  For a set $S$ of $n$ disjoint line segments in $\mathbb{R}^{2}$, the
visibility counting problem is to preprocess $S$ such that the number of
visible segments in $S$ from any query point $p$ can be computed quickly. There
have been approximation algorithms for this problem with trade off between
space and query time. We propose a new randomized algorithm to compute the
exact answer of the problem. For any $0<\alpha<1$, the space, preprocessing
time and query time are $O_{\epsilon}(n^{4-4\alpha})$,
$O_{\epsilon}(n^{4-2\alpha})$ and $O_{\epsilon}(n^{2\alpha})$, respectively.
Where $O_{\epsilon}(f(n)) = O(f(n)n^{\epsilon})$ and $\epsilon>0$ is an
arbitrary constant number.
