Segmentation and intensity estimation of microarray images using a gamma-t mixture model

We present a new approach to the analysis of images for complementary DNA microarray experiments. The image segmentation and intensity estimation are performed simultaneously by adopting a two-component mixture model. One component of this mixture corresponds to the distribution of the background intensity, while the other corresponds to the distribution of the foreground intensity. The intensity measurement is a bivariate vector consisting of red and green intensities. The background intensity component is modeled by the bivariate gamma distribution, whose marginal densities for the red and green intensities are independent three-parameter gamma distributions with different parameters. The foreground intensity component is taken to be the bivariate t distribution, with the constraint that the mean of the foreground is greater than that of the background for each of the two colors. The degrees of freedom of this t distribution are inferred from the data but they could be specified in advance to reduce the computation time. Also, the covariance matrix is not restricted to being diagonal and so it allows for nonzero correlation between R and G foreground intensities. This gamma-t mixture model is fitted by maximum likelihood via the EM algorithm. A final step is executed whereby nonparametric (kernel) smoothing is undertaken of the posterior probabilities of component membership. The main advantages of this approach are: (1) it enjoys the well-known strengths of a mixture model, namely flexibility and adaptability to the data; (2) it considers the segmentation and intensity simultaneously and not separately as in commonly used existing software, and it also works with the red and green intensities in a bivariate framework as opposed to their separate estimation via univariate methods; (3) the use of the three-parameter gamma distribution for the background red and green intensities provides a much better fit than the normal (log normal) or t distributions; (4) the use of the bivariate t distribution for the foreground intensity provides a model that is less sensitive to extreme observations; (5) as a consequence of the aforementioned properties, it allows segmentation to be undertaken for a wide range of spot shapes, including doughnut, sickle shape and artifacts.

We apply our method for gridding, segmentation and estimation to cDNA microarray real images and artificial data. Our method provides better segmentation results in spot shapes as well as intensity estimation than Spot and spotSegmentation R language softwares. It detected blank spots as well as bright artifact for the real data, and estimated spot intensities with high-accuracy for the synthetic data.

The algorithms were implemented in Matlab. The Matlab codes implementing both the gridding and segmentation/estimation are available upon request.

Supplementary material is available at Bioinformatics online.