Title :
Approximation with active B-spline curves and surfaces
Author :
Pottmann, Helmut ; Leopoldseder, Stefan ; Hofer, Michael
Author_Institution :
Inst. of Geometry, Vienna Univ. of Technol., Austria
Abstract :
An active contour model for parametric curve and surface approximation is presented. The active curve or surface adapts to the model shape to be approximated in an optimization algorithm. The quasi-Newton optimization procedure in each iteration step minimizes a quadratic function which is built up with the help of local quadratic approximants of the squared distance function of the model shape and an internal energy which has a smoothing and regularization effect. The approach completely avoids the parametrization problem. We also show how to use a similar strategy for the solution of variational problems for curves on surfaces. Examples are the geodesic path connecting two points on a surface and interpolating or approximating spline curves on surfaces. Finally we indicate how the latter topic leads to the variational design of smooth motions which interpolate or approximate given positions.
Keywords :
computational geometry; curve fitting; interpolation; iterative methods; minimisation; splines (mathematics); surface fitting; variational techniques; active B-spline curves; active B-spline surfaces; active contour model; geodesic path; internal energy; interpolation; iteration step; local quadratic approximants; optimization algorithm; parametric curve approximation; parametric surface approximation; quadratic function; quasi-Newton optimization; regularization effect; smooth motions; smoothing effect; squared distance function; variational problems; Active contours; Application software; Character generation; Computer vision; Geometry; Least squares approximation; Parameter estimation; Polynomials; Smoothing methods; Spline;
Conference_Titel :
Computer Graphics and Applications, 2002. Proceedings. 10th Pacific Conference on
Print_ISBN :
0-7695-1784-6
DOI :
10.1109/PCCGA.2002.1167835