Simultaneous estimation of vanishing points and their converging lines using the EM algorithm

This paper introduces a new method for the simultaneous computation of sets of lines meeting at multiple vanishing points through the use of the Expectation–Maximisation (EM) algorithm. The proposed method is based on the formulation of novel error functions in the projective plane between lines and points which involve the use of non-linear optimisation procedures that allow to treat equally finite and infinite vanishing points. These functions are included into the EM framework, which handles the multi-modality of the problem naturally with mixture models. Results show that the proposed method of joint computation of vanishing points and lines converging at such points enhances the robustness and the accuracy of locating these points.

Graphical abstractFigure optionsDownload full-size imageDownload high-quality image (97 K)Download as PowerPoint slideHighlights► Simultaneous estimation of vanishing points and their converging lines. ► Multiple estimation of finite and infinite vanishing points. ► Multiple-steps Expectation–Maximisation formulation. ► Enhanced accuracy compared with robust approaches based on MSAC.