Hybrid Focal Stereo Networks for Pattern Analysis in Homogeneous Scenes

In this paper we address the problem of multiple camera calibration in the presence of a homogeneous scene, and without the possibility of employing calibration object based methods. The proposed solution exploits salient features present in a larger field of view, but instead of employing active vision we replace the cameras with stereo rigs featuring a long focal analysis camera, as well as a short focal registration camera. Thus, we are able to propose an accurate solution which does not require intrinsic variation models as in the case of zooming cameras. Moreover, the availability of the two views simultaneously in each rig allows for pose re-estimation between rigs as often as necessary. The algorithm has been successfully validated in an indoor setting, as well as on a difficult scene featuring a highly dense pilgrim crowd in Makkah.Comment: 13 pages, 6 figures, submitted to Machine Vision and Application

Identification of criticality in neuronal avalanches: II. A theoretical and empirical investigation of the Driven case

The observation of apparent power laws in neuronal systems has led to the suggestion that the brain is at, or close to, a critical state and may be a self-organised critical system. Within the framework of self-organised criticality a separation of timescales is thought to be crucial for the observation of power-law dynamics and computational models are often constructed with this property. However, this is not necessarily a characteristic of physiological neural networks—external input does not only occur when the network is at rest/a steady state. In this paper we study a simple neuronal network model driven by a continuous external input (i.e. the model does not have an explicit separation of timescales from seeding the system only when in the quiescent state) and analytically tuned to operate in the region of a critical state (it reaches the critical regime exactly in the absence of input—the case studied in the companion paper to this article). The system displays avalanche dynamics in the form of cascades of neuronal firing separated by periods of silence. We observe partial scale-free behaviour in the distribution of avalanche size for low levels of external input. We analytically derive the distributions of waiting times and investigate their temporal behaviour in relation to different levels of external input, showing that the system’s dynamics can exhibit partial long-range temporal correlations. We further show that as the system approaches the critical state by two alternative ‘routes’, different markers of criticality (partial scale-free behaviour and long-range temporal correlations) are displayed. This suggests that signatures of criticality exhibited by a particular system in close proximity to a critical state are dependent on the region in parameter space at which the system (currently) resides

Identification of criticality in neuronal avalanches: I. A theoretical investigation of the non-driven case

In this paper, we study a simple model of a purely excitatory neural network that, by construction, operates at a critical point. This model allows us to consider various markers of criticality and illustrate how they should perform in a finite-size system. By calculating the exact distribution of avalanche sizes, we are able to show that, over a limited range of avalanche sizes which we precisely identify, the distribution has scale free properties but is not a power law. This suggests that it would be inappropriate to dismiss a system as not being critical purely based on an inability to rigorously fit a power law distribution as has been recently advocated. In assessing whether a system, especially a finite-size one, is critical it is thus important to consider other possible markers. We illustrate one of these by showing the divergence of susceptibility as the critical point of the system is approached. Finally, we provide evidence that power laws may underlie other observables of the system that may be more amenable to robust experimental assessment

Self-Calibration of Cameras with Euclidean Image Plane in Case of Two Views and Known Relative Rotation Angle

The internal calibration of a pinhole camera is given by five parameters that are combined into an upper-triangular $3\times 3$ calibration matrix. If the skew parameter is zero and the aspect ratio is equal to one, then the camera is said to have Euclidean image plane. In this paper, we propose a non-iterative self-calibration algorithm for a camera with Euclidean image plane in case the remaining three internal parameters --- the focal length and the principal point coordinates --- are fixed but unknown. The algorithm requires a set of $N \geq 7$ point correspondences in two views and also the measured relative rotation angle between the views. We show that the problem generically has six solutions (including complex ones). The algorithm has been implemented and tested both on synthetic data and on publicly available real dataset. The experiments demonstrate that the method is correct, numerically stable and robust.Comment: 13 pages, 7 eps-figure

Normal frames and the validity of the equivalence principle. III. The case along smooth maps with separable points of self-intersection

The equivalence principle is treated on a mathematically rigorous base on sufficiently general subsets of a differentiable manifold. This is carried out using the basis of derivations of the tensor algebra over that manifold. Necessary and/or sufficient conditions of existence, uniqueness, and holonomicity of these bases in which the components of the derivations of the tensor algebra over it vanish on these subsets, are studied. The linear connections are considered in this context. It is shown that the equivalence principle is identically valid at any point, and along any path, in every gravitational theory based on linear connections. On higher dimensional submanifolds it may be valid only in certain exceptional cases.Comment: 15 standard LaTeX 2e (11pt, A4) pages. The package amsfonts is require

