A Cosmic Watershed: the WVF Void Detection Technique

On megaparsec scales the Universe is permeated by an intricate filigree of clusters, filaments, sheets and voids, the Cosmic Web. For the understanding of its dynamical and hierarchical history it is crucial to identify objectively its complex morphological components. One of the most characteristic aspects is that of the dominant underdense Voids, the product of a hierarchical process driven by the collapse of minor voids in addition to the merging of large ones. In this study we present an objective void finder technique which involves a minimum of assumptions about the scale, structure and shape of voids. Our void finding method, the Watershed Void Finder (WVF), is based upon the Watershed Transform, a well-known technique for the segmentation of images. Importantly, the technique has the potential to trace the existing manifestations of a void hierarchy. The basic watershed transform is augmented by a variety of correction procedures to remove spurious structure resulting from sampling noise. This study contains a detailed description of the WVF. We demonstrate how it is able to trace and identify, relatively parameter free, voids and their surrounding (filamentary and planar) boundaries. We test the technique on a set of Kinematic Voronoi models, heuristic spatial models for a cellular distribution of matter. Comparison of the WVF segmentations of low noise and high noise Voronoi models with the quantitatively known spatial characteristics of the intrinsic Voronoi tessellation shows that the size and shape of the voids are succesfully retrieved. WVF manages to even reproduce the full void size distribution function.Comment: 24 pages, 15 figures, MNRAS accepted, for full resolution, see http://www.astro.rug.nl/~weygaert/tim1publication/watershed.pd

Patch-type Segmentation of Voxel Shapes using Simplified Surface Skeletons

We present a new method for decomposing a 3D voxel shape into disjoint segments using the shape’s simplified surface-skeleton. The surface skeleton of a shape consists of 2D manifolds inside its volume. Each skeleton point has a maximally inscribed ball that touches the boundary in at least two contact points. A key observation is that the boundaries of the simplified fore- and background skeletons map one-to-one to increasingly fuzzy, soft convex, respectively concave, edges of the shape. Using this property, we build a method for segmentation of 3D shapes which has several desirable properties. Our method segments both noisy shapes and shapes with soft edges which vanish over low-curvature regions. Multiscale segmentations can be obtained by varying the simplification level of the skeleton. We present a voxel-based implementation of our approach and illustrate it on several realistic examples.

A Framework for Symmetric Part Detection in Cluttered Scenes

The role of symmetry in computer vision has waxed and waned in importance during the evolution of the field from its earliest days. At first figuring prominently in support of bottom-up indexing, it fell out of favor as shape gave way to appearance and recognition gave way to detection. With a strong prior in the form of a target object, the role of the weaker priors offered by perceptual grouping was greatly diminished. However, as the field returns to the problem of recognition from a large database, the bottom-up recovery of the parts that make up the objects in a cluttered scene is critical for their recognition. The medial axis community has long exploited the ubiquitous regularity of symmetry as a basis for the decomposition of a closed contour into medial parts. However, today's recognition systems are faced with cluttered scenes, and the assumption that a closed contour exists, i.e. that figure-ground segmentation has been solved, renders much of the medial axis community's work inapplicable. In this article, we review a computational framework, previously reported in Lee et al. (2013), Levinshtein et al. (2009, 2013), that bridges the representation power of the medial axis and the need to recover and group an object's parts in a cluttered scene. Our framework is rooted in the idea that a maximally inscribed disc, the building block of a medial axis, can be modeled as a compact superpixel in the image. We evaluate the method on images of cluttered scenes.Comment: 10 pages, 8 figure