Evaluation of two-view geometry methods with automatic ground-truth generation

A large number of methods have been published that aim to evaluate various components of multi-view geometry systems. Most of these have focused on the feature extraction, description and matching stages (the visual front end), since geometry computation can be evaluated through simulation. Many data sets are constrained to small scale scenes or planar scenes that are not challenging to new algorithms, or require special equipment. This paper presents a method for automatically generating geometry ground truth and challenging test cases from high spatio-temporal resolution video. The objective of the system is to enable data collection at any physical scale, in any location and in various parts of the electromagnetic spectrum. The data generation process consists of collecting high resolution video, computing accurate sparse 3D reconstruction, video frame culling and down sampling, and test case selection. The evaluation process consists of applying a test 2-view geometry method to every test case and comparing the results to the ground truth. This system facilitates the evaluation of the whole geometry computation process or any part thereof against data compatible with a realistic application. A collection of example data sets and evaluations is included to demonstrate the range of applications of the proposed system.

Analysis of terrain geometry representations for traversability of a Mars rover

For a planetary rover to successfully traverse across unstructured terrain autonomously, one of the major challenges is to assess its local traversability such that it can plan a trajectory to achieve its mission goals efficiently while minimising risk to the vehicle itself. This paper aims to provide a comparative study on different approaches for representing the geometry of Martian terrain for the purpose of evaluating terrain traversability. An accurate representation of the geometric properties of the terrain is essential as it can directly affect the determination of traversability for a ground vehicle. We explore current state-of-the-art techniques for terrain estimation, in particular Gaussian Processes (GP) in various forms, and discuss the suitability of each technique in the context of an unstructured Martian terrain. Furthermore, we present the limitations of regression techniques in terms of spatial correlation and continuity assumptions, and the impact on traversability analysis of a planetary rover across unstructured terrain. The analysis was performed on datasets of the Mars Yard at the Powerhouse Museum in Sydney, obtained using the onboard RGB-D camera.

Are in vitro estimates of cell diffusivity and cell proliferation rate sensitive to assay geometry?

Cells respond to various biochemical and physical cues during wound–healing and tumour progression. In vitro assays used to study these processes are typically conducted in one particular geometry and it is unclear how the assay geometry affects the capacity of cell populations to spread, or whether the relevant mechanisms, such as cell motility and cell proliferation, are somehow sensitive to the geometry of the assay. In this work we use a circular barrier assay to characterise the spreading of cell populations in two different geometries. Assay 1 describes a tumour–like geometry where a cell population spreads outwards into an open space. Assay 2 describes a wound–like geometry where a cell population spreads inwards to close a void. We use a combination of discrete and continuum mathematical models and automated image processing methods to obtain independent estimates of the effective cell diffusivity, D, and the effective cell proliferation rate, λ. Using our parameterised mathematical model we confirm that our estimates of D and λ accurately predict the time–evolution of the location of the leading edge and the cell density profiles for both assay 1 and assay 2. Our work suggests that the effective cell diffusivity is up to 50% lower for assay 2 compared to assay 1, whereas the effective cell proliferation rate is up to 30% lower for assay 2 compared to assay 1.

Object tracking via non-Euclidean geometry : a Grassmann approach

A robust visual tracking system requires an object appearance model that is able to handle occlusion, pose, and illumination variations in the video stream. This can be difficult to accomplish when the model is trained using only a single image. In this paper, we first propose a tracking approach based on affine subspaces (constructed from several images) which are able to accommodate the abovementioned variations. We use affine subspaces not only to represent the object, but also the candidate areas that the object may occupy. We furthermore propose a novel approach to measure affine subspace-to-subspace distance via the use of non-Euclidean geometry of Grassmann manifolds. The tracking problem is then considered as an inference task in a Markov Chain Monte Carlo framework via particle filtering. Quantitative evaluation on challenging video sequences indicates that the proposed approach obtains considerably better performance than several recent state-of-the-art methods such as Tracking-Learning-Detection and MILtrack.

Surface magnetoplasma waves at the interface between a plasma-like medium and a metal in the Voigt geometry

Theoretical and experimental results associated with the studies of different properties of surface-type waves (SW) in plasma-like medium-metal structures are reviewed. The propagation of surface waves in the Voigt geometry (the SW propagate across the external magnetic field, which is parallel to the interface) is considered. Various problems dealing with the linear properties of the SW (dispersion characteristics, electromagnetic fields topography, influence of the inhomogeneity of the medium, etc.); excitation mechanisms of the plasma-metal waveguide structures (parametric, drift, diffraction, etc. mechanisms); nonlinear effects associated with SW propagation (higher harmonics generation, self-interaction, nonlinear damping, nonlinear interactions, etc.) are presented. In many cases the results are valid for both gaseous and solid-state plasmas. © 1999 Elsevier Science B.V. All rights reserved.

