Median and Mode Ellipse Parameterization for Robust Contour Fitting

TL;DR

This paper introduces a robust curve parameterization method using median and mode of ellipse perimeters, effectively fitting arbitrary closed contours in noisy data, demonstrated on fuel droplet images.

Contribution

The paper presents a novel robust contour fitting algorithm based on median and mode ellipse parameterization, improving accuracy in noisy and occluded data scenarios.

Findings

Outperforms existing ellipse fitting algorithms in robustness

Accurately parameterizes arbitrary closed contours

Improves area and edge measurement in fuel droplet images

Abstract

Problems that require the parameterization of closed contours arise frequently in computer vision applications. This article introduces a new curve parameterization algorithm that is able to fit a closed curve to a set of points while being robust to the presence of outliers and occlusions in the data. This robustness property makes this algorithm applicable to computer vision applications where misclassification of features may lead to outliers. The algorithm starts by fitting ellipses to numerous five point subsets from the source data. The closed curve is parameterized by determining the median perimeter of the set of ellipses. The resulting curve is not an ellipse, allowing arbitrary closed contours to be parameterized. The use of the modal perimeter rather than the median perimeter is also explored. A detailed comparison is made between the proposed curve fitting algorithm and existing robust ellipse fitting algorithms. Finally, the utility of the algorithm for computer vision applications is demonstrated through the parameterization of the boundary of fuel droplets during combustion. The performance of the proposed algorithm and the performance of existing algorithms are compared to a ground truth segmentation of the fuel droplet images, which demonstrates improved performance for both area quantification and edge deviation.