An improved rotation-invariant thinning algorithm

Ahmed & Ward have recently presented an elegant, rule-based rotation-invariant thinning algorithm to produce a single-pixel wide skeleton from a binary image. We show examples where this algorithm fails on two-pixel wide lines and propose a modified method which corrects this shortcoming based on graph connectivity

Likelihood-Free Parallel Tempering

Approximate Bayesian Computational (ABC) methods (or likelihood-free methods) have appeared in the past fifteen years as useful methods to perform Bayesian analyses when the likelihood is analytically or computationally intractable. Several ABC methods have been proposed: Monte Carlo Markov Chains (MCMC) methods have been developped by Marjoramet al. (2003) and by Bortotet al. (2007) for instance, and sequential methods have been proposed among others by Sissonet al. (2007), Beaumont et al. (2009) and Del Moral et al. (2009). Until now, while ABC-MCMC methods remain the reference, sequential ABC methods have appeared to outperforms them (see for example McKinley et al. (2009) or Sisson et al. (2007)). In this paper a new algorithm combining population-based MCMC methods with ABC requirements is proposed, using an analogy with the Parallel Tempering algorithm (Geyer, 1991). Performances are compared with existing ABC algorithms on simulations and on a real example

Combined 3D thinning and greedy algorithm to approximate realistic particles with corrected mechanical properties

The shape of irregular particles has significant influence on micro- and macro-scopic behavior of granular systems. This paper presents a combined 3D thinning and greedy set-covering algorithm to approximate realistic particles with a clump of overlapping spheres for discrete element method (DEM) simulations. First, the particle medial surface (or surface skeleton), from which all candidate (maximal inscribed) spheres can be generated, is computed by the topological 3D thinning. Then, the clump generation procedure is converted into a greedy set-covering (SCP) problem. To correct the mass distribution due to highly overlapped spheres inside the clump, linear programming (LP) is used to adjust the density of each component sphere, such that the aggregate properties mass, center of mass and inertia tensor are identical or close enough to the prototypical particle. In order to find the optimal approximation accuracy (volume coverage: ratio of clump's volume to the original particle's volume), particle flow of 3 different shapes in a rotating drum are conducted. It was observed that the dynamic angle of repose starts to converge for all particle shapes at 85% volume coverage (spheres per clump < 30), which implies the possible optimal resolution to capture the mechanical behavior of the system.Comment: 34 pages, 13 figure

Gap Filling of 3-D Microvascular Networks by Tensor Voting

We present a new algorithm which merges discontinuities in 3-D images of tubular structures presenting undesirable gaps. The application of the proposed method is mainly associated to large 3-D images of microvascular networks. In order to recover the real network topology, we need to fill the gaps between the closest discontinuous vessels. The algorithm presented in this paper aims at achieving this goal. This algorithm is based on the skeletonization of the segmented network followed by a tensor voting method. It permits to merge the most common kinds of discontinuities found in microvascular networks. It is robust, easy to use, and relatively fast. The microvascular network images were obtained using synchrotron tomography imaging at the European Synchrotron Radiation Facility. These images exhibit samples of intracortical networks. Representative results are illustrated

NEFI: Network Extraction From Images

Networks and network-like structures are amongst the central building blocks of many technological and biological systems. Given a mathematical graph representation of a network, methods from graph theory enable a precise investigation of its properties. Software for the analysis of graphs is widely available and has been applied to graphs describing large scale networks such as social networks, protein-interaction networks, etc. In these applications, graph acquisition, i.e., the extraction of a mathematical graph from a network, is relatively simple. However, for many network-like structures, e.g. leaf venations, slime molds and mud cracks, data collection relies on images where graph extraction requires domain-specific solutions or even manual. Here we introduce Network Extraction From Images, NEFI, a software tool that automatically extracts accurate graphs from images of a wide range of networks originating in various domains. While there is previous work on graph extraction from images, theoretical results are fully accessible only to an expert audience and ready-to-use implementations for non-experts are rarely available or insufficiently documented. NEFI provides a novel platform allowing practitioners from many disciplines to easily extract graph representations from images by supplying flexible tools from image processing, computer vision and graph theory bundled in a convenient package. Thus, NEFI constitutes a scalable alternative to tedious and error-prone manual graph extraction and special purpose tools. We anticipate NEFI to enable the collection of larger datasets by reducing the time spent on graph extraction. The analysis of these new datasets may open up the possibility to gain new insights into the structure and function of various types of networks. NEFI is open source and available http://nefi.mpi-inf.mpg.de