Video normals from colored lights

We present an algorithm and the associated single-view capture methodology to acquire the detailed 3D shape, bends, and wrinkles of deforming surfaces. Moving 3D data has been difficult to obtain by methods that rely on known surface features, structured light, or silhouettes. Multispectral photometric stereo is an attractive alternative because it can recover a dense normal field from an untextured surface. We show how to capture such data, which in turn allows us to demonstrate the strengths and limitations of our simple frame-to-frame registration over time. Experiments were performed on monocular video sequences of untextured cloth and faces with and without white makeup. Subjects were filmed under spatially separated red, green, and blue lights. Our first finding is that the color photometric stereo setup is able to produce smoothly varying per-frame reconstructions with high detail. Second, when these 3D reconstructions are augmented with 2D tracking results, one can register both the surfaces and relax the homogenous-color restriction of the single-hue subject. Quantitative and qualitative experiments explore both the practicality and limitations of this simple multispectral capture system.

The accuracy of parameter estimation from noisy data, with application to resonance peak estimation in distributed Brillouin sensing

Distributed Brillouin sensing of strain and temperature works by making spatially resolved measurements of the position of the measurand-dependent extremum of the resonance curve associated with the scattering process in the weakly nonlinear regime. Typically, measurements of backscattered Stokes intensity (the dependent variable) are made at a number of predetermined fixed frequencies covering the design measurand range of the apparatus and combined to yield an estimate of the position of the extremum. The measurand can then be found because its relationship to the position of the extremum is assumed known. We present analytical expressions relating the relative error in the extremum position to experimental errors in the dependent variable. This is done for two cases: (i) a simple non-parametric estimate of the mean based on moments and (ii) the case in which a least squares technique is used to fit a Lorentzian to the data. The question of statistical bias in the estimates is discussed and in the second case we go further and present for the first time a general method by which the probability density function (PDF) of errors in the fitted parameters can be obtained in closed form in terms of the PDFs of the errors in the noisy data.

Theory and data for area summation of contrast with and without uncertainty:evidence for a noisy energy model

Contrast sensitivity improves with the area of a sine-wave grating, but why? Here we assess this phenomenon against contemporary models involving spatial summation, probability summation, uncertainty, and stochastic noise. Using a two-interval forced-choice procedure we measured contrast sensitivity for circular patches of sine-wave gratings with various diameters that were blocked or interleaved across trials to produce low and high extrinsic uncertainty, respectively. Summation curves were steep initially, becoming shallower thereafter. For the smaller stimuli, sensitivity was slightly worse for the interleaved design than for the blocked design. Neither area nor blocking affected the slope of the psychometric function. We derived model predictions for noisy mechanisms and extrinsic uncertainty that was either low or high. The contrast transducer was either linear (c1.0) or nonlinear (c2.0), and pooling was either linear or a MAX operation. There was either no intrinsic uncertainty, or it was fixed or proportional to stimulus size. Of these 10 canonical models, only the nonlinear transducer with linear pooling (the noisy energy model) described the main forms of the data for both experimental designs. We also show how a cross-correlator can be modified to fit our results and provide a contemporary presentation of the relation between summation and the slope of the psychometric function.

The accuracy of parameter estimation from noisy data, with application to resonance peak estimation in distributed Brillouin sensing

Distributed Brillouin sensing of strain and temperature works by making spatially resolved measurements of the position of the measurand-dependent extremum of the resonance curve associated with the scattering process in the weakly nonlinear regime. Typically, measurements of backscattered Stokes intensity (the dependent variable) are made at a number of predetermined fixed frequencies covering the design measurand range of the apparatus and combined to yield an estimate of the position of the extremum. The measurand can then be found because its relationship to the position of the extremum is assumed known. We present analytical expressions relating the relative error in the extremum position to experimental errors in the dependent variable. This is done for two cases: (i) a simple non-parametric estimate of the mean based on moments and (ii) the case in which a least squares technique is used to fit a Lorentzian to the data. The question of statistical bias in the estimates is discussed and in the second case we go further and present for the first time a general method by which the probability density function (PDF) of errors in the fitted parameters can be obtained in closed form in terms of the PDFs of the errors in the noisy data.

