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Fitting an ellipse to an arbitrary shape: Implications for strain analysis

Publication ,  Journal Article
Mulchrone, KF; Choudhury, KR
Published in: Journal of Structural Geology
January 1, 2004

An ellipse can be fit to an arbitrary shape using a linear least squares approach applied to boundary data. Alternatively, this problem can also be solved by calculating the second moments of the entire region, a technique popular in image analysis applications. If the irregular shape can be approximated by a polygon then Greens theorem allows efficient calculation of the second moments. If the shape is pixelated then the second moments can be calculated by a simple summation process. By considering the behaviour of these fitting methods with increasing deformation it is shown that as an arbitrary shape passively deforms, the best-fit ellipse also behaves as if it were deforming passively. This implies that all techniques of strain analysis that were previously restricted to populations of elliptical objects may now be applied to populations of arbitrary shapes, provided the best-fit ellipse is calculated by one of the methods described here. Furthermore it implies that selective sampling based on shape or methods of weighting based upon shape are invalid and tend to bias the raw data. © 2003 Elsevier Ltd. All rights reserved.

Duke Scholars

Published In

Journal of Structural Geology

DOI

ISSN

0191-8141

Publication Date

January 1, 2004

Volume

26

Issue

1

Start / End Page

143 / 153

Related Subject Headings

  • Geochemistry & Geophysics
  • 3705 Geology
  • 0403 Geology
 

Citation

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Mulchrone, K. F., & Choudhury, K. R. (2004). Fitting an ellipse to an arbitrary shape: Implications for strain analysis. Journal of Structural Geology, 26(1), 143–153. https://doi.org/10.1016/S0191-8141(03)00093-2
Mulchrone, K. F., and K. R. Choudhury. “Fitting an ellipse to an arbitrary shape: Implications for strain analysis.” Journal of Structural Geology 26, no. 1 (January 1, 2004): 143–53. https://doi.org/10.1016/S0191-8141(03)00093-2.
Mulchrone KF, Choudhury KR. Fitting an ellipse to an arbitrary shape: Implications for strain analysis. Journal of Structural Geology. 2004 Jan 1;26(1):143–53.
Mulchrone, K. F., and K. R. Choudhury. “Fitting an ellipse to an arbitrary shape: Implications for strain analysis.” Journal of Structural Geology, vol. 26, no. 1, Jan. 2004, pp. 143–53. Scopus, doi:10.1016/S0191-8141(03)00093-2.
Mulchrone KF, Choudhury KR. Fitting an ellipse to an arbitrary shape: Implications for strain analysis. Journal of Structural Geology. 2004 Jan 1;26(1):143–153.
Journal cover image

Published In

Journal of Structural Geology

DOI

ISSN

0191-8141

Publication Date

January 1, 2004

Volume

26

Issue

1

Start / End Page

143 / 153

Related Subject Headings

  • Geochemistry & Geophysics
  • 3705 Geology
  • 0403 Geology