Conic Fitting in Geometric Algebra Setting

被引：12

作者：

Hrdina, Jaroslav ^{[1
]}

Navrat, Ales ^{[1
]}

Vasik, Petr ^{[1
]}

机构：

[1] Brno Univ Technol, Inst Math, Fac Mech Engn, Brno, Czech Republic

来源：

ADVANCES IN APPLIED CLIFFORD ALGEBRAS | 2019年 / 29卷 / 04期

关键词：

Conformal geometric algebra; Geometric algebra for conics; Clifford algebra; Conic fitting;

D O I：

10.1007/s00006-019-0989-5

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We present an algorithm for a conic fitting based on a generalization of planar version of conformal geometric algebra to geometric algebra for conics (GAC). We introduce a novel normalization condition that follows naturally from this setting and which is invariant with respect to rotations and scaling. Finally, we provide a comparison to standard methods demonstrated on examples in MATLAB.

引用

页数：13

共 11 条

[1] [Anonymous], SIAM FRONT APPL MATH
[2] FITTING CONIC SECTIONS TO SCATTERED DATA
BOOKSTEIN, FL
[J]. COMPUTER GRAPHICS AND IMAGE PROCESSING, 1979, 9 (01): : 56 - 71
[3] Total Least Squares Fitting of k-Spheres in n-D Euclidean Space Using an (n+2)-D Isometric Representation
Dorst, Leo
[J]. JOURNAL OF MATHEMATICAL IMAGING AND VISION, 2014, 50 (03) : 214 - 234
[4] Direct least square fitting of ellipses
Fitzgibbon, A
Pilu, M
Fisher, RB
[J]. IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE, 1999, 21 (05) : 476 - 480
[5] Fitzgibbon A. W., 1995, BMVC '95 Proceedings of the 6th British Machine Vision Conference, P513
[6] LEAST-SQUARES FITTING OF CIRCLES AND ELLIPSES
GANDER, W
GOLUB, GH
STREBEL, R
[J]. BIT, 1994, 34 (04): : 558 - 578
[7] Hildenbrand D., 2019, Introduction to Geometric Algebra Computing
[8] Geometric Algebra for Conics
Hrdina, Jaroslav
Navrat, Ales
Vasik, Petr
[J]. ADVANCES IN APPLIED CLIFFORD ALGEBRAS, 2018, 28 (03)
[9] Perwass C, 2009, GEOM COMPUT, V4, P1
[10] Pratt V., 1985, Computer Graphics, V19, P151, DOI 10.1145/325165.325225

← 1 2 →