Some new methods for the determination of vanishing points using line segments are presented. By indicating the identity between a method using Thales' theorem and a Gaussian sphere based method we show that the knowledge of the position of the projection center is not necessary as mostly assumed. This fact allows an accuracy improvement of a number of former methods using Gaussian sphere representation. We show by presenting some simulation experiments that the methods give very accurate results even in the case of very strong disturbances. With the knowledge of the noise value of the segment end positions, the random error can be estimated and the uncertainty of the calculated vanishing point can be determined.