Finite volume distance field solution applied to medial axis transform

Accurate and efficient computation of the nearest wall distance d (or level set) is important for many areas of computational science/engineering. Differential equation-based distance/ level set algorithms, such as the hyperbolic-natured Eikonal equation, have demonstrated valuable computational efficiency. Here, in the context, as an 'auxiliary' equation to the main flow equations, the Eikonal equation is solved efficiently with two different finite volume approaches (the cell vertex and cell-centered). Application of the distance solution is studied for various geometries. Moreover, a procedure using the differential field to obtain the medial axis transform (MAT) for different geometries is presented. The latter provides a skeleton representation of geometric models that has many useful analysis properties. As an alternative approach to the pure geometric methods (e.g. the Voronoi approach), the current d-MAT procedure bypasses many difficulties that are usually encountered by pure geometric methods, especially in three dimensional space. It is also shown that the d-MAT approach provides the potential to sculpt/control the MAT form for specialized solution purposes. Copyright © 2010 by the American Institute of Aeronautics and Astronautics, Inc.

Semantic Discriminant mapping for classification and browsing of remote sensing textures and objects

We present a new approach based on Discriminant Analysis to map a high dimensional image feature space onto a subspace which has the following advantages: 1. each dimension corresponds to a semantic likelihood, 2. an efficient and simple multiclass classifier is proposed and 3. it is low dimensional. This mapping is learnt from a given set of labeled images with a class groundtruth. In the new space a classifier is naturally derived which performs as well as a linear SVM. We will show that projecting images in this new space provides a database browsing tool which is meaningful to the user. Results are presented on a remote sensing database with eight classes, made available online. The output semantic space is a low dimensional feature space which opens perspectives for other recognition tasks. © 2005 IEEE.

High order schemes on three-dimensional general polyhedral meshes - Application to the level set method

In this article, we detail the methodology developed to construct arbitrarily high order schemes - linear and WENO - on 3D mixed-element unstructured meshes made up of general convex polyhedral elements. The approach is tailored specifically for the solution of scalar level set equations for application to incompressible two-phase flow problems. The construction of WENO schemes on 3D unstructured meshes is notoriously difficult, as it involves a much higher level of complexity than 2D approaches. This due to the multiplicity of geometrical considerations introduced by the extra dimension, especially on mixed-element meshes. Therefore, we have specifically developed a number of algorithms to handle mixed-element meshes composed of convex polyhedra with convex polygonal faces. The contribution of this work concerns several areas of interest: the formulation of an improved methodology in 3D, the minimisation of computational runtime in the implementation through the maximum use of pre-processing operations, the generation of novel methods to handle complex 3D mixed-element meshes and finally the application of the method to the transport of a scalar level set. © 2012 Global-Science Press.

Automated sparse 3D point cloud generation of infrastructure using its distinctive visual features

The commercial far-range (>10 m) spatial data collection methods for acquiring infrastructure’s geometric data are not completely automated because of the necessary manual pre- and/or post-processing work. The required amount of human intervention and, in some cases, the high equipment costs associated with these methods impede their adoption by the majority of infrastructure mapping activities. This paper presents an automated stereo vision-based method, as an alternative and inexpensive solution, to producing a sparse Euclidean 3D point cloud of an infrastructure scene utilizing two video streams captured by a set of two calibrated cameras. In this process SURF features are automatically detected and matched between each pair of stereo video frames. 3D coordinates of the matched feature points are then calculated via triangulation. The detected SURF features in two successive video frames are automatically matched and the RANSAC algorithm is used to discard mismatches. The quaternion motion estimation method is then used along with bundle adjustment optimization to register successive point clouds. The method was tested on a database of infrastructure stereo video streams. The validity and statistical significance of the results were evaluated by comparing the spatial distance of randomly selected feature points with their corresponding tape measurements.

Mapping the global flow of steel: from steelmaking to end-use goods.

Our society is addicted to steel. Global demand for steel has risen to 1.4 billion tonnes a year and is set to at least double by 2050, while the steel industry generates nearly a 10th of the world's energy related CO₂ emissions. Meeting our 2050 climate change targets would require a 75% reduction in CO₂ emissions for every tonne of steel produced and finding credible solutions is proving a challenge. The starting point for understanding the environmental impacts of steel production is to accurately map the global steel supply chain and identify the biggest steel flows where actions can be directed to deliver the largest impact. In this paper we present a map of global steel, which for the first time traces steel flows from steelmaking, through casting, forming, and rolling, to the fabrication of final goods. The diagram reveals the relative scale of steel flows and shows where efforts to improve energy and material efficiency should be focused.

The most persistent soft-clique in a set of sampled graphs

When searching for characteristic subpatterns in potentially noisy graph data, it appears self-evident that having multiple observations would be better than having just one. However, it turns out that the inconsistencies introduced when different graph instances have different edge sets pose a serious challenge. In this work we address this challenge for the problem of finding maximum weighted cliques. We introduce the concept of most persistent soft-clique. This is subset of vertices, that 1) is almost fully or at least densely connected, 2) occurs in all or almost all graph instances, and 3) has the maximum weight. We present a measure of clique-ness, that essentially counts the number of edge missing to make a subset of vertices into a clique. With this measure, we show that the problem of finding the most persistent soft-clique problem can be cast either as: a) a max-min two person game optimization problem, or b) a min-min soft margin optimization problem. Both formulations lead to the same solution when using a partial Lagrangian method to solve the optimization problems. By experiments on synthetic data and on real social network data we show that the proposed method is able to reliably find soft cliques in graph data, even if that is distorted by random noise or unreliable observations. Copyright 2012 by the author(s)/owner(s).