Projective curvature and integral invariants
type: Item
instance of: scholarly article
title: Projective curvature and integral invariants
zbMATH Open document ID: 1035.53026
DOI: 10.1023/A:1020617228313
author: M. S. Hickman
author: Christopher E. Hann
published in: Acta Applicandae Mathematicae
publication date: 2003-03-11T00:00:00Z
review text: It is known, that the projective group and its three subgroups namely the Euclidean group \(E(2)\), special affine group \(SA(2)\) and the full affine group \(A(2)\) play an important role in computer vision. The fundamental invariant of the projective group is the projective curvature which characterises curves under a projective transformation. It depends on seventh order derivatives and hence is very sensitive to noise and of little practical use in planar object recognition. To get over the above problem, the authors propose an extension of all Lie group actions on \(\mathbb{R}^2\) to coordinates defined by potentials so that the resulting invariants will depend on integrals rather than derivatives and so will not be sensitive to noise. In this process the authors derive explicit formulas for the extended group action in the case of the full affine group and fail to determine it in the case of the projective group. The determination of the projective integral invariants that are not dependent on derivatives and the incorporation of this in finding an efficient planar object recognition algorithm are problems yet to be resolved.
Mathematics Subject Classification ID: 53A55
Mathematics Subject Classification ID: 68T10
Mathematics Subject Classification ID: 53A20
zbMATH DE Number: 1879601
zbMATH Keywords: projective curvature
zbMATH Keywords: integral invariants
zbMATH Keywords: projective group
zbMATH Keywords: affine group
zbMATH Keywords: planar object recognition algorithm
reviewed by: Madathum K. Viswanath
MaRDI profile type: Publication
full work available at URL: a:1020617228313
OpenAlex ID: W2113635274
description: scientific article; zbMATH DE number 1879601