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Image alignment and stitching: a tutorial
, 2006
"... This tutorial reviews image alignment and image stitching algorithms. Image alignment algorithms can discover the correspondence relationships among images with varying degrees of overlap. They are ideally suited for applications such as video stabilization, summarization, and the creation of panora ..."
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Cited by 118 (2 self)
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This tutorial reviews image alignment and image stitching algorithms. Image alignment algorithms can discover the correspondence relationships among images with varying degrees of overlap. They are ideally suited for applications such as video stabilization, summarization, and the creation of panoramic mosaics. Image stitching algorithms take the alignment estimates produced by such registration algorithms and blend the images in a seamless manner, taking care to deal with potential problems such as blurring or ghosting caused by parallax and scene movement as well as varying image exposures. This tutorial reviews the basic motion models underlying alignment and stitching algorithms, describes effective direct (pixelbased) and featurebased alignment algorithms, and describes blending algorithms used to produce
Parameter Estimation In The Presence Of Bounded Data Uncertainties
 SIAM J. Matrix Anal. Appl
, 1998
"... . We formulate and solve a new parameter estimation problem in the presence of data uncertainties. The new method is suitable when apriori bounds on the uncertain data are available, and its solution leads to more meaningful results especially when compared with other methods such as total leastsq ..."
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Cited by 55 (7 self)
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. We formulate and solve a new parameter estimation problem in the presence of data uncertainties. The new method is suitable when apriori bounds on the uncertain data are available, and its solution leads to more meaningful results especially when compared with other methods such as total leastsquares and robust estimation. Its superior performance is due to the fact that the new method guarantees that the effect of the uncertainties will never be unnecessarily overestimated, beyond what is reasonably assumed by the apriori bounds. A geometric interpretation of the solution is provided, along with a closed form expression for it. We also consider the case in which only selected columns of the coefficient matrix are subject to perturbations. Key words. Leastsquares estimation, regularized leastsquares, ridge regression, total leastsquares, robust estimation, modeling errors, secular equation. AMS subject classifications. 15A06, 65F05, 65F10, 65F35, 65K10, 93C41, 93E10, 93E24 1....
An Implicit Loop Method for Kinematic Calibration and Its Application to ClosedChain Mechanisms
 IEEE TRANS. ROBOTICS AND AUTOMATION
, 1995
"... A unified formulation for the calibration of both seriallink robots and robotic mechanisms having kinematic closedloops is presented and applied experimentally to two 6degree offreedom devices: the RSI 6DOF Hand Controller and the MEL "Modified Stewart Platform." The unification is ba ..."
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Cited by 39 (7 self)
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A unified formulation for the calibration of both seriallink robots and robotic mechanisms having kinematic closedloops is presented and applied experimentally to two 6degree offreedom devices: the RSI 6DOF Hand Controller and the MEL "Modified Stewart Platform." The unification is based on an equivalence between endeffector measurements and constraints imposed by the closure of kinematic loops. Errors are allocated to the joints such that the loop equations are satisfied exactly, which eliminates the issue of equation scaling and simplifies the treatment of multiloop mechanisms. For the experiments reported here, no external measuring devices are used; instead we rely on measurements of displacements in some of the passive joints of the devices. Using a priori estimates of the statistics of the measurement errors and the parameter errors, the method estimates the parameters and their accuracy, and tests for unmodelled factors.
The Effects of Array Calibration Errors on DFBased Signal Copy Performance
 IEEE Trans. on Signal Processing
, 1995
"... This paper studies the effect of array calibration errors on the performance of various DF (direction finding) based signal copy algorithms. Unlike blind copy methods, this class of algorithms requires an estimate of the directions of arrival (DOAs) of the signals in order to compute the copy weight ..."
