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Color Feature Detection

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 [18] [9]. 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 gif. The clustering uses Expectation Maximization (EM) to find a probability distribution model for pool table colors [5] [19]. 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 gif. The mixture model is described by Equation gif where tex2html_wrap_inline339 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 gif. 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

Tony Jebara
Wed Feb 18 18:52:15 EST 1998