Results 1  10
of
62
Optimal motion and structure estimation
 IEEE Trans. Pattern Anal. Mach. Intell
, 1993
"... This paper studies optimal estimation for motion and structure from point correspondences. (1) A study of the characteristics of thc problem provides insight into the need for optimal estimation. (2) Methods have been developed for optimal estimation with known or unknown noise distribution. The sim ..."
Abstract

Cited by 136 (5 self)
 Add to MetaCart
This paper studies optimal estimation for motion and structure from point correspondences. (1) A study of the characteristics of thc problem provides insight into the need for optimal estimation. (2) Methods have been developed for optimal estimation with known or unknown noise distribution. The simulations showed that the optimal estimations achieve remarkable improvement over the preliminary estimates given by the linear algorithm. (3) An approach to estimating errors in the optimized solution is presented. (4) The performance of the algorithm is compared with a theoretical lower bound CramCrRao bound. Simulations show that the actual errors have essentially reached the bound. (5) A batch leastsquares technique (LevenbergMarquardt) and a sequential leastsquares technique (iterated extended Kalman filtering) are analyzed and compared. The analysis and experiments show that, in general, a batch technique will perform better than a sequential technique for any nonlinear problems. Recursive batch processing technique is proposed for nonlinear problems that require recursive estimation. 1.
THE EFFECT OF UNLABELED SAMPLES IN REDUCING THE SMALL SAMPLE SIZE PROBLEM AND MITIGATING THE HUGHES PHENOMENON
, 1994
"... ..."
An Introduction to Estimation Theory
 OFFICE NOTE SERIES ON GLOBAL MODELING AND DATA ASSIMILATION
, 1997
"... Despite the explosive growth of activity in the field of Earth System data assimilation over the past decade or so, there remains a substantial gap between theory and practice. The present article attempts to bridge this gap by exposing some of the central concepts of estimation theory and connectin ..."
Abstract

Cited by 105 (6 self)
 Add to MetaCart
Despite the explosive growth of activity in the field of Earth System data assimilation over the past decade or so, there remains a substantial gap between theory and practice. The present article attempts to bridge this gap by exposing some of the central concepts of estimation theory and connecting them with current and future data assimilation approaches. Estimation theory provides a broad and natural mathematical foundation for data assimilation science. Stochasticdynamic modeling and stochastic observation modeling are described first. Optimality criteria for linear and nonlinear state estimation problems are then explored, leading to conditionalmean estimation procedures such as the Kalman filter and some of its generalizations, and to conditionalmode estimation procedures such as variational methods. A detailed derivation of the Kalman filter is given to illustrate the role of key probabilistic concepts and assumptions. Extensions of the Kalman filter to nonlinear observat...
An Unsupervised Ensemble Learning Method for Nonlinear Dynamic StateSpace Models
 Neural Computation
, 2001
"... A Bayesian ensemble learning method is introduced for unsupervised extraction of dynamic processes from noisy data. The data are assumed to be generated by an unknown nonlinear mapping from unknown factors. The dynamics of the factors are modeled using a nonlinear statespace model. The nonlinear map ..."
Abstract

Cited by 89 (32 self)
 Add to MetaCart
(Show Context)
A Bayesian ensemble learning method is introduced for unsupervised extraction of dynamic processes from noisy data. The data are assumed to be generated by an unknown nonlinear mapping from unknown factors. The dynamics of the factors are modeled using a nonlinear statespace model. The nonlinear mappings in the model are represented using multilayer perceptron networks. The proposed method is computationally demanding, but it allows the use of higher dimensional nonlinear latent variable models than other existing approaches. Experiments with chaotic data show that the new method is able to blindly estimate the factors and the dynamic process which have generated the data. It clearly outperforms currently available nonlinear prediction techniques in this very di#cult test problem.
An Algorithmic Overview of Surface Registration . . .
 MEDICAL IMAGE ANALYSIS
, 2000
"... This paper presents a literature survey of automatic 3D surface registration techniques emphasizing the mathematical and algorithmic underpinnings of the subject. The relevance of surface registration to medical imaging is that there is much useful anatomical information in the form of collected ..."
Abstract

Cited by 67 (1 self)
 Add to MetaCart
This paper presents a literature survey of automatic 3D surface registration techniques emphasizing the mathematical and algorithmic underpinnings of the subject. The relevance of surface registration to medical imaging is that there is much useful anatomical information in the form of collected surface points which originate from complimentary modalities and which must be reconciled. Surface registration
Shape Ambiguities in Structure from Motion
 PAMI
, 1996
"... This technical report examines the fundamental ambiguities and uncertainties inherent in recovering structure from motion. By examining the eigenvectors associated with null or small eigenvalues of the Hessian matrix, we can quantify the exact nature of these ambiguities and predict how they affect ..."
Abstract

