Robust Optimization Techniques in Computer Vision
This half-day tutorial will be given in conjunction with the European Conference on Computer Vision 2014 in Zurich, Switzerland, in the morning of 7 September 2014. It is a newly developed course including both classical methods such as RANSAC and more recent approaches based on branch & bound and convex optimization for robust model estimation and the problem of handling outliers in computer vision.
The tutorial is organized by
- Olof Enqvist, Chalmers University of Technology,
Fredrik Kahl, Chalmers University of Technology and Lund University,
Richard Hartley Australian National University and
National ICT Australia (NICTA).
Many important problems in computer vision, such as structure from motion and image
registration, involve model estimation in presence of a significant number of outliers. Due
to the outliers, simple estimation techniques such as least squares perform very poorly.
To deal with this issue, vision researchers have come up with a number of techniques
that are robust to outliers, such as Hough transform and RANSAC (random sample
consensus). These methods will be analyzed with respect to statistical modeling, worst-case
and average exectution times and how to choose the balance between the number
of outliers and the number of inliers. Apart from these classical techniques we will
also describe recent advances in robust model estimation. This includes sampling based
techniques with guaranteed optimality for low-dimensional problems and optimization
of semi-robust norms for high-dimensional problems. We will see how to solve low-dimensional
estimation problems with over 99% outliers in a few seconds, as well as how
to detect outliers in structure from motion problems with thousands of variables.
Slides: Session 1, Session 2 in ppt with animations, Session 2 in pdf without animations, Session 3.
- Session 1: Statistical models of robust regression. Introduction, motivations and applications. Relation to robust statistics. Occasional vs. frequent large-scale measurement noise (outliers). Low- vs. high-dimensional model estimation. Optimal vs. approximate methods. Multiple model fitting. Computational complexity.
- Session 2: Robust estimation with low-dimensional models. Hough transform. M-estimators. RANSAC and its variants. Branch and bound methods. Optimal methods. Fast approximate methods. Applications: Feature-based registration, multiple-view geometry, image-based localization.
- Session 3: Robust estimation with high-dimensional models. Robust norms and convex optimization. L_infinity-norm optimization with outliers. L_1-norm optimization on manifolds.
Applications: Multiple-view geometry, large-scale structure-from-motion and subspace estimation.
Half-day course. Time: Morning, 7 September, 2014.
There will be three sessions, following the topic description above.
We target both beginners in the field of computer vision and more experienced researchers interested in learning more about recent advances.
All course notes and slides will be distributed to the attendees.
Olof Enqvist got his MSc degree from Linköping University in 2006, and a PhD in mathematics from Lund University in 2011. He currently works as assistant professor at Chalmers University in Göteborg, Sweden. A large part of his research has been dealing with outliers and optimization in computer vision problems and he has published several papers on the topic at ECCV, ICCV and CVPR.
Fredrik Kahl received his MSc degree in computer science in 1995 and his PhD in mathematics in 2001, both from Lund
University, Sweden. He was a postdoctoral research fellow at the Australian National University in 2003-2004 and at the University of
California, San Diego in 2004-2005. He currently has a joint professor position at Chalmers University of Technology and Lund University.
Primary research areas include geometric computer vision problems, medical image analysis and optimization methods.
In 2005, he was awarded the Marr Prize for work on multiple view geometry, in 2008 he obtained an ERC Starting Independent Research Grant from the European Research Council,
and the same year, he received a Future Research Leader Grant from the Swedish Foundation for Strategic Research.
Richard Hartley is currently with the Computer Vision Group at the Research
School of in- formation Sciences and Engineering (RSISE), Australian National
University (ANU), Canberra, and also with National ICT Australia (NICTA), a
government-funded research institute. He worked in the areas computer-aided electronic
design system, described in his book Digit Serial Computation, and computer
vision, particularly in multiview geometry. He is the winner of the Significant Senior
Computer Vision Researcher Award at ICCV 2011. He was the program chair
for ICCV 2013 (Sydney) and a fellow of the Australian Science Academy.