Wrapping the cube and other polyhedra

An infinite series of twofold, two-way weavings of the cube, corresponding to 'wrappings', or double covers of the cube, is described with the aid of the two-parameter Goldberg- Coxeter construction. The strands of all such wrappings correspond to the central circuits (CCs) of octahedrites (four-regular polyhedral graphs with square and triangular faces), which for the cube necessarily have octahedral symmetry. Removing the symmetry constraint leads to wrappings of other eight-vertex convex polyhedra. Moreover, wrappings of convex polyhedra with fewer vertices can be generated by generalizing from octahedrites to i-hedrites, which additionally include digonal faces. When the strands of a wrapping correspond to the CCs of a four-regular graph that includes faces of size greater than 4, non-convex 'crinkled' wrappings are generated. The various generalizations have implications for activities as diverse as the construction of woven-closed baskets and the manufacture of advanced composite components of complex geometry. © 2012 The Royal Society.

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).

ChESS - Quick and Robust Detection of Chess-board Features

Localization of chess-board vertices is a common task in computer vision, underpinning many applications, but relatively little work focusses on designing a specific feature detector that is fast, accurate and robust. In this paper the `Chess-board Extraction by Subtraction and Summation' (ChESS) feature detector, designed to exclusively respond to chess-board vertices, is presented. The method proposed is robust against noise, poor lighting and poor contrast, requires no prior knowledge of the extent of the chess-board pattern, is computationally very efficient, and provides a strength measure of detected features. Such a detector has significant application both in the key field of camera calibration, as well as in Structured Light 3D reconstruction. Evidence is presented showing its robustness, accuracy, and efficiency in comparison to other commonly used detectors both under simulation and in experimental 3D reconstruction of flat plate and cylindrical objects

ChESS - Quick and robust detection of chess-board features

Localization of chess-board vertices is a common task in computer vision, underpinning many applications, but relatively little work focusses on designing a specific feature detector that is fast, accurate and robust. In this paper the 'Chess-board Extraction by Subtraction and Summation' (ChESS) feature detector, designed to exclusively respond to chess-board vertices, is presented. The method proposed is robust against noise, poor lighting and poor contrast, requires no prior knowledge of the extent of the chess-board pattern, is computationally very efficient, and provides a strength measure of detected features. Such a detector has significant application both in the key field of camera calibration, as well as in structured light 3D reconstruction. Evidence is presented showing its superior robustness, accuracy, and efficiency in comparison to other commonly used detectors, including Harris & Stephens and SUSAN, both under simulation and in experimental 3D reconstruction of flat plate and cylindrical objects. © 2013 Elsevier Inc. All rights reserved.

Robust recognition of chess-boards under deformation

Current methods for formation of detected chess-board vertices into a grid structure tend to be weak in situations with a warped grid, and false and missing vertex-features. In this paper we present a highly robust, yet efficient, scheme suitable for inference of regular 2D square mesh structure from vertices recorded both during projection of a chess-board pattern onto 3D objects, and in the more simple case of camera calibration. Examples of the method's performance in a lung function measuring application, observing chess-boards projected on to patients' chests, are given. The method presented is resilient to significant surface deformation, and tolerates inexact vertex-feature detection. This robustness results from the scheme's novel exploitation of feature orientation information. © 2013 IEEE.

Dense active appearance models using a bounded diameter minimum spanning tree

We present a method for producing dense Active Appearance Models (AAMs), suitable for video-realistic synthesis. To this end we estimate a joint alignment of all training images using a set of pairwise registrations and ensure that these pairwise registrations are only calculated between similar images. This is achieved by defining a graph on the image set whose edge weights correspond to registration errors and computing a bounded diameter minimum spanning tree (BDMST). Dense optical flow is used to compute pairwise registration and we introduce a flow refinement method to align small scale texture. Once registration between training images has been established we propose a method to add vertices to the AAM in a way that minimises error between the observed flow fields and a flow field interpolated between the AAM mesh points. We demonstrate a significant improvement in model compactness using the proposed method and show it dealing with cases that are problematic for current state-of-the-art approaches.