Unknown Radial Distortion Centers in Multiple View Geometry Problems

The radial undistortion model proposed by Fitzgibbon and the radial fundamental matrix were early steps to extend classical epipolar geometry to distorted cameras. Later minimal solvers have been proposed to find relative pose and radial distortion, given point correspondences between images. However, a big drawback of all these approaches is that they require the distortion center to be exactly known. In this paper we show how the distortion center can be absorbed into a new radial fundamental matrix. This new formulation is much more practical in reality as it allows also digital zoom, cropped images and camera-lens systems where the distortion center does not exactly coincide with the image center. In particular we start from the setting where only one of the two images contains radial distortion, analyze the structure of the particular radial fundamental matrix and show that the technique also generalizes to other linear multi-view relationships like trifocal tensor and homography. For the new radial fundamental matrix we propose different estimation algorithms from 9,10 and 11 points. We show how to extract the epipoles and prove the practical applicability on several epipolar geometry image pairs with strong distortion that - to the best of our knowledge - no other existing algorithm can handle properly.

One-sided Radial-Fundamental Matrix Estimation

For modern consumer cameras often approximate calibration data is available, making applications such as 3D reconstruction or photo registration easier as compared to the pure uncalibrated setting. In this paper we address the setting with calibrateduncalibrated image pairs: for one image intrinsic parameters are assumed to be known, whereas the second view has unknown distortion and calibration parameters. This situation arises e.g. when one would like to register archive imagery to recently taken photos. A commonly adopted strategy for determining epipolar geometry is based on feature matching and minimal solvers inside a RANSAC framework. However, only very few existing solutions apply to the calibrated-uncalibrated setting. We propose a simple and numerically stable two-step scheme to first estimate radial distortion parameters and subsequently the focal length using novel solvers. We demonstrate the performance on synthetic and real datasets.

Hyperspectral imagery framework for unmixing and dimensionality estimation

In hyperspectral imagery a pixel typically consists mixture of spectral signatures of reference substances, also called endmembers. Linear spectral mixture analysis, or linear unmixing, aims at estimating the number of endmembers, their spectral signatures, and their abundance fractions. This paper proposes a framework for hyperpsectral unmixing. A blind method (SISAL) is used for the estimation of the unknown endmember signature and their abundance fractions. This method solve a non-convex problem by a sequence of augmented Lagrangian optimizations, where the positivity constraints, forcing the spectral vectors to belong to the convex hull of the endmember signatures, are replaced by soft constraints. The proposed framework simultaneously estimates the number of endmembers present in the hyperspectral image by an algorithm based on the minimum description length (MDL) principle. Experimental results on both synthetic and real hyperspectral data demonstrate the effectiveness of the proposed algorithm.

Modelação e identificação de motor DC

O modelo matemático de um sistema real permite o conhecimento do seu comportamento dinâmico e é geralmente utilizado em problemas de engenharia. Por vezes os parâmetros utilizados pelo modelo são desconhecidos ou imprecisos. O envelhecimento e o desgaste do material são fatores a ter em conta pois podem causar alterações no comportamento do sistema real, podendo ser necessário efetuar uma nova estimação dos seus parâmetros. Para resolver este problema é utilizado o software desenvolvido pela empresa MathWorks, nomeadamente, o Matlab e o Simulink, em conjunto com a plataforma Arduíno cujo Hardware é open-source. A partir de dados obtidos do sistema real será aplicado um Ajuste de curvas (Curve Fitting) pelo Método dos Mínimos Quadrados de forma a aproximar o modelo simulado ao modelo do sistema real. O sistema desenvolvido permite a obtenção de novos valores dos parâmetros, de uma forma simples e eficaz, com vista a uma melhor aproximação do sistema real em estudo. A solução encontrada é validada com recurso a diferentes sinais de entrada aplicados ao sistema e os seus resultados comparados com os resultados do novo modelo obtido. O desempenho da solução encontrada é avaliado através do método das somas quadráticas dos erros entre resultados obtidos através de simulação e resultados obtidos experimentalmente do sistema real.

An Extension of Estimation of Domain of Attraction for Fractional Order Linear System Subject to Saturation Control

This paper employs the Lyapunov direct method for the stability analysis of fractional order linear systems subject to input saturation. A new stability condition based on saturation function is adopted for estimating the domain of attraction via ellipsoid approach. To further improve this estimation, the auxiliary feedback is also supported by the concept of stability region. The advantages of the proposed method are twofold: (1) it is straightforward to handle the problem both in analysis and design because of using Lyapunov method, (2) the estimation leads to less conservative results. A numerical example illustrates the feasibility of the proposed method.

