Parameterized families of polynomials for bounded algebraic curveand surface fitting
Taubin, G.
Cukierman, F.
Sullivan, S.
Ponce, J.
Kriegman, D.J.
Exploratory Comput. Vision Group, IBM Thomas J. Watson Res. Center, Yorktown Heights, NY;
This paper appears in: Pattern Analysis and Machine Intelligence, IEEE Transactions on
Publication Date: Mar 1994
Volume: 16,
Issue: 3
On page(s): 287-303
ISSN: 0162-8828
References Cited: 45
CODEN: ITPIDJ
INSPEC Accession Number: 4679817
Digital Object Identifier: 10.1109/34.276128
Current Version Published: 2002-08-06
Abstract
Interest in algebraic curves and surfaces of high degree as
geometric models or shape descriptors for different model-based computer
vision tasks has increased in recent years, and although their
properties make them a natural choice for object recognition and
positioning applications, algebraic curve and surface fitting algorithms
often suffer from instability problems. One of the main reasons for
these problems is that, while the data sets are always bounded, the
resulting algebraic curves or surfaces are, in most cases, unbounded. In
this paper, the authors propose to constrain the polynomials to a family
with bounded zero sets, and use only members of this family in the
fitting process. For every even number d the authors introduce a new
parameterized family of polynomials of degree d whose level sets are
always bounded, in particular, its zero sets. This family has the same
number of degrees of freedom as a general polynomial of the same degree.
Three methods for fitting members of this polynomial family to measured
data points are introduced. Experimental results of fitting curves to
sets of points in R2 and surfaces to sets of points
in R3 are presented
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