Global Optimization Techniques in Camera-Robot Calibration
Type of document
disertační práceAuthor
Heller, Jan
Supervisor
Pajdla, Tomáš
Field of study
Umělá inteligence a biokybernetikaStudy program
Elektrotechnika a informatikaInstitutions assigning rank
České vysoké učení technické v Praze. Fakulta elektrotechnická. Katedra kybernetikyMetadata
Show full item recordAbstract
The need to relate measurements made by a camera to a different known coordinate system
arises in many engineering applications. Historically, it appeared for the first time in the
connection with cameras mounted on robotic systems. This problem is commonly known as
hand-eye calibration. In this thesis, we study the problem of hand-eye calibration as well as
a problem closely connected to it—the problem of robot-world calibration. The first objective
of this work is to apply recent results in mathematical optimization to provide globally
optimal solution to these problems. The second objective is to formulate and study these
problems as minimization problems under some geometrically meaningful error measures
using image measurements directly. We also study global optimizers in situation where image
measurements are not available using the classical problem formulations. The solutions
presented in this thesis are compared to existing methods and validated by both synthetic and
real world data experiments.
In the first part of the thesis, we survey the state of the art of the camera-robot calibration
as well as of the main concepts of the geometrical computer vision. Further, we review
several results in the globally optimization techniques and their application in the computer
vision.
Next, we formulate the problem of hand-eye calibration as a minimization problem under
some geometrically meaningful error measures. We provide two solutions; the first solution
employs a Structure-from-Motion approach and the Second Order Cone Programming optimization
and the second one uses the Brand-and-Bound optimization strategy. Both solutions
provide globally optimal minimizers and work with image measurements directly, instead of
using them as a pre-step for explicitly calculating camera poses. Using a similar approach,
we also formulate a minimization task for the robot-world calibration problem. This time, to
solve the task we use the method of Linear Matrix Inequality relaxations.
Further, we investigate the problem of hand-eye calibration in situations, where the information
about the rotation of the robot is not known. This problem arises when the robot
is not calibrated or the information from the robot is not available. We use the method of
Gröbner basis to deal with this scenario.
Finally, we revisit the classical formulation of the hand-eye and robot-world calibration.
Using the method of Linear Matrix Inequality relaxations, we provide several global optimizers
in situations, where image measurements are not available and the calibration has to
be estimated from robot and camera poses only.
Collections
- Disertační práce - 13000 [713]
The following license files are associated with this item: