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Multiscale geometric analysis for 3D catalogs

We have developed tools for analysis of 3D volumetric data which allow sensitive characterizations of filamentary structures in 3D point clouds. These tools rapidly compute multiscale X-ray transforms of the data volume. Subcubes of varying locations and scales are extracted from the data volume and each is analyzed by integrating along a strategically chosen set of line segments covering all different orientations. The underlying motivation is that point clouds with different degrees of filamentarity will lead to multiscale X-ray coefficients having different distributions 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.