A two-stage algorithm for discontinuity-preserving surface reconstruction

Author

Sinha, Sarvajit S. ; Schunck, Brian G.

Author_Institution

Dept. of Electr. Eng. & Comput. Sci., Michigan Univ., Ann Arbor, MI, USA

Volume

14

Issue

1

fYear

1992

fDate

1/1/1992 12:00:00 AM

Firstpage

36

Lastpage

55

Abstract

A two-stage algorithm for visual surface reconstruction from scattered data while preserving discontinuities is presented. The first stage consists of a robust local approximation algorithm (the moving least median of squares (MLMS) of error) to clean the data and create a grid from the original scattered data points. This process is discontinuity preserving. The second stage introduces a weighted bicubic spline (WBS) as a surface descriptor. The WBS has a factor in the regularizing term that adapts the behavior of the spline across discontinuities. The weighted bicubic approximating spline can approximate data with step discontinuities with no discernible distortion in the approximating surface. The combination of robust surface fitting and WBSs removes outliers and reduces Gaussian noise. Either stage by itself would not effectively remove both kinds of noise. Experimental results with the two-stage algorithm are presented

Keywords

least squares approximations; picture processing; splines (mathematics); discontinuities; discontinuity-preserving surface reconstruction; least squares approximations; moving least median of squares; picture processing; robust surface fitting; two-stage algorithm; weighted bicubic spline; Approximation algorithms; Gaussian noise; Least squares approximation; Least squares methods; Noise robustness; Scattering; Spline; Surface cleaning; Surface fitting; Surface reconstruction;

fLanguage

English

Journal_Title

Pattern Analysis and Machine Intelligence, IEEE Transactions on

Publisher

ieee

ISSN

0162-8828

Type

jour

DOI

10.1109/34.107012

Filename

107012