Beyond Intermediates: The Role of Consumption and Commuting in the Construction of Local Input-Output Tables

It is a well-established fact in the literature on simulating Input-Output tables that mechanical methods for estimating intermediate trade lead to biased results where cross-hauling is underestimated and Type-I multipliers are overstated. Repeated findings to this effect have led to a primary emphasis on advocating the accurate estimation of intermediate trade flows. This paper reviews previous research and argues for a qualification of the consensus view: When simulating IO tables, construction approaches need to consider spill-over effects driven by wage and consumption flows. In particular, for the case of metropolitan economies, wage and consumption flows are important if accurate Type-II multipliers are to be obtained. This is demonstrated by constructing an interregional Input-Output table, which captures interdependencies between a city and its commuter belt, nested within the wider regional economy. In addition to identifying interdependencies caused by interregional intermediate purchases, data on subregional household incomes and commuter flows are used to identify interdependencies from wage payments and household consumption. The construction of the table is varied around a range of assumptions on intermediate trade and household consumption to capture the sensitivity of multipliers.

Perfusion-CT guided intravenous thrombolysis in patients with unknown-onset stroke: a randomized, double-blind, placebo-controlled, pilot feasibility trial.

INTRODUCTION: Patients with unknown stroke onset are generally excluded from acute recanalisation treatments. We designed a pilot study to assess feasibility of a trial of perfusion computed tomography (PCT)-guided thrombolysis in patients with ischemic tissue at risk of infarction and unknown stroke onset. METHODS: Patients with a supratentorial stroke of unknown onset in the middle cerebral artery territory and significant volume of at-risk tissue on PCT were randomized to intravenous thrombolysis with alteplase (0.9 mg/kg) or placebo. Feasibility endpoints were randomization and blinded treatment of patients within 2 h after hospital arrival, and the correct application (estimation) of the perfusion imaging criteria. RESULTS: At baseline, there was a trend towards older age [69.5 (57-78) vs. 49 (44-78) years] in the thrombolysis group (n = 6) compared to placebo (n = 6). Regarding feasibility, hospital arrival to treatment delay was above the allowed 2 h in three patients (25%). There were two protocol violations (17%) regarding PCT, both underestimating the predicted infarct in patients randomized in the placebo group. No symptomatic hemorrhage or death occurred during the first 7 days. Three of the four (75%) and one of the five (20%) patients were recanalized in the thrombolysis and placebo group respectively. The volume of non-infarcted at-risk tissue was 84 (44-206) cm(3) in the treatment arm and 29 (8-105) cm(3) in the placebo arm. CONCLUSIONS: This pilot study shows that a randomized PCT-guided thrombolysis trial in patients with stroke of unknown onset may be feasible if issues such as treatment delays and reliable identification of tissue at risk of infarction tissue are resolved. Safety and efficiency of such an approach need to be established.

Multiuser detection in a dynamic environment — Part II: Joint user identification and parameter estimation

The problem of jointly estimating the number, the identities, and the data of active users in a time-varying multiuser environment was examined in a companion paper (IEEE Trans. Information Theory, vol. 53, no. 9, September 2007), at whose core was the use of the theory of finite random sets on countable spaces. Here we extend that theory to encompass the more general problem of estimating unknown continuous parameters of the active-user signals. This problem is solved here by applying the theory of random finite sets constructed on hybrid spaces. We doso deriving Bayesian recursions that describe the evolution withtime of a posteriori densities of the unknown parameters and data.Unlike in the above cited paper, wherein one could evaluate theexact multiuser set posterior density, here the continuous-parameter Bayesian recursions do not admit closed-form expressions. To circumvent this difficulty, we develop numerical approximationsfor the receivers that are based on Sequential Monte Carlo (SMC)methods (“particle filtering”). Simulation results, referring to acode-divisin multiple-access (CDMA) system, are presented toillustrate the theory.

Sequential estimation of multipath MIMO-OFDM channels

Wireless “MIMO” systems, employing multiple transmit and receive antennas, promise a significant increase of channel capacity, while orthogonal frequency-division multiplexing (OFDM) is attracting a good deal of attention due to its robustness to multipath fading. Thus, the combination of both techniques is an attractive proposition for radio transmission. The goal of this paper is the description and analysis of a new and novel pilot-aided estimator of multipath block-fading channels. Typical models leading to estimation algorithms assume the number of multipath components and delays to be constant (and often known), while their amplitudes are allowed to vary with time. Our estimator is focused instead on the more realistic assumption that the number of channel taps is also unknown and varies with time following a known probabilistic model. The estimation problem arising from these assumptions is solved using Random-Set Theory (RST), whereby one regards the multipath-channel response as a single set-valued random entity.Within this framework, Bayesian recursive equations determine the evolution with time of the channel estimator. Due to the lack of a closed form for the solution of Bayesian equations, a (Rao–Blackwellized) particle filter (RBPF) implementation ofthe channel estimator is advocated. Since the resulting estimator exhibits a complexity which grows exponentially with the number of multipath components, a simplified version is also introduced. Simulation results describing the performance of our channel estimator demonstrate its effectiveness.

