Improving the Stability of Algebraic Curves for Applications
Abstract
- An algebraic curve is defined as the zero set of a polynomial in two
variables.
Algebraic curves are practical for modeling shapes much more complicated
than conics or superquadrics.
The main drawback in representing shapes by algebraic curves has been
the lack of repeatability in fitting algebraic curves to data.
Usually, arguments against using algebraic curves involve references
to mathematicians Wilkinson (see [acton] chapter 7) and
Runge (see [davis] chapter 4). The first goal of this article is
to understand the stability issue of algebraic curve fitting. Then a fitting method
based on ridge regression and restricting the representation to well
behaved subsets of polynomials is proposed, and its properties are
investigated. The fitting algorithm is of sufficient stability for very fast
position-invariant shape recognition, position estimation, and shape tracking,
based on invariants and new representations.
Among appropriate applications are shape-based indexing into image databases.
Reference
@article{jpt-ip99,
author = {T. Tasdizen and J.-P. Tarel and D.B. Cooper},
title = {Improving the Stability of Algebraic Curves for Applications},
journal = {IEEE Transactions on Image Processing},
volume = {9},
number = {3},
year = {2000},
pages = {405-416},
month = {March},
note = {http://perso.lcpc.fr/tarel.jean-philippe/publis/ip00.html}
}
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