The Multiscale Morphology Filter: Identifying and Extracting Spatial Patterns in the Galaxy Distribution

Aims. We present here a new method, MMF, for automatically segmenting cosmic structure into its basic components: clusters, filaments, and walls. Importantly, the segmentation is scale independent, so all structures are identified without prejudice as to their size or shape. The method is ideally suited for extracting catalogues of clusters, walls, and filaments from samples of galaxies in redshift surveys or from particles in cosmological N-body simulations: it makes no prior assumptions about the scale or shape of the structures. Methods. Our Multiscale Morphology Filter (MMF) method has been developed on the basis of visualization and feature extraction techniques in computer vision and medical research. The density or intensity field of the sample is smoothed over a range of scales. The smoothed signals are processed through a morphology response filter whose form is dictated by the particular morphological feature it seeks to extract, and depends on the local shape and spatial coherence of the intensity field. The morphology signal at each location is then defined to be the one with the maximum response across the full range of smoothing scales. The success of our method in identifying anisotropic features such as filaments and walls depends critically on the use of an optimally defined intensity field. This is accomplished by applying the DTFE reconstruction methodology to the sample particle or galaxy distribution. Results. We have tested our MMF Filter against a set of heuristic models of weblike patterns such as are seen in the Megaparsec cosmic matter distribution. To test its effectiveness in the context of more realistic configurations we also present preliminary results from the MMF analysis of an N-body model. Comparison with alternative prescriptions for feature extraction shows that MMF is a remarkably strong structure finder