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Cited by 19 (5 self)
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This paper studies the effect of array calibration errors on the performance of various DF (direction finding) based signal copy algorithms. Unlike blind copy methods, this class of algorithms requires an estimate of the directions of arrival (DOAs) of the signals in order to compute the copy weight vectors. Under the assumption that the observation time is sufficiently long, the following algorithms are studied: classical beamforming, least squares, total least squares, linearly constrained minimum variance beamforming, and structured stochastic estimation. Expressions for the meansquare error of the signal estimates are derived as a function of the calibration errors for both the case where the DOAs are known precisely and for the case where the DOAs must be estimated. This work was supported by a contract from ESystems, Inc., Greenville Division (Dr. William A. Gardner, Principal Investigator), and by the National Science Foundation under grant MIP9110112. 1. Introduction An im...
Renaut, A regularized total least squares algorithm
 in Total Least Squares and ErrorsinVariables Modeling: Analysis, Algorithms and Applications, S. Van Huffel and P. Lemmerling, eds
, 2002
"... Keywords: Errorcontaminated systems Ax ≈ b, for which A is illconditioned, are considered. Such systems may be solved using Tikhonovlike regularized total least squares (RTLS) methods. Golub et al, 1999, presented a direct algorithm for the solution of the Lagrange multiplier formulation for the ..."
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Cited by 15 (4 self)
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Keywords: Errorcontaminated systems Ax ≈ b, for which A is illconditioned, are considered. Such systems may be solved using Tikhonovlike regularized total least squares (RTLS) methods. Golub et al, 1999, presented a direct algorithm for the solution of the Lagrange multiplier formulation for the RTLS problem. Here we present a parameter independent algorithm for the approximate RTLS solution. The algorithm, which utilizes the shifted inverse power method, relies only on a prescribed estimate for the regularization constraint condition and does not require the specification of other regularization parameters. An extension of the algorithm for nonsmooth solutions is also presented. total least squares, illconditioned problem, regularization. 1.
Linear Regression with Gaussian Model Uncertainty: Algorithms and Bounds
"... We consider the problem of estimating an unknown deterministic parameter vector in a linear regression model with random Gaussian uncertainty in the mixing matrix. We prove that the maximum likelihood (ML) estimator is a regularized least squares estimator and develop three alternative approaches f ..."
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Cited by 14 (3 self)
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We consider the problem of estimating an unknown deterministic parameter vector in a linear regression model with random Gaussian uncertainty in the mixing matrix. We prove that the maximum likelihood (ML) estimator is a regularized least squares estimator and develop three alternative approaches for finding the regularization parameter which maximizes the likelihood. We analyze the performance using the Cramér Rao bound (CRB) on the mean squared error, and show that the degradation in performance due the uncertainty is not as severe as may be expected. Next, we address the problem again assuming that the variances of the noise and the elements in the model matrix are unknown and derive the associated CRB and ML estimator. We compare our methods to known results on linear regression in the error in variables (EIV) model. We discuss the similarity between these two competing approaches, and provide a thorough comparison which sheds light on their theoretical and practical differences.
REGRESSION ON MANIFOLDS: ESTIMATION OF THE EXTERIOR DERIVATIVE
 SUBMITTED TO THE ANNALS OF STATISTICS
, 2010
"... Collinearity and nearcollinearity of predictors cause difficulties when doing regression. In these cases, variable selection becomes untenable because of mathematical issues concerning the existence and numerical stability of the regression coefficients, and interpretation of the coefficients is am ..."
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Cited by 13 (3 self)
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Collinearity and nearcollinearity of predictors cause difficulties when doing regression. In these cases, variable selection becomes untenable because of mathematical issues concerning the existence and numerical stability of the regression coefficients, and interpretation of the coefficients is ambiguous because gradients are not defined. Using a differential geometric interpretation, in which the regression coefficients are interpreted as estimates of the exterior derivative of a function, we develop a new method to do regression in the presence of collinearities. Our regularization scheme can improve estimation error, and it can be easily modified to include lassotype regularization. These estimators also have simple extensions to the “large p, small n” context.
