Fredrik Kahl, Research

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Fredrik Kahl, Research

I am an applied mathematician interested in optimization and modelling, especially for applications in computer vision, pattern recognition and medical imaging.

Latest news: We received the Best Paper Award at OMNIVIS 2011 for Non-Sequential Structure from Motion.

See also the research of my group. Research interests include:

Optimization. We seek to improve general optimization methods, for discrete and continuous optimization problems, as well as hybrid problems. For optimization methods applied to geometric reconstruction problems, see Multiple View Geometry.

Selected papers:
Multiple View Geometry. While standard algorithms in computer vision suffer from either non-optimality (for example, the 8-point algorithm) or local minima (for example, bundle adjustment) - or a combination of both - we pursue the goal of globally optimal solutions.

Note that the paper Globally Optimal Estimates for Geometric Reconstruction Problems received the ICCV 2005 Marr Prize Award.
Critical curves and surfaces. In the early 20th century it was noted that for two images of certain scene configurations, there is not a unique solution to the reconstruction problem. Together with Richard Hartley, we have done a complete classification of all such critical configurations. These results will still be true in 100 years even though noone tends to read them today...
Matching and registration. The matching problem is to find corresponding points in different images. One of the main difficulties is to be able to handle large amount of outliers, that is, false matches.
Medical image analysis. The need for reliable methods for handling the massive amount of data involved in medical imaging is a great challenge.
Applications.
Image segmentation. This is an interesting, variational problem, both from a modelling and an optimization perspective, but also an important tool in medical imaging.
Photometric stereo. The appearance of a surface is dependent on the incident angle of light. By varying the light source direction, it is possible to recover the surface geometry using multiple images from a static camera.
Surface Reconstruction. Constructing 3D models from images is a key problem and there is a lot of interesting theory.
Auto-calibration and critical motions. Auto- (or self-) calibration is the use of calibration constraints, e.g., constant intrinsic parameters, in order to recover Euclidean scene information. However, in certain situations auto-calibration fails to recover unique Euclidean structure, caused by critical motions of the camera.
Deformable structure and motion. The world is not a rigid place, and there is a need for algorithms which can handle non-rigid objects as well.
Structure and motion from geometric features. Most reconstruction algorithms use only point features. Approaches using lines, conics and other more complex scene primitives are developed.
Previously, I have been involved in the following European research projects:
- LAVA - Learning for Adaptive Visual Assistance - is about applying learning techniques to vision tasks.
- VISIRE is directed towards reconstruction of indoor environments (for example, complete reconstructions of museums) from digital video.
- INVIEW involves view synthesis and view interpolation as well as estimation of surface properties in order to generate fly-through sequences of an arbitrary scene.
- CUMULI stands for Computational Understanding of MULtiple Images.
See also publications.

Publisher: Fredrik Kahl, fredrik@maths.lth.se
Last updated: July 29, 2008