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

Several types of geological problem involve fitting an ellipse to sparse data in order to define a property such as strain or curvature. The sensitivity of ellipse-fitting algorithms to noise in input geological data is often poorly documented. Here we compare the performance of some well-known approaches to this problem in geology against each other and an algorithm developed for machine vision. The specific methods tested here are an analytical method, a Mohr diagram method, two least squares methods and a constrained ellipse approach. The algorithms were tested on artificial datasets of known elliptical and noise properties. These results allow the selection of an ellipse fitting method in a variety of geological applications and also allow an assessment of the absolute and relative accuracy of a chosen method for various combinations of sample numbers and noise levels. For the most accurate semi axis magnitude and orientation estimates with five or more input data, the ‘mean object’ least squares approach is recommended. However, the other least squares method also yields good results and is also suitable for three or four data points. Where curvature data is being assessed, the least squares method is preferred as it can handle negative principal curvature values.