Robotics and Computer Vision Lab

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저 자 Tae-Hyun Oh
학 회 KAIST
논문일시(Year) 2017
논문일시(Month) 5

제목: 사전 정보를 이용한 강인한 행렬 계수 최적화 

 

Committee: 

In So Kweon (Dept. of EE)

Jinwoo Shin (Dept. of EE)

Jong Chul Ye (Dept. of Bio and Brain Engineering, Dept. Mathematical Sciences)

Junmo Kim (Dept. of EE)

Yasuyuki Matsushita (Osaka University)

 

Abstract:

Low-rank matrix recovery arises from many engineering and applied science problems. Rank minimization is a crucial regularizer to derive a low-rank solution, which has attracted much attention. Since directly solving rank minimization is an NP-hard problem, its tightest convex surrogate has been solved instead. In literature, while the convex relaxation has proven that under some mild conditions, exact recoverability is guaranteed, i.e., the global optimal solution of the approximate problem matches the global optimal one of the original NP-hard problem, many real-world problems do not often satisfy these conditions. Furthermore, in this case, the optimal solution of the convex surrogate is departing from the true solution.

This is a problem caused by the approximation gap. Although many non-convex approaches have been proposed to reduce the gap, there has been no remarkable improvement. In this regard, I focus on the fact that the approaches have not exploited prior information according to the data generation procedure of each problem. In this dissertation, I leverage prior information, which naturally arises from each problem definition itself, so that performance degradation caused by the gap can be improved. The contributions of this dissertation are as follows.

(1) By proposing a soft rank constraint, the rank of a low-rank solution is encouraged to be close to the target rank. By virtue of this simple additional information, it properly deals with a deficient number of data regimes where the convex nuclear norm approach fails.

(2) I propose a method to learn priors from data in the empirical Bayesian manner. This method demonstrates the state-of-the-art performance. Surprisingly, the proposed method outperforms the matrix completion method, which assumes the perfect knowledge of exact outlier locations, without such prior knowledge.

(3) I extend the learning prior approach such that the prior information of rank and fractional outlier location is leveraged, i.e., robust matrix completion with rank prior. This further improves the success regimes of the algorithm.

The proposed methods are applied to the various real computer vision problems to demonstrate their practicality (in terms of quality and efficiency). The above three contributions have shown the fundamental performance improvement. This implies that the applicability range has widened far beyond at least the vast range of applications of the existing problems, e.g., PCA and matrix completion. Namely, the practicality of the low-rank approach has improved dramatically.


List of Articles
» Robust Low-rank Optimization with Priors
Tae-Hyun Oh
KAIST 2017 / 5
22. A Novel Low-Rank Constraint Method with the Sparsity Model for Moving Object Analysis
Tae-Hyun Oh
KAIST 2012 / 08
21. [Book] Metric Invariants for Camera Calibration: Designing algorithms from algebraic rank analysis
Jun-sik Kim, In So Kweon
LAP LAMBERT Academic Publishing (October 4, 2011) 2011 / 10
20. [BOOK] Catadioptric Vision for Robotic Applications
Jean-Charles Bazin, In So Kweon
LAMBERT Academic Publishing 2011 / 01
19. [Book] Object Identification and Categorization with Visual Context
Sungho Kim, In So Kweon
KAIST 2008 / 05
18. Hierarchical Graphical Model-based Methods for Object Identification and Categorization with Visual Context
Sungho Kim
KAIST 2007 / 02
17. Metric reconstruction from images using rank-deficient relations
Jun-sik Kim
KAIST 2006 / 02
16. Robust Correspondence Search under Photometric Variations and Image Ambiguity
Kukjin Yoon
KAIST 2006 / 02
15. Catadioptric vision based localization and mapping for indoor mobile robot
Gijeong Jang
KAIST 2005 / 08
14. Appearance-cloning : Photo-consistent 3D modeling from multi-view images
Howon Kim
KAIST 2004 / 08
13. Shot Detection and Temporal Interest Point for Event-based Clustering and its Application to Golf Videos
Seunghoon Han
KAIST 2004 / 08
12. High-speed automatic edge detection using pixel group statistics and fuzzy-based automatic thresholding
Dongsu Kim
KAIST 2003 / 02
11. Image-based Visual Servoing for Linear Path Control
Jaeseung Cho
KAIST 2002 / 08
10. Chromatic invariant based image retrieval for three dimensional objects
Jiyeun Kim
KAIST 2002 / 02
9. Mobile robot navigation using fuzzy based sensor fusion
Wangheon Lee
KAIST 2001 / 08
8. Robust and direct estimation of camera motion and 3-D structure from stereo image sequence
Seongkee Park
KAIST 2000 / 08
7. A biprism stereo camera system
Doohyun Lee
KAIST 2000 / 08
6. Robust motion estimation and statistical change detection in image sequences under time-varying illumination
Youngsu Moon
KAIST 2000 / 08
5. 3D structure recovery and motion segmentation using uncalibrated cameras
Jongeun Ha
KAIST 2000 / 02
4. Optimization-based approaches in computer vision
Dongjoong Kang
KAIST 1999 / 02
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