Advanced data driven visualisation for geo-spatial data

Most current 3D landscape visualisation systems either use bespoke hardware solutions, or offer a limited amount of interaction and detail when used in realtime mode. We are developing a modular, data driven 3D visualisation system that can be readily customised to specific requirements. By utilising the latest software engineering methods and bringing a dynamic data driven approach to geo-spatial data visualisation we will deliver an unparalleled level of customisation in near-photo realistic, realtime 3D landscape visualisation. In this paper we show the system framework and describe how this employs data driven techniques. In particular we discuss how data driven approaches are applied to the spatiotemporal management aspect of the application framework, and describe the advantages these convey.

Data assimilation for precipitation nowcasting using Bayesian inference

This work introduces a new variational Bayes data assimilation method for the stochastic estimation of precipitation dynamics using radar observations for short term probabilistic forecasting (nowcasting). A previously developed spatial rainfall model based on the decomposition of the observed precipitation field using a basis function expansion captures the precipitation intensity from radar images as a set of ‘rain cells’. The prior distributions for the basis function parameters are carefully chosen to have a conjugate structure for the precipitation field model to allow a novel variational Bayes method to be applied to estimate the posterior distributions in closed form, based on solving an optimisation problem, in a spirit similar to 3D VAR analysis, but seeking approximations to the posterior distribution rather than simply the most probable state. A hierarchical Kalman filter is used to estimate the advection field based on the assimilated precipitation fields at two times. The model is applied to tracking precipitation dynamics in a realistic setting, using UK Met Office radar data from both a summer convective event and a winter frontal event. The performance of the model is assessed both traditionally and using probabilistic measures of fit based on ROC curves. The model is shown to provide very good assimilation characteristics, and promising forecast skill. Improvements to the forecasting scheme are discussed

Visual data mining: integrating machine learning with information visualization

Today, the data available to tackle many scientific challenges is vast in quantity and diverse in nature. The exploration of heterogeneous information spaces requires suitable mining algorithms as well as effective visual interfaces. Most existing systems concentrate either on mining algorithms or on visualization techniques. Though visual methods developed in information visualization have been helpful, for improved understanding of a complex large high-dimensional dataset, there is a need for an effective projection of such a dataset onto a lower-dimension (2D or 3D) manifold. This paper introduces a flexible visual data mining framework which combines advanced projection algorithms developed in the machine learning domain and visual techniques developed in the information visualization domain. The framework follows Shneiderman’s mantra to provide an effective user interface. The advantage of such an interface is that the user is directly involved in the data mining process. We integrate principled projection methods, such as Generative Topographic Mapping (GTM) and Hierarchical GTM (HGTM), with powerful visual techniques, such as magnification factors, directional curvatures, parallel coordinates, billboarding, and user interaction facilities, to provide an integrated visual data mining framework. Results on a real life high-dimensional dataset from the chemoinformatics domain are also reported and discussed. Projection results of GTM are analytically compared with the projection results from other traditional projection methods, and it is also shown that the HGTM algorithm provides additional value for large datasets. The computational complexity of these algorithms is discussed to demonstrate their suitability for the visual data mining framework.

Addressing missing data in geochemistry: a non-linear approach

Exploratory analysis of petroleum geochemical data seeks to find common patterns to help distinguish between different source rocks, oils and gases, and to explain their source, maturity and any intra-reservoir alteration. However, at the outset, one is typically faced with (a) a large matrix of samples, each with a range of molecular and isotopic properties, (b) a spatially and temporally unrepresentative sampling pattern, (c) noisy data and (d) often, a large number of missing values. This inhibits analysis using conventional statistical methods. Typically, visualisation methods like principal components analysis are used, but these methods are not easily able to deal with missing data nor can they capture non-linear structure in the data. One approach to discovering complex, non-linear structure in the data is through the use of linked plots, or brushing, while ignoring the missing data. In this paper we introduce a complementary approach based on a non-linear probabilistic model. Generative topographic mapping enables the visualisation of the effects of very many variables on a single plot, while also dealing with missing data. We show how using generative topographic mapping also provides an optimal method with which to replace missing values in two geochemical datasets, particularly where a large proportion of the data is missing.