Rectification from Radially-Distorted Scales

This paper introduces the first minimal solvers that jointly estimate lens distortion and affine rectification from repetitions of rigidly transformed coplanar local features. The proposed solvers incorporate lens distortion into the camera model and extend accurate rectification to wide-angle images that contain nearly any type of coplanar repeated content. We demonstrate a principled approach to generating stable minimal solvers by the Grobner basis method, which is accomplished by sampling feasible monomial bases to maximize numerical stability. Synthetic and real-image experiments confirm that the solvers give accurate rectifications from noisy measurements when used in a RANSAC-based estimator. The proposed solvers demonstrate superior robustness to noise compared to the state-of-the-art. The solvers work on scenes without straight lines and, in general, relax the strong assumptions on scene content made by the state-of-the-art. Accurate rectifications on imagery that was taken with narrow focal length to near fish-eye lenses demonstrate the wide applicability of the proposed method. The method is fully automated, and the code is publicly available at https://github.com/prittjam/repeats.Comment: pre-prin

A 3D Face Modelling Approach for Pose-Invariant Face Recognition in a Human-Robot Environment

Face analysis techniques have become a crucial component of human-machine interaction in the fields of assistive and humanoid robotics. However, the variations in head-pose that arise naturally in these environments are still a great challenge. In this paper, we present a real-time capable 3D face modelling framework for 2D in-the-wild images that is applicable for robotics. The fitting of the 3D Morphable Model is based exclusively on automatically detected landmarks. After fitting, the face can be corrected in pose and transformed back to a frontal 2D representation that is more suitable for face recognition. We conduct face recognition experiments with non-frontal images from the MUCT database and uncontrolled, in the wild images from the PaSC database, the most challenging face recognition database to date, showing an improved performance. Finally, we present our SCITOS G5 robot system, which incorporates our framework as a means of image pre-processing for face analysis

Auto-parallel equation as Euler-Lagrange's equation in spaces with affine connections and metrics

The auto-parallel equation over spaces with affine connections and metrics is considered as a result of the application of the method of Lagrangians with covariant derivatives (MLCD) on a given Lagrangian density.Comment: 19 pages, LaTe

High fluxes of deep volatiles from ocean island volcanoes: Insights from El Hierro, Canary Islands

Basaltic volcanism contributes significant fluxes of volatiles (CO2, H2O, S, F, Cl) to the Earth’s surface environment. Quantifying volatile fluxes requires initial melt volatile concentrations to be determined, which can be accessed through crystal-hosted melt inclusions. However, melt inclusions in volatile-rich mafic alkaline basalts, such as those erupted at ocean islands, often trap partially degassed melts, meaning that magmatic volatile fluxes from these tectonic settings are often significantly underestimated. We have measured major, trace element and volatile concentrations in melt inclusions from a series of young (<20 ka) basanites from El Hierro, Canary Islands. Our melt inclusions show some of the highest CO2 (up to 3600 ppm) and S (up to 4290 ppm) concentrations measured in ocean island basalts to date, in agreement with data from the recent 2011-2012 eruption. Volatile enrichment is observed in melt inclusions with crystallisation-controlled major element compositions and highly variable trace element ratios such as La/Yb. We use volatile-trace element ratios to calculate original magmatic CO2 contents up to 4.2 wt%, which indicates at least 65% of the original CO2 was degassed prior to melt inclusion trapping. The trace element contents and ratios of El Hierro magmas are best reproduced by 1-8% partial melting of a garnet lherzolite mantle source. Our projected CO2 (200-680 ppm) and S (265-450 ppm) concentrations for the source are consistent with upper estimates for primitive mantle. However, El Hierro magmas have elevated F/Nd and F/Cl in comparison with melts from a primitive mantle, indicating that the mantle must also contain a component enriched in F and other volatiles, most probably recycled oceanic lithosphere. Our modelled original magmatic CO2 contents indicates that, per mass unit, volatile fluxes from El Hierro magmas are up to two orders of magnitude greater than from typical mid-ocean ridge basalts and 1.5 to 7 times greater than from recent Icelandic eruptions, indicating large variability in the primary volatile content of magmas formed in di fferent geodynamic settings, or even within di fferent ocean islands. Our results highlight the importance of characterising mantle heterogeneity in order to accurately constrain both short- and long-term magmatic volatile emissions and fluxes from ocean island volcanoes.NERC studentship NE/L002469/1 NERC grant 526 IMF600/101