Three-dimensional geological modelling of the Galilee and central Eromanga basins, Australia: New insights into aquifer/aquitard geometry and potential influence of faults on inter-connectivity

Study region The Galilee and Eromanga basins are located in central Queensland, Australia. Both basins are components of the Great Artesian Basin which host some of the most significant groundwater resources in Australia. Study focus This study evaluates the influence of regional faults on groundwater flow in an aquifer/aquitard interbedded succession that form one of the largest Artesian Basins in the world. In order to assess the significance of regional faults as potential barriers or conduits to groundwater flow, vertical displacements of the major aquifers and aquitards were studied at each major fault and the general hydraulic relationship of units that are juxtaposed by the faults were considered. A three-dimensional (3D) geological model of the Galilee and Eromanga basins was developed based on integration of well log data, seismic surfaces, surface geology and elevation data. Geological structures were mapped in detail and major faults were characterised. New hydrological insights for the region Major faults that have been described in previous studies have been confirmed within the 3D geological model domain and a preliminary assessment of their hydraulic significance has been conducted. Previously unknown faults such as the Thomson River Fault (herein named) have also been identified in this study.

Formation of the three-dimensional geometry of the red blood cell membrane

Red blood cells (RBCs) are nonnucleated liquid capsules, enclosed in deformable viscoelastic membranes with complex three dimensional geometrical structures. Generally, RBC membranes are highly incompressible and resistant to areal changes. However, RBC membranes show a planar shear deformation and out of plane bending deformation. The behaviour of RBCs in blood vessels is investigated using numerical models. All the characteristics of RBC membranes should be addressed to develop a more accurate and stable model. This article presents an effective methodology to model the three dimensional geometry of the RBC membrane with the aid of commercial software COMSOL Multiphysics 4.2a and Fortran programming. Initially, a mesh is generated for a sphere using the COMSOL Multiphysics software to represent the RBC membrane. The elastic energy of the membrane is considered to determine a stable membrane shape. Then, the actual biconcave shape of the membrane is obtained based on the principle of virtual work, when the total energy is minimised. The geometry of the RBC membrane could be used with meshfree particle methods to simulate motion and deformation of RBCs in micro-capillaries

The dependence of computed tomography number to relative electron density conversion on phantom geometry and its impact on planned dose

A computed tomography number to relative electron density (CT-RED) calibration is performed when commissioning a radiotherapy CT scanner by imaging a calibration phantom with inserts of specified RED and recording the CT number displayed. In this work, CT-RED calibrations were generated using several commercially available phantoms to observe the effect of phantom geometry on conversion to electron density and, ultimately, the dose calculation in a treatment planning system. Using an anthropomorphic phantom as a gold standard, the CT number of a material was found to depend strongly on the amount and type of scattering material surrounding the volume of interest, with the largest variation observed for the highest density material tested, cortical bone. Cortical bone gave a maximum CT number difference of 1,110 when a cylindrical insert of diameter 28 mm scanned free in air was compared to that in the form of a 30 × 30 cm2 slab. The effect of using each CT-RED calibration on planned dose to a patient was quantified using a commercially available treatment planning system. When all calibrations were compared to the anthropomorphic calibration, the largest percentage dose difference was 4.2 % which occurred when the CT-RED calibration curve was acquired with heterogeneity inserts removed from the phantom and scanned free in air. The maximum dose difference observed between two dedicated CT-RED phantoms was ±2.1 %. A phantom that is to be used for CT-RED calibrations must have sufficient water equivalent scattering material surrounding the heterogeneous objects that are to be used for calibration.

The equilibrium geometry and electronic structure of Bi nanolines on clean and hydrogenated Si(001) surfaces

The equilibrium geometry, electronic structure and energetic stability of Bi nanolines on clean and hydrogenated Si(001) surfaces have been examined by means of ab initio total energy calculations and scanning tunnelling microscopy. For the Bi nanolines on a clean Si surface the two most plausible structural models, the Miki or M model (Miki et al 1999 Phys. Rev. B 59 14868) and the Haiku or H model (Owen et al 2002 Phys. Rev. Lett. 88 226104), have been examined in detail. The results of the total energy calculations support the stability of the H model over the M model, in agreement with previous theoretical results. For Bi nanolines on the hydrogenated Si(001) surface, we find that an atomic configuration derived from the H model is also more stable than an atomic configuration derived from the M model. However, the energetically less stable (M) model exhibits better agreement with experimental measurements for equilibrium geometry. The electronic structures of the H and M models are very similar. Both models exhibit a semiconducting character, with the highest occupied Bi-derived bands lying at ~0.5 eV below the valence band maximum. Simulated and experimental STM images confirm that at a low negative bias the Bi lines exhibit an 'antiwire' property for both structural models.

