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Keywords
(3)
Camera Motion
Factorization Method
Singular Value Decomposition
Related Publications
(8)
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Shape and motion from image streams under orthography: a factorization method
Shape and motion from image streams under orthography: a factorization method,10.1007/BF00129684,International Journal of Computer Vision,Carlo Tomasi
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Shape and motion from image streams under orthography: a factorization method
(
Citations: 1100
)
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Carlo Tomasi
,
Takeo Kanade
Inferring scene geometry and
camera motion
from a stream of images is possible in principle, but is an illconditioned problem when the objects are distant with respect to their size. We have developed a
factorization method
that can overcome this difficulty by recovering shape and motion under orthography without computing depth as an intermediate step.An image stream can be represented by the 2FxP measurement matrix of the image coordinates of P points tracked through F frames. We show that under orthographic projection this matrix is of rank 3.Based on this observation, the
factorization method
uses the singularvalue decomposition technique to factor the measurement matrix into two matrices which represent object shape and camera rotation respectively. Two of the three translation components are computed in a preprocessing stage. The method can also handle and obtain a full solution from a partially filledin measurement matrix that may result from occlusions or tracking failures.The method gives accurate results, and does not introduce smoothing in either shape or motion. We demonstrate this with a series of experiments on laboratory and outdoor image streams, with and without occlusions.
Journal:
International Journal of Computer Vision  IJCV
, vol. 9, no. 2, pp. 137154, 1992
DOI:
10.1007/BF00129684
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Citation Context
(742)
...Because the hierarchical generative model we propose multiplies signals related to form and motion, the inference of these properties depends on each other and can be considered as a factorization problem (Tomasi & Kanade,
1992
; Koenderink & Van Doorn,
1997
; Memisevic & Hinton,
2007
)...
Charles F. Cadieu
,
et al.
Learning IntermediateLevel Representations of Form and Motion from Na...
...While the multilinear relationships described in this body of work greatly expanded conceptual understanding, in practice the most successful line of investigation for 3D reconstruction has been the application of factorization approaches to structure recovery beginning with the seminal work by Tomasi and Kanade in [
16
]...
...The key observation in [
16
], [17] was the rank 3 theorem...
...While this framework was seminal, the algorithm to estimate the metric structure of the nonrigid object did not have the stability of the rigid factorization approach of Tomasi and Kanade [
16
]...
...In order to estimate Qkj, orthonormality constraints of camera rotations Ri can be exploited, following an approach similar to [
16
]...
Ijaz Akhter
,
et al.
Trajectory Space: A Dual Representation for Nonrigid Structure from Mo...
...These include factorization methods [
28
], which in some cases can solve SfM in closed form...
David Crandall
,
et al.
Discretecontinuous optimization for largescale structure from motion
...The basic idea is straightforward: For each camera, we can apply the factorization algorithm (e.g., [
48
]) to reconstruct the observed 3D points, and the two reconstruction results differ by an unknown linear transform...
...Therefore, the 3D points Xj can be computed by factorizing the data matrices M1; M2 [
48
]...
S M Nejhum Shahed
,
et al.
HigherDimensional Affine Registration and Vision Applications
...that one can solve for the shape using, say the factorization scheme of [
19
], the shape recovery is trivial even in the presence of occlusion...
Appu Shaji
,
et al.
Resolving occlusion in multiframe reconstruction of deformable surface...
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Sort by:
Citations
(1100)
Learning IntermediateLevel Representations of Form and Motion from Natural Movies
Charles F. Cadieu
,
Bruno A. Olshausen
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Neural Computation  NECO
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