Wavelets and the study of the distant Universe

The large-scale distribution of galaxies in the Universe exhibits structures at various scales, these so-called groups, clusters, and superclusters of galaxies being more or less hierarchically organized. A specific vision model is needed in order to detect, describe, and classify each component of this hierarchy. To do so, we have developed a multiscale vision model based on an unfolding into a scale space allowing us to detect structures of different sizes. A discrete wavelet transform is done by the a trous algorithm. The algorithm is implemented for astronomical images and also for lists of object positions, currently called catalogues in astronomical literature. Some applications on astrophysical data of cosmological interest are briefly described: (1) inventory procedures for galaxy counts on wide-field images, (2) processing of X-ray cluster images lending to the analyses of the total matter distribution, and (3) detection of large-scale structures from galaxy counts, From the analyses of N-body simulations we show that the vision model from the wavelet transform provides a new statistical indicator on cosmological scenarios.