Genetic search for optimally-constrained multiple-line fitting of discrete data points

Multiple Neutral Data Fitting

A method is proposed for estimating the relationship between a number of variables; this differs from regression where the emphasis is on predicting one of the variables. Regression assumes that only one of the variables has error or natural variability, whereas our technique does not make this assumption; instead, it treats all variables in the same way and produces models which are units inva...

Geometrically-constrained balloon fitting for multiple connected ellipses

This paper presents a framework to fit data to a model consisting of multiple connected ellipses. For each iteration of the fitting algorithm, the representation of the multiple ellipses is mapped to a Gaussian mixture model (GMM) and the connections are mapped to geometric constraints for the GMM. The fitting is a modified constrained expectation maximisation (EM) method on the GMM (maximising...

Data envelope fitting with constrained polynomial splines

Estimation of support frontiers and boundaries often involves monotone and/or concave edge data smoothing. This estimation problem arises in various unrelated contexts, such as optimal cost and production assessments in econometrics and master curve prediction in the reliability programs of nuclear reactors. Very few constrained estimators of the support boundary of a bivariate distribution hav...

Fitting Quadratic Curves to Data Points

Fitting quadratic curves (a.k.a. conic sections, or conics) to data points (digitized images) is a fundamental task in image processing and computer vision. This problem reduces to minimization of a certain function over the parameter space of conics. Here we undertake a thorough investigation of that space and the properties of the objective function on it. We determine under what conditions t...

What's in a Set of Points? (Straight Line Fitting)