The renormalized curvature scale space and the evolution propertiesof planar curves
Mackworth, S.K.
Mokhtarian, F.
Dept. of Comput. Sci., British Columbia Univ., Vancouver, BC;
This paper appears in: Computer Vision and Pattern Recognition, 1988. Proceedings CVPR '88., Computer Society Conference on
Publication Date: 5-9 Jun 1988
On page(s): 318-326
Meeting Date: 06/05/1988 - 06/09/1988
Location: Ann Arbor, MI, USA
ISBN: 0-8186-0862-5
References Cited: 10
INSPEC Accession Number: 3248007
Digital Object Identifier: 10.1109/CVPR.1988.196255
Current Version Published: 2002-08-06
Abstract
The curvature scale-space image of a planar curve is computed by
convolving a path-based parametric representation of the curve with a
Gaussian function of variance σ2, extracting the zeros
of curvature of the convolved curves and combining them in a scale space
representation of the curve. For any given curve Γ, the process of
generating the ordered sequence of curves
{Γσ|σ⩾0} is the evolution of Γ.
It is shown that the normalized arc length parameter of a curve is, in
general, not the normalized arch length parameter of a convolved version
of that curve. A novel method of computing the curvature scale space
image reparametrizes each convolved curve by its normalized arc length
parameter. Zeros of curvature are then expressed in that new
parametrization. The result is the renormalized curvature scale-space
image and is more suitable for matching curves similar in shape. Scaling
properties of planar curves and the curvature scale space image are also
investigated. It is shown that no new curvature zero-crossings are
created at the higher scales of the curvature scale space image of a
planar curve in C1 if the curve remains in
C1 during evolution. Several results are presented
on the preservation of various properties of planar curves under the
evolution process
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