journal of structural geology：构造地质学杂志.pdfVIP

Journal of Structural Geology 30 (2008) 1593–1602 Contents lists available at ScienceDirect Journal of Structural Geology journal homepage: www.el /locate/jsg Non-linear least squares ellipse fitting using the genetic algorithm with applications to strain analysis 1 * Anandaroop Ray , Deepak C. Srivastava Department of Earth Sciences, IIT Roorkee, Roorkee, UA 247667, India a r t i c l e i n f o a b s t r a c t Article history: Several methods of strain estimation require the best-fit ellipse through a set of points either for defining Received 28 February 2008 elliptical shapes of distorted objects, and/or for tracing the finite strain ellipse. Fitting an ellipse to Received in revised form scattered points by solving a least squares problem can involve a linear as well as non-linear formulation. 10 September 2008 This article outlines both approaches and their relative merits and limitations and, proposes a simple yet Accepted 11 September 2008 Available online 1 October 2008 powerful non-linear method of solution utilizing the genetic algorithm. Algebraic methods solve the linear least squares problem, and are relatively straightforward and fast. However, depending upon the type of constraints used, different algebraic methods will yield somewhat Keywords: Best-fit ellipse