We focus on the detection of orthogonal vanishing points using line segments extracted from a single view, and using these for camera self-calibration. Recent methods view this problem as a two-stage process. Vanishing points are extracted through line segment clustering and subsequently likely orthogonal candidates are selected for calibration. Unfortunately, such an approach is easily distracted by the presence of clutter. Furthermore, geometric constraints imposed by the camera and scene orthogonality are not enforced during detection, leading to inaccurate results which are often inadmissible for calibration. To overcome these limitations, we present a RANSAC-based approach using a minimal solution for estimating three orthogonal vanishing points and focal length from a set of four lines, aligned with either two or three orthogonal directions. In addition, we propose to refine the estimates using an efficient and robust Maximum Likelihood Estimator. Extensive experiments on stan...