Source wavelet estimation for waveform inversion of crosshole georadar data

AbstractFor a wide range of environmental, hydrological, and engineering applications there is a fast growing need for high-resolution imaging. In this context, waveform tomographic imaging of crosshole georadar data is a powerful method able to provide images of pertinent electrical properties in near-surface environments with unprecedented spatial resolution. In contrast, conventional ray-based tomographic methods, which consider only a very limited part of the recorded signal (first-arrival traveltimes and maximum first-cycle amplitudes), suffer from inherent limitations in resolution and may prove to be inadequate in complex environments. For a typical crosshole georadar survey the potential improvement in resolution when using waveform-based approaches instead of ray-based approaches is in the range of one order-of- magnitude. Moreover, the spatial resolution of waveform-based inversions is comparable to that of common logging methods. While in exploration seismology waveform tomographic imaging has become well established over the past two decades, it is comparably still underdeveloped in the georadar domain despite corresponding needs. Recently, different groups have presented finite-difference time-domain waveform inversion schemes for crosshole georadar data, which are adaptations and extensions of Tarantola's seminal nonlinear generalized least-squares approach developed for the seismic case. First applications of these new crosshole georadar waveform inversion schemes on synthetic and field data have shown promising results. However, there is little known about the limits and performance of such schemes in complex environments. To this end, the general motivation of my thesis is the evaluation of the robustness and limitations of waveform inversion algorithms for crosshole georadar data in order to apply such schemes to a wide range of real world problems.One crucial issue to making applicable and effective any waveform scheme to real-world crosshole georadar problems is the accurate estimation of the source wavelet, which is unknown in reality. Waveform inversion schemes for crosshole georadar data require forward simulations of the wavefield in order to iteratively solve the inverse problem. Therefore, accurate knowledge of the source wavelet is critically important for successful application of such schemes. Relatively small differences in the estimated source wavelet shape can lead to large differences in the resulting tomograms. In the first part of my thesis, I explore the viability and robustness of a relatively simple iterative deconvolution technique that incorporates the estimation of the source wavelet into the waveform inversion procedure rather than adding additional model parameters into the inversion problem. Extensive tests indicate that this source wavelet estimation technique is simple yet effective, and is able to provide remarkably accurate and robust estimates of the source wavelet in the presence of strong heterogeneity in both the dielectric permittivity and electrical conductivity as well as significant ambient noise in the recorded data. Furthermore, our tests also indicate that the approach is insensitive to the phase characteristics of the starting wavelet, which is not the case when directly incorporating the wavelet estimation into the inverse problem.Another critical issue with crosshole georadar waveform inversion schemes which clearly needs to be investigated is the consequence of the common assumption of frequency- independent electromagnetic constitutive parameters. This is crucial since in reality, these parameters are known to be frequency-dependent and complex and thus recorded georadar data may show significant dispersive behaviour. In particular, in the presence of water, there is a wide body of evidence showing that the dielectric permittivity can be significantly frequency dependent over the GPR frequency range, due to a variety of relaxation processes. The second part of my thesis is therefore dedicated to the evaluation of the reconstruction limits of a non-dispersive crosshole georadar waveform inversion scheme in the presence of varying degrees of dielectric dispersion. I show that the inversion algorithm, combined with the iterative deconvolution-based source wavelet estimation procedure that is partially able to account for the frequency-dependent effects through an "effective" wavelet, performs remarkably well in weakly to moderately dispersive environments and has the ability to provide adequate tomographic reconstructions.

A finite-population revenue management model and a risk-ratio procedure for the joint estimation of population size and parameters

Many dynamic revenue management models divide the sale period into a finite number of periods T and assume, invoking a fine-enough grid of time, that each period sees at most one booking request. These Poisson-type assumptions restrict the variability of the demand in the model, but researchers and practitioners were willing to overlook this for the benefit of tractability of the models. In this paper, we criticize this model from another angle. Estimating the discrete finite-period model poses problems of indeterminacy and non-robustness: Arbitrarily fixing T leads to arbitrary control values and on the other hand estimating T from data adds an additional layer of indeterminacy. To counter this, we first propose an alternate finite-population model that avoids this problem of fixing T and allows a wider range of demand distributions, while retaining the useful marginal-value properties of the finite-period model. The finite-population model still requires jointly estimating market size and the parameters of the customer purchase model without observing no-purchases. Estimation of market-size when no-purchases are unobservable has rarely been attempted in the marketing or revenue management literature. Indeed, we point out that it is akin to the classical statistical problem of estimating the parameters of a binomial distribution with unknown population size and success probability, and hence likely to be challenging. However, when the purchase probabilities are given by a functional form such as a multinomial-logit model, we propose an estimation heuristic that exploits the specification of the functional form, the variety of the offer sets in a typical RM setting, and qualitative knowledge of arrival rates. Finally we perform simulations to show that the estimator is very promising in obtaining unbiased estimates of population size and the model parameters.

