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Curve Fitting using Orthogonal Splines

IP.com Disclosure Number: IPCOM000110496D
Original Publication Date: 1992-Dec-01
Included in the Prior Art Database: 2005-Mar-25
Document File: 2 page(s) / 66K

Publishing Venue

IBM

Related People

Flickner, M: AUTHOR [+4]

Abstract

This article presents a novel methodology for approximating the contours or silhouettes of binary objects in image processing and graphics applications. The problem of fitting parametric curves and surfaces to discrete data is a central problem in image processing, graphics and other applications. Traditional methods based on smooth curve fitting use standard finite-support spline bases for a least-squares approximation.

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Curve Fitting using Orthogonal Splines

       This article presents a novel methodology for
approximating the contours or silhouettes of binary objects in image
processing and graphics applications.  The problem of fitting
parametric curves and surfaces to discrete data is a central problem
in image processing, graphics and other applications.  Traditional
methods based on smooth curve fitting use standard finite-support
spline bases for a least-squares approximation.

      The new technique reported in this article shows a novel method
in which the approximation is computed by using orthogonal splines
for an arbitrary number of curve pieces (also called knots).  This
method has three advantages over conventional techniques, namely, a
better representation of the shape by a new set of control points, a
faster computational procedure is obtained, and the fitting exhibits
less sensitivity to noise.

      The new spline basis {O(i)},i=0,...,k-1, is computed by a
direct orthogonalization method applied to the B-spline basis.  This
computation is done in a symbolic way, so that the rational
coefficients of the new basis can be written in terms of the standard
B-spline basis by using infinite precision.  The coefficients of the
new basis are then approximated to a fixed number of bits for
numerical purposes.

      Once the new orthogonal basis {O(i)},i=0,...,k-1,is computed,
the fitting process becomes a simple sequence of inner products with
the given da...