Multiscale Geometric Analysis for 3-D Catalogues

We have developed tools for analysis of 3-D volumetric data which allow sensitive characterizations of point clouds containing filamentary structures. Our approach involves multiscale X-ray transforms of the data volume. The idea is that cubes of all different locations and scales are extracted from the data volume and then analyzed by integrating along lines (X-Rays) of all different orientations and scales. The underlying principle is that point clouds with different amounts of filamentarity will lead to different distributions for the X-ray coefficients when viewed at the right scale. The multiscale approach guarantees that information from all scales is available; by extracting the information from the transform in a statistically appropriate fashion, we can sensitively resolve differences in details of the filamentarity. We will describe the algorithm and the results of comparing different simulated galaxy distributions.