled. Previous work did not model this occlusion process, the benefits and importance of which are experimentally verified. Like other multiframe stereo algorithms, the computational and memory costs of this approach increase linearly with each additional view. Experimental results are shown for two outdoor scenes. It is clearly demonstrated that the number of correspondence errors is significantly reduced as the number of views/cameras is increased.
Journal:
Computer Vision and Image Understanding  CVIU
, vol. 63, no. 3, pp. 542567, 1996
DOI:
10.1006/cviu.1996.0040
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Citation Context
(207)
...Dynamic programming (DP) approaches to stereo matching have been widely used [
9
, 10]...
Carlos D. Castillo
,
et al.
WideBaseline Stereo for Face Recognition with Large Pose Variation
...Dynamic programming has been used widely as a semiglobal optimization method for the estimation of disparity d along image scanlines [
9
], [10]...
...In the later, for each cell in the search grid there are only three candidate matches preceding the current cell [
9
]...
Lazaros Nalpantidis
,
et al.
Robust 3D vision for robots using dynamic programming
...epipolar line. Second one is ordering constraint which determines the order of neighboring correspondences [
9
]...
ChangIl Kim
,
et al.
Fast Stereo Matching of Feature Links
...In the area of dense stereo, however (e.g., [17], [
8
], [4], [6], [15], [20]), the issue of restricting attention to a volume, with a limited range of depth or equivalently disparity, has not been addressed...
Ankur Agarwal
,
et al.
Dense Stereo Matching over the Panum Band
...programming Baker, Binford [23] Belhumeur [24, 11] Belhumeur, Mumford [25] Cox, Hingorani, Rao, Maggs [
26
] Dhond, Aggarwal [27] Geiger, Ladendorf, Yuille [28] Intille, Bobick [29] Bobick, Intille [30] Ohta, Kanade [31] Birchfield, Tomasi [32] x One dimensional discrete approach to the smoothness (inside the scanlines) x Dependent upon the ordering constraint x Errors with low texture regions (horizontal streaks) and thin foreground objects ...
Miran Gosta
,
et al.
Accomplishments and challenges of computer stereo vision
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Citations
(314)
Image match algorithm through correlation coefficient computation in micro stereovision
Wang YueZong
,
Yang CaiZhi
,
Yin ShuJuan
,
Yin WenJia
Published in 2011.
WideBaseline Stereo for Face Recognition with Large Pose Variation
Carlos D. Castillo
,
David W. Jacobs
Conference:
Computer Vision and Pattern Recognition  CVPR
, pp. 537544, 2011
Robust 3D vision for robots using dynamic programming
Lazaros Nalpantidis
,
John Kalomiros
,
Antonios Gasteratos
Conference:
IEEE International Workshop on Imaging Systems and Techniques  IST
, 2011
Fast Stereo Matching of Feature Links
ChangIl Kim
,
SoonYong Park
Conference:
International Conference on 3D Imaging, Modeling, Processing, Visualization and Transmission  3DIMPVT
, 2011
Dense Stereo Matching over the Panum Band
(
Citations: 2
)
Ankur Agarwal
,
Andrew Blake
Journal:
IEEE Transactions on Pattern Analysis and Machine Intelligence  PAMI
, vol. 32, no. 3, pp. 416430, 2010