Abstract We present a novel vanishing point detection algorithm for uncalibrated monocular images of man-made environments. We advance the state-of-the-art by a new model of measurement error in the line segment extraction and minimizing its impact on the vanishing point estimation. Our contribution is twofold: 1) Beyond existing hand-crafted models, we formally derive a novel consistency measure, which captures the stochastic nature of the correlation between line segments and vanishing points due to the measurement error, and use this new consistency measure to improve the line segment clustering. 2) We propose a novel minimum error vanishing point estimation approach by optimally weighing the contribution of each line segment pair in the cluster towards the vanishing point estimation. Unlike existing works, our algorithm provides an optimal solution that minimizes the uncertainty of the vanishing point in terms of the trace of its covariance, in a closed-form. We test our algorithm and compare it with the state-of-the-art on two public datasets: York Urban Dataset and Eurasian Cities Dataset. The experiments show that our approach outperforms the state-of-the-art.