Statistical segmentation methods for DNA microarray images

To be more specific, the segmentation problem is stated mathematically as follows. Suppose y^Cy5 = (y^Cy5 _ij |i = 1,2, …, m; j = 1,2, …, n) is an integer-valued matrix representing the Cy5 image, and y^Cy3 = (y^Cy3 _{i j} |i = 1,2, …, m; j = 1,2, …, n) denote an integer-valued matrix representing the Cy3 image. Each element of an image is a pixel. Assume that k clusters c = (c_i|i = 1,2, …, k) are considered, where each cluster represents one category of pixel intensities. In practice, we assume that there are only two clusters, foreground and background, denoted as c₁ and c₂, respectively. The segmentation problem aims to assign each pixel of y^Cy5 or y^Cy3 to one of the classes, c. For example, considering the two-class problem, the result of the segmentation problem will be a binary image z, where the values of the elements in z are either 0 or 1. The binary value represents where each pixel belongs either background or foreground [4, 5].