Joint nonparametric alignment for analyzing spatial gene expression patterns in Drosophila imaginal discs

To compare spatial patterns of gene expression, one must analyze a large number of images as current methods are only able to measure a small number of genes at a time. Bringing images of corresponding tissues into alignment is a critical first step in making a meaningful comparative analysis of these spatial patterns. Significant image noise and variability in the shapes make it hard to pick a canonical shape model. In this paper, we address these problems by combining segmentation and unsupervised shape learning algorithms. We first segment images to acquire structures of interest, then jointly align the shapes of these acquired structures using an unsupervised nonparametric maximum likelihood algorithm along the lines of ´congealing´ (E. G. Miller et al., 2000), while simultaneously learning the underlying shape model and associated transformations. The learned transformations are applied to corresponding images to bring them into alignment in one step. We demonstrate the results for images of various classes of Drosophila imaginal discs and discuss the methodology used for a quantitative analysis of spatial gene expression patterns.