Paper Info
Title
Length Estimation for Curves with Different Samplings
Abstract
This paper* looks at the problem of approximating the length of the unknown parametric curve 驴: [0, 1] 驴 IRn from points qi = 驴(ti), where the parameters ti are not given. When the ti are uniformly distributed Lagrange interpolation by piecewise polynomials provides efficient length estimates, but in other cases this method can behave very badly [15]. In the present paper we apply this simple algorithm when the ti are sampled in what we call an 驴-uniform fashion, where 0 驴 驴 驴 1. Convergence of length estimates using Lagrange interpolants is not as rapid as for uniform sampling, but better than for some of the examples of [15]. As a side-issue we also consider the task of approximating 驴 up to parameterization, and numerical experiments are carried out to investigate sharpness of our theoretical results. The results may be of interest in computer vision, computer graphics, approximation and complexity theory, digital and computational geometry, and digital image analysis.
Year
DOI
Venue
2000
10.1007/3-540-45576-0_20
Digital and Image Geometry, Advanced Lectures [based on a winter school held at Dagstuhl Castle, Germany in December 2000]
Keywords
DocType
ISBN
complexity theory,digital image analysis,computer vision,lagrange interpolants,uniform fashion,uniform sampling,length estimation,efficient length estimate,different samplings,present paper,lagrange interpolation,computer graphics
Conference
3-540-43079-2
Citations 
PageRank 
References 
10
1.01
11
Authors
3
Name
Order
Citations
PageRank
Lyle Noakes114922.67
Ryszard Kozera216326.54
Reinhard Klette31743228.94