Optimal estimation of two-qubit pure-state entanglement

We present optimal measuring strategies for an estimation of the entanglement of unknown two-qubit pure states and of the degree of mixing of unknown single-qubit mixed states, of which N identical copies are available. The most general measuring strategies are considered in both situations, to conclude in the first case that a local, although collective, measurement suffices to estimate entanglement, a nonlocal property, optimally.

Malaria haplotype frequency estimation.

We present a Bayesian approach for estimating the relative frequencies of multi-single nucleotide polymorphism (SNP) haplotypes in populations of the malaria parasite Plasmodium falciparum by using microarray SNP data from human blood samples. Each sample comes from a malaria patient and contains one or several parasite clones that may genetically differ. Samples containing multiple parasite clones with different genetic markers pose a special challenge. The situation is comparable with a polyploid organism. The data from each blood sample indicates whether the parasites in the blood carry a mutant or a wildtype allele at various selected genomic positions. If both mutant and wildtype alleles are detected at a given position in a multiply infected sample, the data indicates the presence of both alleles, but the ratio is unknown. Thus, the data only partially reveals which specific combinations of genetic markers (i.e. haplotypes across the examined SNPs) occur in distinct parasite clones. In addition, SNP data may contain errors at non-negligible rates. We use a multinomial mixture model with partially missing observations to represent this data and a Markov chain Monte Carlo method to estimate the haplotype frequencies in a population. Our approach addresses both challenges, multiple infections and data errors.

Revisiting Field Capacity (FC): variation of definition of FC and its estimation from pedotransfer functions

Taking into account the nature of the hydrological processes involved in in situ measurement of Field Capacity (FC), this study proposes a variation of the definition of FC aiming not only at minimizing the inadequacies of its determination, but also at maintaining its original, practical meaning. Analysis of FC data for 22 Brazilian soils and additional FC data from the literature, all measured according to the proposed definition, which is based on a 48-h drainage time after infiltration by shallow ponding, indicates a weak dependency on the amount of infiltrated water, antecedent moisture level, soil morphology, and the level of the groundwater table, but a strong dependency on basic soil properties. The dependence on basic soil properties allowed determination of FC of the 22 soil profiles by pedotransfer functions (PTFs) using the input variables usually adopted in prediction of soil water retention. Among the input variables, soil moisture content θ (6 kPa) had the greatest impact. Indeed, a linear PTF based only on it resulted in an FC with a root mean squared residue less than 0.04 m³ m-3 for most soils individually. Such a PTF proved to be a better FC predictor than the traditional method of using moisture content at an arbitrary suction. Our FC data were compatible with an equivalent and broader USA database found in the literature, mainly for medium-texture soil samples. One reason for differences between FCs of the two data sets of fine-textured soils is due to their different drainage times. Thus, a standardized procedure for in situ determination of FC is recommended.

Protein-ligand binding free energy estimation using molecular mechanics and continuum electrostatics. Application to HIV-1 protease inhibitors.

A method is proposed for the estimation of absolute binding free energy of interaction between proteins and ligands. Conformational sampling of the protein-ligand complex is performed by molecular dynamics (MD) in vacuo and the solvent effect is calculated a posteriori by solving the Poisson or the Poisson-Boltzmann equation for selected frames of the trajectory. The binding free energy is written as a linear combination of the buried surface upon complexation, SASbur, the electrostatic interaction energy between the ligand and the protein, Eelec, and the difference of the solvation free energies of the complex and the isolated ligand and protein, deltaGsolv. The method uses the buried surface upon complexation to account for the non-polar contribution to the binding free energy because it is less sensitive to the details of the structure than the van der Waals interaction energy. The parameters of the method are developed for a training set of 16 HIV-1 protease-inhibitor complexes of known 3D structure. A correlation coefficient of 0.91 was obtained with an unsigned mean error of 0.8 kcal/mol. When applied to a set of 25 HIV-1 protease-inhibitor complexes of unknown 3D structures, the method provides a satisfactory correlation between the calculated binding free energy and the experimental pIC5o without reparametrization.