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 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.
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.
Original language  English 

Qualification  Doctor 
Awarding Institution 

Supervisors/Advisors 

Award date  1996 May 30 
Publisher  
ISBN (Print)  9162820222 
Publication status  Published  1996 
Bibliographical note
Defence detailsDate: 19960530
Time: 10:15
Place: MHbuilding, MH:C, Lund
External reviewer(s)
Name: Yuille, Alan
Title: Prof.
Affiliation: Harvard Robotics Laboratory, Harvard University

Subject classification (UKÄ)
 Mathematics
Free 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