Robust Ellipse Fitting Using Hierarchical Gaussian Mixture Models

Fitting ellipses from unrecognized data is a fundamental problem in computer vision and pattern recognition. Classic least-squares based methods are sensitive to outliers. To address this problem, in this paper, we present a novel and effective method called
hierarchical Gaussian mixture models
(HGMM) for ellipse fitting in noisy, outliers-contained, and occluded settings on the basis of
Gaussian mixture models
(GMM). This method is crafted into two layers to significantly improve its fitting accuracy and robustness for data containing outliers/noise and has been proven to effectively narrow down the iterative interval of the kernel bandwidth, thereby speeding up ellipse fitting. Extensive experiments are conducted on synthetic data including substantial outliers (up to 60%) and strong noise (up to 200%) as well as on real images including complex benchmark images with heavy occlusion and images from versatile applications. We compare our results with those of representative state-of-the-art methods and demonstrate that our proposed method has several salient advantages, such as its high robustness against outliers and noise, high fitting accuracy, and improved performance.