The geometry of Bi nanolines on Si(0 0 1)

A study of the Bi nanoline geometry on Si(0 0 1) has been performed using a combination of ab initio theoretical technique and scanning tunnelling microscopy (STM). Our calculations demonstrate decisively that the recently proposed Haiku geometry is a lower energy configuration than any of the previously proposed line geometries. Furthermore, we have made comparisons between STM constant-current topographs of the lines and Tersoff–Haman STM simulations. Although the Haiku and the Miki geometries both reproduce the main features of the constant-current topographs, the simulated STM images of the Miki geometry have a dark stripe between the dimer rows that does not correspond well with experiment.

A follow up MRI-based geometry and computational fluid dynamics study of carotid bifurcation

Cardiovascular disease is the leading causes of death in the developed world. Wall shear stress (WSS) is associated with the initiation and progression of atherogenesis. This study combined the recent advances in MR imaging and computational fluid dynamics (CFD) and evaluated the patient-specific carotid bifurcation. The patient was followed up for 3 years. The geometry changes (tortuosity, curvature, ICA/CCA area ratios, central to the cross-sectional curvature, maximum stenosis) and the CFD factors (Velocity distribute, Wall Shear Stress (WSS) and Oscillatory Shear Index (OSI)) were compared at different time points.The carotid stenosis was a slight increase in the central to the cross-sectional curvature, and it was minor and variable curvature changes for carotid centerline. The OSI distribution presents ahigh-values in the same region where carotid stenosis and normal border, indicating complex flow and recirculation.The significant geometric changes observed during the follow-up may also cause significant changes in bifurcation hemodynamics.

Study of tracheal collapsibility, compliance and stress by considering its asymmetric geometry

The shape of tracheal cartilage has been widely treated as symmetric in analytical and numerical models. However, according to both histological images and in vivo medical image, tracheal cartilage is of highly asymmetric shape. Taking the cartilage as symmetric structure will induce bias in calculation of the collapse behavior, as well as compliance and muscular stress. However, this has been rarely discussed. In this paper, tracheal collapse is represented by considering its asymmetric shape. For comparison, the symmetric shape, which is reconstructed by half of the cartilage, is also presented. A comparison of cross-sectional area, compliance of airway and stress in the muscular membrane, determined by asymmetric shape and symmetric shape is made. The result indicates that the symmetric assumption brings a small error, around 5% in predicting the cross-sectional area under loading conditions. The relative error of compliance is more than 10%. Particularly when the pressure is close to zero, the error could be more than 50%. The model considering the symmetric shape results in a significant difference in predicting stress in muscular membrane by either under- or over-estimating it. In conclusion, tracheal cartilage should not be treated as a symmetric structure. The results obtained in this study are helpful in evaluating the error induced by the assumption in geometry.

Fluid-structure interaction study on human arterial plaque with patient specific geometry and boundary conditions

Atherosclerotic plaque rupture has been extensively considered as the leading cause of death in western countries. It is believed that high stresses within plaque can be an important factor on triggering the rupture of the plaque. Stress analysis in the coronary and carotid arteries with plaque have been developed by many researchers from 2D to 3-D models, from structure analysis only to the Fluid-Structure Interaction (FSI) models[1].

Geometry-free stochastic analysis of BDS triple frequency signals

The paper presents a geometry-free approach to assess the variation of covariance matrices of undifferenced triple frequency GNSS measurements and its impact on positioning solutions. Four independent geometryfree/ ionosphere-free (GFIF) models formed from original triple-frequency code and phase signals allow for effective computation of variance-covariance matrices using real data. Variance Component Estimation (VCE) algorithms are implemented to obtain the covariance matrices for three pseudorange and three carrier-phase signals epoch-by-epoch. Covariance results from the triple frequency Beidou System (BDS) and GPS data sets demonstrate that the estimated standard deviation varies in consistence with the amplitude of actual GFIF error time series. The single point positioning (SPP) results from BDS ionosphere-free measurements at four MGEX stations demonstrate an improvement of up to about 50% in Up direction relative to the results based on a mean square statistics. Additionally, a more extensive SPP analysis at 95 global MGEX stations based on GPS ionosphere-free measurements shows an average improvement of about 10% relative to the traditional results. This finding provides a preliminary confirmation that adequate consideration of the variation of covariance leads to the improvement of GNSS state solutions.