Algebraic Curves That Work Better
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.
A regularized fast linear 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 new invariants and representations, and is appropriate to open
as well as closed curves of unorganized data.
Among appropriate applications are shape-based indexing into image databases.
Reference
@INPROCEEDINGS{jpt-cvpr99,
author = {Tasdizen, T. and Tarel, J.-P. and Cooper, D.B.},
title = {Algebraic Curves That Work Better},
booktitle = {IEEE Conference on Computer Vision and Pattern Recognition (CVPR'99)},
address = {Fort Collins, Colorado, USA},
date = {June 23-25},
volume = {II},
pages = {35-41},
year = {1999},
note = {http://perso.lcpc.fr/tarel.jean-philippe/publis/cvpr99.html}
}
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