Figure: The color training samples
Figure: Fitting a Gaussian Mixture
To find the pool table, we train a probabilistic color model of the green felt that covers it  . This is done by taking multiple training samples of several images of a pool table under many imaging situations (offline). Each pixel in this distribution forms a 3 element vector, [R G B] which corresponds to the red, green and blue components of the color. We perform clustering on this distribution of pixels which is shown in Figure . The clustering uses Expectation Maximization (EM) to find a probability distribution model for pool table colors  . This model is a mixture of Gaussians (the appropriate number of Gaussians is determined a priori with cross-validation). The EM algorithm iterates by adjusting the parameters of the Gaussian probability model to maximize the likelihood of the training samples. The probability distribution model starts off in a random configuration and converges to the configuration in Figure . The mixture model is described by Equation where is an (R,G,B) vector.
When a new image is acquired, the likelihood of each pixel is evaluated using this model and if it is above a threshold of probability, it is labeled as a piece of the pool table. Then, a connected component analysis is used to gather adjacent green pixels to determine larger regions of grouped table pixels in the image. This process is demonstrated in Figure . The largest connected region of green pixels is selected as the table top and proceeds through the algorithm for further processing.
Figure: Pool Table Localization