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In this paper, we propose a new methodology for analysis of microarray images. First, a new gridding algorithm is proposed for determining the individual spots and their borders. Then, a Gaussian mixture model (GMM) approach is presented for the analysis of the individual spot images. The main advantages of the proposed methodology are modeling flexibility and adaptability to the data, which are well-known strengths of GMM. The maximum likelihood and maximum a posteriori approaches are used to estimate the GMM parameters via the expectation maximization algorithm. The proposed approach has the ability to detect and compensate for artifacts that might occur in microarray images. This is accomplished by a model-based criterion that selects the number of the mixture components. We present numerical experiments with artificial and real data where we compare the proposed approach with previous ones and existing software tools for microarray image analysis and demonstrate its advantages. Index Terms--Cross-validated likelihood, DNA microarray image analysis, expectation-maximization algorithm, Gaussian mixture models, Markov random fields, maximum a posteriori, maximum likelihood, microarray gridding.

Gaussian mixture models (GMMs) constitute a well-known type of prubabilistic neural networks. One of their many successful applications is in image segmentation, where spatially constrained mixture models have been trained using the expectation-maximization (EM) framework. In this letter, we elaborate on this method and propose a new methodology for the M-step of the EM algorithm that is based on a novel constrained optimization formulation. Numerical experiments using simulated images illustrate the superior performance of our method in terms of the attained maximum value of the objective function and segmentation accuracy compared to previous implementations of this approach. Index Terms--Covex quadratic programming (QP), expectation-maximization (EM), Gaussian mixture model (GMM), image segmentation, Markov random field (MRF).