We are particularly interested in the contour of the pool table since
this identifies its shape and periphery where the pockets lie. We
quickly compute the centroid of the pool table and compute the most
radially distant points at each angle from the center as in
Figure 
(a).
Since we know that the pool table top is a quadrilateral object we
model its contour as a set of 4 lines. This is done by fitting
the distribution of contour pixels using an EM algorithm where each
sample 
is a (u,v) vector. In this vector, u is the horizontal
coordinate and v is the vertical coordinate of the contour pixel. A
mixture model consisting of four Gaussians is updating using EM as
shown in Figure (b) and (c). The model converges so that the
thin Gaussians form lines that approximate the sides of the table. The
dominant eigenvector of each Gaussian is along its main axis and is
used to compute a linear model as shown.
Figure: Pool Table Contour Lines via
EM
Thus, we have four line equations describing the boundary of the pool table in each image frame. It is possible to compute intersections to find pool table corners and to determine the lengths of the sides. In addition, we can accurately specify the interior and periphery of the pool table.