Direct least-squares fitting of algebraic surfaces

  title={Direct least-squares fitting of algebraic surfaces},
  author={Vaughan R. Pratt},
In the course of developing a system for fitting smooth curves to camera input we have developed several direct (i.e. noniterative) methods for fitting a shape (line, circle, conic, cubic, plane, sphere, quadric, etc.) to a set of points, namely exact fit, simple fit, spherical fit, and blend fit. These methods are all dimension-independent, being just as suitable for 3D surfaces as for the 2D curves they were originally developed for.Exact fit generalizes to arbitrary shapes (in the sense of… CONTINUE READING
Highly Influential
This paper has highly influenced 29 other papers. REVIEW HIGHLY INFLUENTIAL CITATIONS
Highly Cited
This paper has 635 citations. REVIEW CITATIONS

From This Paper

Figures, tables, and topics from this paper.


Publications citing this paper.
Showing 1-10 of 263 extracted citations

Mapping forests using an unmanned ground vehicle with 3D LiDAR and graph-SLAM

Computers and Electronics in Agriculture • 2018
View 7 Excerpts
Highly Influenced

Least Squares Fitting of Circles

Journal of Mathematical Imaging and Vision • 2005
View 7 Excerpts
Highly Influenced

Statistical efficiency of curve fitting algorithms

Computational Statistics & Data Analysis • 2004
View 13 Excerpts
Highly Influenced

An estimation of central points of circle markers in a vision system by using Kalman filter and complementary filter

2015 20th International Conference on Methods and Models in Automation and Robotics (MMAR) • 2015
View 6 Excerpts
Highly Influenced

Total Least Squares Fitting of k-Spheres in n-D Euclidean Space Using an (n+2)-D Isometric Representation

Journal of Mathematical Imaging and Vision • 2014
View 7 Excerpts
Highly Influenced

635 Citations

Citations per Year
Semantic Scholar estimates that this publication has 635 citations based on the available data.

See our FAQ for additional information.


Publications referenced by this paper.
Showing 1-9 of 9 references

Pauchon, Edgel-Aggregation and Edge-Description

E.V.S. Nalwa
Eighth International Conference on Pattern Recognition, • 1986
View 6 Excerpts
Highly Influenced

Quadratic blending surfaces for complex corners

The Visual Computer • 1989
View 6 Excerpts
Highly Influenced

Automatic surface generation in computer aided design

The Visual Computer • 1985
View 7 Excerpts
Highly Influenced

Representation of Digitized Contours in Terms of Conic Arcs and Straight-Line Segments

Computer Graphics and Image Processing • 1974
View 5 Excerpts
Highly Influenced

Similar Papers

Loading similar papers…