# Extensions and Applications of Affine Shape

Rikard Berthilsson

Research output: ThesisDoctoral Thesis (compilation)

## Abstract

A central problem in computer vision is to reconstruct the three-dimensional structure of a scene from a set of two-dimensional images. Traditionally this is done by extracting a set of characteristic points in the scene and to compute a reconstruction of these points. In this thesis we propose a novel method that allows reconstruction of a wider class of objects, including curves and surfaces. As always when dealing with measured data, the handling of noise is crucial. In this thesis we analyze the impact of uncertainty in measurements on feature parameters, and how these can be estimated in maximum likelihood sense.

The thesis consists of an introduction and six separate papers. The introduction gives an overview and motivation for the contents of the thesis. Paper I presents an extension of the so called affine shape of finite point configuration to affine shape of for example curves and surfaces. An algorithm for reconstructing curves is also presented. In paper II it is shown how the extension of affine shape can be used to recognize curves and in particular how it can be used to interpret handwriting. Paper III presents an extension to surfaces of the method for reconstructing curves in paper I based on affine shape. The paper also uses results from paper IV, where it is shown how images can be matched by allowing for deformations and using correlation. The matching is done by an iterative algorithm, where the fast Fourier transformation is used in each iteration to speed up computations. Papers V and VI consider statistical issues in computer vision. In paper V we discuss how uncertainties in measurements of point configurations are influencing the shape. More precisely, it is shown how the probability measure of shape can be computed from the probability measure of the point configurations. In paper VI we discuss how the characteristic function can be used to compute maximum likelihood estimates of matching constraints and how to obtain densities of estimated parameters. In particular, we present a novel method for estimating the fundamental matrix.
Original language English Doctor Mathematics (Faculty of Engineering) [unknown], [unknown], Supervisor, External person 1999 Dec 9 Centre for Mathematical Sciences, Lund University 91-628-3915-2 Published - 1999

### Bibliographical note

Defence details

Date: 1999-12-09
Time: 10:15
Place: Room C, Matematikcentrum, Sölvegatan 18, Lund

External reviewer(s)

Name: Maybank, Steve
Title: [unknown]

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• Mathematics

## Free keywords

• Systems engineering
• Matematik
• Mathematics
• density of shape
• maximum likelihood
• matching constraint
• surface
• curve
• handwriting
• recognition
• affine shape
• reconstruction
• computer technology
• Data- och systemvetenskap

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