Thomas Brox, U.C.Berkeley
Andrés Bruhn, Saarland University
Motivation: Many computer vision tasks require point correspondences between images.
While in some of these fields, sparse point correspondences are sufficient,
many others, such as dynamical textures, motion segmentation, 3D motion
analysis, superresolution video, and action recognition, benefit enormously
from dense correspondence fields. Variational methods are particularly well
suited to compute dense optical flow fields, as they combine all available
data with prior assumptions in a sound optimization framework and even
allow for subpixel accuracy.
Goal: This course will provide a comprehensible introduction into the theoretical
background of recent state-of-the-art methods and shows the modelling
options that will allow the participants to adapt the model to their
specific needs. The course will also cover the numerics behind the models
which are decisive for implementation. The focus will be on efficiently
solving the very large linear or nonlinear systems with multigrid methods,
which allow to compute dense flow fields in real-time.
I. Variational Basics (Bruhn)
- Model Assumptions
- Minimzation via Euler-Lagrange
- Basic Numerics (Jacobi, Gauss-Seidel)
II. Modeling Aspects (Brox)
- Discontinuity-Preserving Smoothness Terms
- Robust Data Terms
- Image Features
- Structure Texture Decomposition
- Photometric Invariants
- Large Displacements
- Region Matching and HOG flow
III. Efficient Numerics (Bruhn)
- Linear Solvers
- Succesive Overrelaxation
- Linear Multigrid
- Nonlinear Solvers
- Nested Fixed Point Iteration
- Nonlinear Multigrid (Full Approximation Scheme)
- Implementations on Parallel Hardware
• T.Brox, C.Bregler, J.Malik
Large displacement optical flow.
IEEE Int. Conf. on Computer Vision and Pattern Recognition (CVPR 2009).
(integrates landmarks from region matching to handle large displacements)
• H.Zimmer, A.Bruhn, J.Weickert, L.Valgaerts, A.Salgado, B.Rosenhahn, HP.Seidel
Complementary optic flow.
Int. Conf. on Energy Minimization Methods in Computer Vision and Pattern
Recognition (EMMCVPR 2009).
(new complementary regularizer, top rank result in the Middlebury benchmark)
received the Ph.D. degree in computer science from the
Saarland University, Saarbrücken, Germany in 2005. During his studies,
he spent three months as a visiting researcher at the INRIA Sophia-
Antipolis, France. After his Ph.D., he joined the Computer Vision Group
at the University of Bonn, Germany, as a postdoctoral researcher. From
October 2007 to October 2008 he headed the Intelligent System Group at
the University of Dresden, Germany, as a temporary faculty member. He is
now a postdoctoral fellow in the Computer Vision Group of Jitendra Malik
at U.C. Berkeley.
The scientific work of Thomas Brox comprises about 60 papers in the fields
of segmentation, motion estimation, and tracking. He served on the program
commitees of ICCV, ECCV, and CVPR, and regularly reviews for all major
computer vision journals. In 2004 he received the Longuet-Higgins Best
Paper Award for his work on optical flow at the European Conference on
received a diploma degree in Computer Engineering from the University of
Mannheim, Mannheim, Germany, in 2001 and a Ph.D. degree in Computer
Science from the Saarland University, Saabrücken, Germany, in 2006.
After working as a postdoctoral researcher from 2006 to 2007, he
currently holds the position of an assistant professor in the
Mathematical Image Analysis Group at Saarland University,
Saarbrücken, Germany. His research
interests include optical flow estimation, stereo reconstruction, diffusion
filtering and fast numerical schemes for image processing and computer
vision. Dr. Bruhn served on the programme committee of ICCV, ECCV, ACCV,
and CVPR and regularly reviews for all major computer vision journals.
His publications received several awards, among them the 2004
Longuet-Higgins Best Paper Award of the European Conference on Computer Vision
(ECCV), the 2006 Olympus Prize of the German Pattern Recognition Society
(DAGM), the 2006 Outstanding Dissertation Award of the German Society of
Computer Science (GI), the Swiss Computer Science Society (SI), the
Austrian Computer Society (OCG) and the German Chapters of the ACM
(GChACM) as well as the 2006 Dr. Eduard Martin Prize of the Saarland
University. Moreover, he was nominated as one of two national candidates
for the 2008 Cor Baayen Award of the European Research Consortium for
Informatics and Mathematics (ERCIM).
PART I: Variational Basics
PART II: Modeling Aspects
PART III: Efficient Numerics
Andrés Bruhn /
September 23, 2009