FITTING CONIC SECTIONS TO SCATTERED DATA

被引：337

作者：

BOOKSTEIN, FL

机构：

[1] Center for Human Growth, Development The University of Michigan, Ann Arbor

[2] Departments of Statistics and Biostatistics, The University of Michigan, Ann Arbor

来源：

COMPUTER GRAPHICS AND IMAGE PROCESSING | 1979年 / 9卷 / 01期

关键词：

D O I：

10.1016/0146-664X(79)90082-0

中图分类号：

TP31 [计算机软件];

学科分类号：

081202 ; 0835 ;

摘要：

The problem of fitting conic sections to scattered data has arisen in several applied literatures. The quadratic fromAx2 + Bxy + Cy2 + Dx + Ey + F that is minimized in mean-square is proportional to the ratio of two squared distances along rays through the center of a conic. Considerations of invariance under translation, rotation, and scaling of the data configuration lead to a straightforward method of estimation somewhat different from earlier suggestions. The method permits an extension to conic splines around extended digitized curves, expediting a smooth reconstruction of their curvature. Some examples are presented indicating how the technique might be applied in morphometrics. © 1979 Academic Press, Inc.

引用

页码：56 / 71

页数：16

共 17 条

[1] Paton, Conic sections in chromosome analysis, Pattern Recog., 2, (1970)
[2] Paton, Conic sections in automatic chromosome analysis, Machine Intelligence, 5, (1970)
[3] Biggerstaff, Three variations in dental arch form estimated by a quadratic equation, J. Dent. Res., 51, (1972)
[4] Albano, Representation of digitized contours in terms of conic arcs and straight-line segments, Computer Graphics and Image Processing, 3, (1974)
[5] Cooper, Yalabik, On the computational cost of approximating and recognizing noise-perturbed straight lines and quadratic arcs in the plane, IEEE Transactions on Computers, 100-125, (1976)
[6] Gnanadesikan, Methods for Statistical Data Analysis of Multivariate Observations, (1977)
[7] Pearson, On lines and planes of closest fit to systems of points in space, Philosophical Magazine Series 6, 2, (1901)
[8] Rao, Linear Statistical Inference and Its Applications, (1973)
[9] Poirier, Piecewise regression using cubic splines, J. Amer. Statist. Assoc., 68, (1973)
[10] Wold, Spline functions in data analysis, Technomet., 16, (1974)

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