Comparative testing of ellipse-fitting algorithms: Implications for analysis of strain and curvature

Journal of Structural Geology

Volumn 27, Issue 11, 2005, Pages 1973-1985

  Wynn, Tim J ^a   Stewart, S A ^b  

^a TRACS International   (United Kingdom)

^b BP EXPLORATION   (United Kingdom)

Author keywords

Curvature; Ellipse fitting; Least squares; Mohr circle; Noise; Strain

Indexed keywords

CONSTRAINED ELLIPSE APPROACH; CURVATURE; ELLIPSE-FITTING;

ALGORITHMS; CURVE FITTING; GRAPHIC METHODS; LEAST SQUARES APPROXIMATIONS; MATHEMATICAL MODELS; MATRIX ALGEBRA; STRAIN; STRESSES;

STRUCTURAL GEOLOGY;

ALGORITHM; LEAST SQUARES METHOD; MOHR THEORY; STRAIN ANALYSIS;

EID: 27144476955     PISSN: 01918141     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jsg.2005.06.010     Document Type: Article

References (30)

1. S.J. Ahn W. Rauh Geometric least squares fitting of circle and ellipse International Journal of Pattern Recognition and Artificial Intelligence 13 1999 987-996
2. W.C. Belfield Predicting natural fracture distribution in reservoirs from 3D seismic estimates of structural curvature SPE Paper No. 60298 2000
3. F.L. Bookstein Fitting conic sections to scattered data Computer Graphics and Image Processing 9 1979 56-71
4. D.G. DePaor Strain determination from three known stretches - an exact solution Journal of Structural Geology 10 1988 639-642
5. E.A. Erslev H. Ge Least-squares centre-to-centre and mean object ellipse fabric analysis Journal of Structural Geology 12 1990 1047-1059
6. A. Fitzgibbon M. Pilu R.B. Fisher Direct least square fitting of ellipses IEEE Transactions on Pattern Analysis and Machine Intelligence 21 1999 476-480
7. W. Gander G.H. Golub R. Strebel Least-squares fitting of circles and ellipses BIT 34 1994 558-578
8. D. Hart A.J. Rudman Least-squares fit of an ellipse to anisotropic polar data: Application to azimuthal resistivity surveys in karst regions Computers and Geosciences 23 1997 89-194
9. M.K. Hu Visual pattern recognition using moment invariants IRE Transactions on Information Theory IT-8 1962 179-187
10. R.J. Lisle Least-squares best-fit circles (with applications to Mohr's diagram) Mathematical Geology 24 1992 455-461
11. R.J. Lisle Palaeostrain analysis In: P.L. Hancock (Ed.), Continental Deformation 1994 Pergamon Press Oxford 28-42
12. R.J. Lisle D.M. Ragan Strain from three stretches-a simple Mohr circle solution Journal of Structural Geology 10 1988 905-906
13. R.J. Lisle J.M. Robinson The Mohr circle for curvature and its application to fold description Journal of Structural Geology 17 5 1995 739-750
14. M.A. McNaught Estimating uncertainty in normalized Fry plots using a bootstrap approach Journal of Structural Geology 24 2002 311-322
15. W.D. Means An unfamiliar Mohr circle construction for finite strain Tectonophysics 89 1982 T1-T6
16. K.F. Mulchrone K.R. Choudhury Fitting an ellipse to an arbitrary shape. Implications for strain analysis Journal of Structural Geology 26 2004 143-153
17. G. Murphy A graphical method for the evaluation of principal strains from normal strains Journal of Applied Mechanics 12 1945 209-210
18. J.F. Nye Physical Properties of Crystals 1957 Oxford University Press
19. D.M. Ragan Strain from three measured stretches Journal of Structural Geology 9 1987 897-898
20. J.G. Ramsay M.I. Huber Strain Analysis 1983 Academic Press London
21. P-Y.F. Robin Algebraic calculation of two dimensional strain from point distribution data Journal of Structural Geology 5 1983 552
22. P-Y.F. Robin Determination of fabric and strain ellipsoids from measured sectional ellipses-theory Journal of Structural Geology 24 2002 513-544
23. P.L. Rosin A note on the least-squares fitting of ellipses Pattern Recognition Letters 14 1993 799-808
24. P.L. Rosin Assessing error of fit functions for ellipses Graphical Models and Image Processing 58 1996 494-502
25. D.J. Sanderson The algebraic evaluation of two-dimensional finite strain rosettes Mathematical Geology 9 1977 483-496
26. S.A. Stewart R. Podolski Curvature analysis of gridded geological surfaces In: M.P. Coward T.S. Daltaban H. Johnson (Eds.), Structural Geology in Reservoir Characterisation Special Publication, Geological Society (London) vol. 127 1998 133-147
27. S.A. Stewart T.J. Wynn Mapping spatial variation in rock properties in relationship to spectral curvature Geology 28 2000 691-694
28. G. Taubin Estimation of planar curves surfaces, and nonplanar space-curves defined by implicit equations with applications to edge and range image segmentation IEEE Transactions on Pattern Analysis and Machine Intelligence 13 1991 1115-1138
29. M.R. Teague Image analysis via the general theory of moments Journal of the Optical Society of America 70 1980 920-930
30. S.H. Treagus Mohr circles for strain, simplified Geological Journal 22 1987 119-132