Optimal placement of phasor measurement units via convex relaxation
 IEEE Trans. Power Syst
, 2012
"... Abstract—Instrumenting power networks with phasor measurement units (PMUs) facilitates several tasks including optimum power flow, system control, contingency analysis, visualization, and integration of renewable resources, thus enabling situational awareness—one of the key steps toward realizing th ..."
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Cited by 12 (2 self)
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Abstract—Instrumenting power networks with phasor measurement units (PMUs) facilitates several tasks including optimum power flow, system control, contingency analysis, visualization, and integration of renewable resources, thus enabling situational awareness—one of the key steps toward realizing the smart grid vision. The installation cost of PMUs currently prohibits their deployment on every bus, which in turn motivates their strategic placement across the power grid. As state estimation is at the core of grid monitoring, PMU deployment is optimized here based on estimationtheoretic criteria. Considering both voltage and incident current readings per PMUinstrumented bus and incorporating conventionally derived state estimates under the Bayesian framework, PMU placementisformulatedasanoptimal experimental design task. To bypass the combinatorial search involved, a convex relaxation is developed to obtain solutions with numerical optimality guarantees. In the tests performed on standard IEEE 14, 30, and 118bus benchmarks, the proposed relaxation approaches and oftentimes attains the optimum PMU placement. Index Terms—Gradient projection method, maximum aposteriori estimation, optimal experimental design, phasor measurement units, SCADA measurements, semidefinite programming. I.
A Stable and Efficient Algorithm for the Indefinite Linear LeastSquares Problem
 SIAM J. Matrix Anal. Appl
, 1998
"... We develop an algorithm for the solution of indefinite leastsquares problems. Such problems arise in robust estimation, filtering, and control, and numerically stable solutions have been lacking. The algorithm developed herein involves the QR factorization of the coefficient matrix and is provably ..."
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Cited by 9 (0 self)
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We develop an algorithm for the solution of indefinite leastsquares problems. Such problems arise in robust estimation, filtering, and control, and numerically stable solutions have been lacking. The algorithm developed herein involves the QR factorization of the coefficient matrix and is provably numerically stable. keywords Indefinite leastsquares problems, error analysis, backward stability. 1 Introduction Many optimization criteria have been used for parameter estimation, starting with the standard leastsquares formulation of Gauss (ca. 1795) and moving to more recent works on total leastsquares (TLS) and robust (or H 1 ) estimation (see, e.g., [3, 4, 6, 7, 8, 9]). The latter formulations have been motivated by an increasing interest in estimators that are less sensitive to data uncertainties and measurement errors. They can both be shown to require the minimization of indefinite quadratic forms, where the standard inner product of two vectors, say a T b, is replaced by an...
An Efficient Algorithm For A Bounded ErrorsInVariables Model
"... . We pose and solve a parameter estimation problem in the presence of bounded data uncertainties. The problem involves a minimization step and admits a closed form solution in terms of the positive root of a secular equation. Key words. Leastsquares estimation, total leastsquares, modeling errors ..."
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Cited by 9 (2 self)
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. We pose and solve a parameter estimation problem in the presence of bounded data uncertainties. The problem involves a minimization step and admits a closed form solution in terms of the positive root of a secular equation. Key words. Leastsquares estimation, total leastsquares, modeling errors, secular equation. AMS subject classifications. 15A06, 65F05, 65F10, 65F35, 65K10, 93C41, 93E10, 93E24 1. Introduction. Parameter estimation in the presence of data uncertainties is a problem of considerable practical importance, and many estimators have been proposed in the literature with the intent of handling modeling errors and measurement noise. Among the most notable is the total leastsquares method [1, 2, 3, 4], also known as orthogonal regression or errorsinvariables method in statistics and system identification [5]. In contrast to the standard leastsquares problem, the TLS formulation allows for errors in the data matrix. Its performance may degrade in some situations where ...