Details
| Original language | English |
|---|---|
| Title of host publication | Computer Vision, ACCV 2010 |
| Subtitle of host publication | 10th Asian Conference on Computer Vision, Revised Selected Papers |
| Pages | 464-476 |
| Number of pages | 13 |
| Publication status | Published - 2011 |
| Event | 10th Asian Conference on Computer Vision, ACCV 2010 - Queenstown, New Zealand Duration: 8 Nov 2010 → 12 Nov 2010 |
Publication series
| Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
|---|---|
| Number | PART 2 |
| Volume | 6493 LNCS |
| ISSN (Print) | 0302-9743 |
| ISSN (electronic) | 1611-3349 |
Abstract
Computing a 1-dimensional linear subspace is an important problem in many computer vision algorithms. Its importance stems from the fact that maximizing a linear homogeneous equation system can be interpreted as subspace fitting problem. It is trivial to compute the solution if all coefficients of the equation system are known, yet for the case of incomplete data, only approximation methods based on variations of gradient descent have been developed. In this work, an algorithm is presented in which the data is embedded in projective spaces. We prove that the intersection of these projective spaces is identical to the desired subspace. Whereas other algorithms approximate this subspace iteratively, computing the intersection of projective spaces defines a linear problem. This solution is therefore not an approximation but exact in the absence of noise. We derive an upper boundary on the number of missing entries the algorithm can handle. Experiments with synthetic data confirm that the proposed algorithm successfully fits subspaces to data even if more than 90% of the data is missing. We demonstrate an example application with real image sequences.
ASJC Scopus subject areas
- Mathematics(all)
- Theoretical Computer Science
- Computer Science(all)
- General Computer Science
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Computer Vision, ACCV 2010: 10th Asian Conference on Computer Vision, Revised Selected Papers. PART 2. ed. 2011. p. 464-476 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 6493 LNCS, No. PART 2).
Research output: Chapter in book/report/conference proceeding › Conference contribution › Research › peer review
}
TY - GEN
T1 - A linear solution to 1-dimensional subspace fitting under incomplete data
AU - Ackermann, Hanno
AU - Rosenhahn, Bodo
PY - 2011
Y1 - 2011
N2 - Computing a 1-dimensional linear subspace is an important problem in many computer vision algorithms. Its importance stems from the fact that maximizing a linear homogeneous equation system can be interpreted as subspace fitting problem. It is trivial to compute the solution if all coefficients of the equation system are known, yet for the case of incomplete data, only approximation methods based on variations of gradient descent have been developed. In this work, an algorithm is presented in which the data is embedded in projective spaces. We prove that the intersection of these projective spaces is identical to the desired subspace. Whereas other algorithms approximate this subspace iteratively, computing the intersection of projective spaces defines a linear problem. This solution is therefore not an approximation but exact in the absence of noise. We derive an upper boundary on the number of missing entries the algorithm can handle. Experiments with synthetic data confirm that the proposed algorithm successfully fits subspaces to data even if more than 90% of the data is missing. We demonstrate an example application with real image sequences.
AB - Computing a 1-dimensional linear subspace is an important problem in many computer vision algorithms. Its importance stems from the fact that maximizing a linear homogeneous equation system can be interpreted as subspace fitting problem. It is trivial to compute the solution if all coefficients of the equation system are known, yet for the case of incomplete data, only approximation methods based on variations of gradient descent have been developed. In this work, an algorithm is presented in which the data is embedded in projective spaces. We prove that the intersection of these projective spaces is identical to the desired subspace. Whereas other algorithms approximate this subspace iteratively, computing the intersection of projective spaces defines a linear problem. This solution is therefore not an approximation but exact in the absence of noise. We derive an upper boundary on the number of missing entries the algorithm can handle. Experiments with synthetic data confirm that the proposed algorithm successfully fits subspaces to data even if more than 90% of the data is missing. We demonstrate an example application with real image sequences.
UR - http://www.scopus.com/inward/record.url?scp=79952501620&partnerID=8YFLogxK
U2 - 10.1007/978-3-642-19309-5_36
DO - 10.1007/978-3-642-19309-5_36
M3 - Conference contribution
AN - SCOPUS:79952501620
SN - 9783642193088
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 464
EP - 476
BT - Computer Vision, ACCV 2010
T2 - 10th Asian Conference on Computer Vision, ACCV 2010
Y2 - 8 November 2010 through 12 November 2010
ER -