A method for two-dimensional registration and construction of the two-dimensional atlas of gene expression patterns in situ.

We apply the fast redundant dyadic wavelet transform to the spatial registration of two-dimensional gene expression patterns of 736 Drosophila melanogaster embryos. This method is superior to the Fourier transform or windowed Fourier transform because of its ability to reduce noise and is of high resolution. In registration of the dataset we use two cost functions based on computing the Euclidean or Mahalanobis distance. The algorithm shows a high level of accuracy. For early temporal classes the cost function based on Mahalanobis distance gives better results. We have reported a method for construction of an integrated dataset elsewhere. In this paper the method is extended to the two-dimensional case. The procedure for data assembly provides for the preservation of some aspects of the nuclear structure of a two-dimensional gene expression pattern. It is based on creating an averaged model that reproduces the spatial distribution of nuclei over the embryo image. The average concentrations of each protein in each averaged nucleus are computed from the series of embryos of the same age.