In this paper we introduce two different representation approaches and propose two techniques
to estimate the position of vanishing points in an image, one based on a probabilistic strategy
and the other focused on a deterministic analysis. Unlike most of the methods so far developed,
which exploit the Gaussian sphere, the new techniques operate in the (r, q) polar parameter space
and in the (x, y) image plane coordinate space. Both the solutions will be described and compared,
also through the discussion of the results obtained from their application to real images.