Short on camera geometry and camera calibration
2010 (English)Report (Other academic)
We will present the basic theory for the camera geometry. Our goal is camera calibration and the tools necessary for this. We start with homogeneous matrices that can be used to describe geometric transformations in a simple manner. Then we consider the pinhole camera model, the simplified camera model that we will show how to calibrate.
A camera matrix describes the mapping from the 3D world to a camera image. The camera matrix can be determined through a number of corresponding points measured in the world and the image. We also demonstrate the common special case of camera calibration when it can be assumed that the world is flat. Then, a plane in the world is transformed to the image plane. Such a plane-to-plane mapping is called a homography.
Finally, we discuss some useful mathematical tools needed for camera calibration. We show that the solution we present for the determination of the camera matrix is equivalent to a least-squares solution. We also show how to solve a homogeneous system of equations using SVD (singular value decomposition).
Place, publisher, year, edition, pages
Linköping: Linköping University Electronic Press, 2010. , 12 p.
LiTH-ISY-R, ISSN 1400-3902 ; 3070
Engineering and Technology
IdentifiersURN: urn:nbn:se:liu:diva-103927ISRN: LiTH-ISY-R-3070OAI: oai:DiVA.org:liu-103927DiVA: diva2:693117