Multiple ellipse fitting by center-based clustering

Abstract

Abstract. This paper deals with the multiple ellipse fitting problem based on a given set of data points in a plane. The presumption is that all data points are derived from k ellipses that should be fitted. The problem is solved by means of center-based clustering, where cluster centers are ellipses. If the Mahalanobis distance-like function is introduced in each cluster, then the cluster center is represented by the corresponding Mahalanobis circle-center. The distance from a point a ∈ R 2 to the Mahalanobis circle is based on the algebraic criterion. The well-known k-means algorithm has been adapted to search for a locally optimal partition of the Mahalanobis circle-centers. Several numerical examples are used to illustrate the proposed algorithm.

Dynamic Granularity Matrix Space Model Based High Robust Multi-Ellipse Center Extraction Method for Camera Calibration

“…Over the past years, many ellipse detection algorithms sprang up and were studied broadly to solve the ellipse detection problem, which can be briefly grouped into several categories: Hough transform method [21][22][23][24], leastsquare fitting method [25][26][27][28][29], clustering method [30][31][32][33][34]. Hough transform has been widely used for detecting geometric primitives such as line segment, circle and ellipse.…”

Investigation of the optimal number of clusters by the adaptive EM algorithm

“…In this paper, the datasets that are modeled by the Gaussian mixture model are observed, and thus the new algorithm is developed based on modification of the well known Expectation Maximization (EM) algorithm [1]. The modification is conducted by the well known Mahalanobis distance, which has great application in data analysis [5,6,7,9], within the hidden variable of the standard EM algorithm. The modification is conducted in sense of the outlier detection [8], which uses the fact that the squared Mahalanobis distance follows a Chi-square distribution for the data that are normally distributed [2,4].…”

Cluster Detection in the Noisy Environment by Using the Modified EM Algorithm

“…Clustering is a widely used exploratory data analysis tool that has been successfully applied to data analysis, image processing, pattern recognition, engineering [2,4,6,7,8,15,17,18], and many other fields. In this paper, we focus on the detection of clusters in a noisy environment based on the well-known EM algorithm [2,3,9,11,18].…”

“…The aim is to disregard noisy data from further calculation in the current clustering step. In the sense of the Gaussian mixture model, the Mahalanobis distance is used, which is widely applied in application in data clustering analysis [8,11,16]. The Mahalanobis distance is used to determine data dispersion within cluster π j by weighted mean and weighted median of data [13,14,19].…”