University of Waterloo
An optical imaging technique called confocal microscopy has been gaining popularity in the biological science community for its capability to visualize genes in action in embryos. Gene expression patterns seen in micrographs reveal the positions and shapes of structures long before they actually form. Having acquired such images for larval growth of Drosophila wing disc, the question arises how they can be used to infer the properties of growth. This is a challenging image understanding problem, and in my talk I will address it using a pattern theoretic model for biological growth called GRID (Growth as Random Iterated Diffeomorphisms). One of the GRID parameters, the growth magnitude, characterizes the local expansion (or contraction) rate throughout the wing disc cellular field. I will propose its estimation directly from the image data based on an appropriate optimization problem formulation and further application of Polak-Ribiere minimization algorithm. The estimate of this parameter will automatically allow estimation of the diffeomorphic transformation underlying the dynamics of gene expression patterns seen in given micrographs.