Self-calibrated, multi-spectral photometric stereo for 3D face capture

This paper addresses the problem of obtaining 3d detailed reconstructions of human faces in real-time and with inexpensive hardware. We present an algorithm based on a monocular multi-spectral photometric-stereo setup. This system is known to capture high-detailed deforming 3d surfaces at high frame rates and without having to use any expensive hardware or synchronized light stage. However, the main challenge of such a setup is the calibration stage, which depends on the lights setup and how they interact with the specific material being captured, in this case, human faces. For this purpose we develop a self-calibration technique where the person being captured is asked to perform a rigid motion in front of the camera, maintaining a neutral expression. Rigidity constrains are then used to compute the head's motion with a structure-from-motion algorithm. Once the motion is obtained, a multi-view stereo algorithm reconstructs a coarse 3d model of the face. This coarse model is then used to estimate the lighting parameters with a stratified approach: In the first step we use a RANSAC search to identify purely diffuse points on the face and to simultaneously estimate this diffuse reflectance model. In the second step we apply non-linear optimization to fit a non-Lambertian reflectance model to the outliers of the previous step. The calibration procedure is validated with synthetic and real data.

Characterization of time-resolved laser differential phase using 3D complementary cumulative distribution functions

An experimental method for characterizing the time-resolved phase noise of a fast switching tunable laser is discussed. The method experimentally determines a complementary cumulative distribution function of the laser's differential phase as a function of time after a switching event. A time resolved bit error rate of differential quadrature phase shift keying formatted data, calculated using the phase noise measurements, was fitted to an experimental time-resolved bit error rate measurement using a field programmable gate array, finding a good agreement between the time-resolved bit error rates.

Does human capital endowment of FDI recipient countries really matter? Evidence from cross-country firm level data

The stylized literature on foreign direct investment suggests that developing countries should invest in the human capital of their labour force in order to attract foreign direct investment. However, if educational quality in developing country is uncertain such that formal education is a noisy signal of human capital, it might be rational for multinational enterprises to focus more on job-specific training than on formal education of the labour force. Using cross-country data from the textiles and garments industry, we demonstrate that training indeed has greater impact on firm efficiency in developing countries than formal education of the work force.

Recovering boundary data in planar heat conduction using boundary integral equation method

We consider a Cauchy problem for the heat equation, where the temperature field is to be reconstructed from the temperature and heat flux given on a part of the boundary of the solution domain. We employ a Landweber type method proposed in [2], where a sequence of mixed well-posed problems are solved at each iteration step to obtain a stable approximation to the original Cauchy problem. We develop an efficient boundary integral equation method for the numerical solution of these mixed problems, based on the method of Rothe. Numerical examples are presented both with exact and noisy data, showing the efficiency and stability of the proposed procedure and approximations.

Determining the temperature from incomplete boundary data

An iterative procedure for determining temperature fields from Cauchy data given on a part of the boundary is presented. At each iteration step, a series of mixed well-posed boundary value problems are solved for the heat operator and its adjoint. A convergence proof of this method in a weighted L2-space is included, as well as a stopping criteria for the case of noisy data. Moreover, a solvability result in a weighted Sobolev space for a parabolic initial boundary value problem of second order with mixed boundary conditions is presented. Regularity of the solution is proved. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Real-time 3D shape sensing and reconstruction scheme based upon fibre optic bragg gratings

An array of FBG curvature sensors are wavelength-interrogated and the recovered data combined with a three-dimensional algorithm to reconstruct in real time the enveloped object with a 1% to 9% volumetric error. © 2012 OSA.

Does human capital endowment of foreign direct investment recipient countries really matter? evidence from cross-country firm level data

The stylized literature on foreign direct investment (FDI) suggests that developing countries should invest in the human capital of their labor force in order to attract FDI. However, if educational quality in developing country is uncertain such that formal education is a noisy signal of human capital, it might be rational for multinational enterprises to focus more on job-specific training than on formal education of the labor force. Using cross-country data from the textiles and garments industry, we demonstrate that training indeed has a greater impact on firm efficiency in developing countries than formal education of the workforce. © 2013 John Wiley & Sons Ltd.