In conventional methods for detecting vanishing points and vanishing lines,
the observed feature points are clustered into collections that represent
different lines. The multiple lines are then detected and the vanishing poi
nts are detected as points of intersection of the lines. The vanishing line
is then detected based on the points of intersection. However, for the pur
pose of optimization, these processes should be integrated and be achieved
simultaneously. In the present paper, we assume that the observed noise mod
el for the feature points is a two-dimensional Gaussian mixture and define
the likelihood function, including obvious vanishing points and a vanishing
line parameters. As a result, the above described simultaneous detection c
an be formulated as a maximum likelihood estimation problem. In addition, a
n iterative computation method for achieving this estimation is proposed ba
sed on the Ehl (Expectation Maximization) algorithm. The proposed method in
volves new techniques by which stable convergence is achieved and computati
onal cost is reduced. The effectiveness of the proposed method that include
s these techniques can be confirmed by computer simulations and real images
.