Invariancy Methods for Points, Curves and Surfaces in Computational Vision
(1996) In University of Lund, Institute of Technology, Department of Mathematics 1996:2. Abstract
 Many issues in computational vision can be understood from the interplay between camera geometry and the structure of images and objects. Typically, the image structure is available and the goal is to reconstruct object structure and camera geometry. This is often difficult due to the complex interdependence between these three entities. The theme of this thesis is to use invariants to solve these and other problems of computational vision. Two types of invariancies are discussed; viewpoint invariance and object invariance.
A viewpoint invariant does not depend on the camera geometry. The classical cross ratio of four collinear points is a typical example. A number of invariants for planar curves are developed and... (More)  Many issues in computational vision can be understood from the interplay between camera geometry and the structure of images and objects. Typically, the image structure is available and the goal is to reconstruct object structure and camera geometry. This is often difficult due to the complex interdependence between these three entities. The theme of this thesis is to use invariants to solve these and other problems of computational vision. Two types of invariancies are discussed; viewpoint invariance and object invariance.
A viewpoint invariant does not depend on the camera geometry. The classical cross ratio of four collinear points is a typical example. A number of invariants for planar curves are developed and discussed. Viewpoint invariants are useful for many purposes, for example to solve recognition problems. This idea is applied to navigation of laser guided vehicles and to the recognition of planar curves.
An object invariant does not depend on the object structure. The epipolar constraint is a typical example. The epipolar constraint is generalised in several directions. Multilinear constraints are derived for both continuous and discrete time motion. Similar constraints are used to solve navigation problems. Generalised epipolar constraints are derived for curves and surfaces.
The invariants are based on pure geometrical properties. To apply these ideas to real images it is necessary to consider practical issues such as noise. Stochastic properties of lowlevel vision are investigated to give guidelines for design of practical algorithms. A theory for interpolation and scalespace smoothing is developed. The resulting lowlevel algorithms, for example edgedetection and correlation, are invariant with respect to the position of the discretisation grid. The ideas are useful in order to understand existing algorithms and to design new ones. (Less)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/17808
 author
 Åström, Karl ^{LU}
 supervisor
 opponent

 Prof. Yuille, Alan, Harvard Robotics Laboratory, Harvard University
 organization
 publishing date
 1996
 type
 Thesis
 publication status
 published
 subject
 keywords
 curved surface, space curve, planar curve, laser guided vehicles, AGV, autonomous guided vehicles, recognition, reconstruction, image sequence, multiple view geometry, affine, invariant, projective, Mathematics, Matematik
 in
 University of Lund, Institute of Technology, Department of Mathematics
 volume
 1996:2
 pages
 212 pages
 publisher
 Department of Mathematics, Lund University
 defense location
 MHbuilding, MH:C, Lund
 defense date
 19960530 10:15:00
 external identifiers

 other:ISRN: LUTTFD2/TFMA96/1006SE
 ISSN
 03478475
 ISBN
 9162820222
 language
 English
 LU publication?
 yes
 id
 961ab7e69d474e1ab994b104c80095c5 (old id 17808)
 date added to LUP
 20160401 15:29:21
 date last changed
 20201222 02:16:37
@phdthesis{961ab7e69d474e1ab994b104c80095c5, abstract = {{Many issues in computational vision can be understood from the interplay between camera geometry and the structure of images and objects. Typically, the image structure is available and the goal is to reconstruct object structure and camera geometry. This is often difficult due to the complex interdependence between these three entities. The theme of this thesis is to use invariants to solve these and other problems of computational vision. Two types of invariancies are discussed; viewpoint invariance and object invariance.<br/><br> <br/><br> A viewpoint invariant does not depend on the camera geometry. The classical cross ratio of four collinear points is a typical example. A number of invariants for planar curves are developed and discussed. Viewpoint invariants are useful for many purposes, for example to solve recognition problems. This idea is applied to navigation of laser guided vehicles and to the recognition of planar curves.<br/><br> <br/><br> An object invariant does not depend on the object structure. The epipolar constraint is a typical example. The epipolar constraint is generalised in several directions. Multilinear constraints are derived for both continuous and discrete time motion. Similar constraints are used to solve navigation problems. Generalised epipolar constraints are derived for curves and surfaces.<br/><br> <br/><br> The invariants are based on pure geometrical properties. To apply these ideas to real images it is necessary to consider practical issues such as noise. Stochastic properties of lowlevel vision are investigated to give guidelines for design of practical algorithms. A theory for interpolation and scalespace smoothing is developed. The resulting lowlevel algorithms, for example edgedetection and correlation, are invariant with respect to the position of the discretisation grid. The ideas are useful in order to understand existing algorithms and to design new ones.}}, author = {{Åström, Karl}}, isbn = {{9162820222}}, issn = {{03478475}}, keywords = {{curved surface; space curve; planar curve; laser guided vehicles; AGV; autonomous guided vehicles; recognition; reconstruction; image sequence; multiple view geometry; affine; invariant; projective; Mathematics; Matematik}}, language = {{eng}}, publisher = {{Department of Mathematics, Lund University}}, school = {{Lund University}}, series = {{University of Lund, Institute of Technology, Department of Mathematics}}, title = {{Invariancy Methods for Points, Curves and Surfaces in Computational Vision}}, volume = {{1996:2}}, year = {{1996}}, }