A Probabilistic Clustering Approach for Detecting Linear Structures in Two-Dimensional Spaces

In this work, a novel probabilistic clustering algorithm suitable for the identification of linear elements in datasets containing linear-shaped clusters is proposed. The algorithm is an expectation-maximization-like procedure applied on a mixture of probability density functions, each one modeling a line segment. To that end, a suitable two-dimensional distribution is defined that models points that are spread around a line segment and is parameterized by the segment endpoints. An elaborate initialization process causes the algorithm to start with an overestimate of the number of the actual clusters (segments) formed by the data points. The clusters are gradually removed through the utilization of suitable merging and elimination mechanisms until the actual clusters are identified. The update of the parameters of the line segments at each iteration results from a least squares fitting procedure. The method is presented in the context of line segment detection problems in digital images whose pixels form straight lines or elongated objects, although it can be utilized in other relevant contexts. Experimental evaluation shows that the proposed approach compares equally well or outperforms relevant state-of-the-art clustering-based and traditional line detection approaches.