Line clustering with vanishing point and vanishing line

In conventional methods for detecting vanishing points and vanishing lines, the observed feature points are clustered into collections which represent different lines. The multiple lines are then detected and the vanishing points are detected as cross points of those lines. The vanishing line is then detected based on the cross points. However, for the purpose of optimization, these processes should be integrated and achieved simultaneously. In the present paper, we assume that the observed noise for the feature points is a two-dimensional Gaussian noise. And we define the likelihood function including obviously vanishing point and vanishing line parameters based on a Gaussian mixture density model. As a result the described simultaneous detection can be formulated as a maximum likelihood estimation problem. In addition, an iterative computation method for achieving this estimation is proposed based on the EM algorithm. The proposed method involves new techniques by which stable convergence is achieved and the computational cost is reduced. The effectiveness of the proposed method including these techniques can be confirmed by some experiments