The Spine of the Cosmic Web

We present the SpineWeb framework for the topological analysis of the Cosmic Web and the identification of its walls, filaments and cluster nodes. Based on the watershed segmentation of the cosmic density field, the SpineWeb method invokes the local adjacency properties of the boundaries between the watershed basins to trace the critical points in the density field and the separatrices defined by them. The separatrices are classified into walls and the spine, the network of filaments and nodes in the matter distribution. Testing the method with a heuristic Voronoi model yields outstanding results. Following the discussion of the test results, we apply the SpineWeb method to a set of cosmological N-body simulations. The latter illustrates the potential for studying the structure and dynamics of the Cosmic Web.Comment: Accepted for publication HIGH-RES version: http://skysrv.pha.jhu.edu/~miguel/SpineWeb

Lesion boundary segmentation using level set methods

This paper addresses the issue of accurate lesion segmentation in retinal imagery, using level set methods and a novel stopping mechanism - an elementary features scheme. Specifically, the curve propagation is guided by a gradient map built using a combination of histogram equalization and robust statistics. The stopping mechanism uses elementary features gathered as the curve deforms over time, and then using a lesionness measure, defined herein, ’looks back in time’ to find the point at which the curve best fits the real object. We implement the level set using a fast upwind scheme and compare the proposed method against five other segmentation algorithms performed on 50 randomly selected images of exudates with a database of clinician marked-up boundaries as ground truth

Image segmentation with adaptive region growing based on a polynomial surface model

A new method for segmenting intensity images into smooth surface segments is presented. The main idea is to divide the image into flat, planar, convex, concave, and saddle patches that coincide as well as possible with meaningful object features in the image. Therefore, we propose an adaptive region growing algorithm based on low-degree polynomial fitting. The algorithm uses a new adaptive thresholding technique with the L∞ fitting cost as a segmentation criterion. The polynomial degree and the fitting error are automatically adapted during the region growing process. The main contribution is that the algorithm detects outliers and edges, distinguishes between strong and smooth intensity transitions and finds surface segments that are bent in a certain way. As a result, the surface segments corresponding to meaningful object features and the contours separating the surface segments coincide with real-image object edges. Moreover, the curvature-based surface shape information facilitates many tasks in image analysis, such as object recognition performed on the polynomial representation. The polynomial representation provides good image approximation while preserving all the necessary details of the objects in the reconstructed images. The method outperforms existing techniques when segmenting images of objects with diffuse reflecting surfaces