Cited by 54 (4 self)
 Add to MetaCart
(Show Context)
This technical report examines the fundamental ambiguities and uncertainties inherent in recovering structure from motion. By examining the eigenvectors associated with null or small eigenvalues of the Hessian matrix, we can quantify the exact nature of these ambiguities and predict how they affect the accuracy of the reconstructed shape. Our results for orthographic cameras show that the basrelief ambiguity is significant even with many images, unless a large amount of rotation is present. Similar results for perspective cameras suggest that three or more frames and a large amount of rotation are required for metrically accurate reconstruction.
Maximumlikelihood estimation of forecast and observation error covariance parameters. Part I: Methodology
, 1998
"... The maximumlikelihood method for estimating observation and forecast error covariance parameters is described. The method is presented in general terms but with particular emphasis on practical aspects of implementation. Issues such as bias estimation and correction, parameter identifiability, esti ..."
Abstract

Cited by 36 (5 self)
 Add to MetaCart
The maximumlikelihood method for estimating observation and forecast error covariance parameters is described. The method is presented in general terms but with particular emphasis on practical aspects of implementation. Issues such as bias estimation and correction, parameter identifiability, estimation accuracy, and robustness of the method, are discussed in detail. The relationship between the maximumlikelihood method and Generalized CrossValidation is briefly addressed. The method can be regarded as a generalization of the traditional procedure for estimating covariance parameters from station data. It does not involve any restrictions on the covariance models and can be used with data from moving observers, provided the parameters to be estimated are identifiable. Any available a priori information about the observation and forecast error distributions can be incorporated into the estimation procedure. Estimates of parameter accuracy due to sampling error are obtained as a byp...
The Coupling of Rotation and Translation in Motion Estimation of Planar Surfaces
"... This paper studies the error sensitivity in the estimation of the 3Dmotion and the normal of a planar surface from an instantaneous motion field. We use the statistical theory of the CramerRao lower bound for the error covariance in the estimated motion and structure parameters which enables the d ..."
Abstract

Cited by 35 (0 self)
 Add to MetaCart
This paper studies the error sensitivity in the estimation of the 3Dmotion and the normal of a planar surface from an instantaneous motion field. We use the statistical theory of the CramerRao lower bound for the error covariance in the estimated motion and structure parameters which enables the derivation of results valid for any unbiased estimator under the assumption of Gaussian noise in the motion eld. The obtained lowerboundmatrix is studied analytically with respect to the measurement noise, size of the field of view and the motiongeometry configuration. The main result of this analysis is the coupling between translation and rotation which is exacerbated if the field of view and the slant of the plane become smaller and the deviation of the translation from the viewing direction becomes larger. Byproducts of this study are the relationships of the uncertainty bounds for every unknown motion parameter to the angle between translation and the planenormal, the size of the field of view, the distance from the perceived plane and the translation magnitude.
An Adaptive Classifier Design for HighDimensional Data Analysis with a Limited Training Data Set
 IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING
, 2001
"... In this paper, we propose a selflearning and selfimproving adaptive classifier to mitigate the problem of small training sample size that can severely affect the recognition accuracy of classifiers when the dimensionality of the multispectral data is high. This proposed adaptive classifier utilize ..."
Abstract

Cited by 26 (3 self)
 Add to MetaCart
In this paper, we propose a selflearning and selfimproving adaptive classifier to mitigate the problem of small training sample size that can severely affect the recognition accuracy of classifiers when the dimensionality of the multispectral data is high. This proposed adaptive classifier utilizes classified samples (referred as semilabeled samples) in addition to original training samples iteratively. In order to control the influence of semilabeled samples, the proposed method gives full weight to the training samples and reduced weight to semilabeled samples. We show that by using additional semilabeled samples that are available without extra cost, the additional class label information may be extracted and utilized to enhance statistics estimation and hence improve the classifier performance, and therefore the Hughes phenomenon (peak phenomenon) may be mitigated. Experimental results show this proposed adaptive classifier can improve the classification accuracy as well as representation of estimated statistics significantly.
Recursive MUSIC: A framework for EEG and MEG source localization
 IEEE Trans. Biomed. Eng
, 1998
"... Abstract—The multiple signal classification (MUSIC) algorithm can be used to locate multiple asynchronous dipolar sources from electroencephalography (EEG) and magnetoencephalography (MEG) data. The algorithm scans a singledipole model through a threedimensional (3D) head volume and computes pro ..."
Abstract

Cited by 25 (1 self)
 Add to MetaCart
(Show Context)
Abstract—The multiple signal classification (MUSIC) algorithm can be used to locate multiple asynchronous dipolar sources from electroencephalography (EEG) and magnetoencephalography (MEG) data. The algorithm scans a singledipole model through a threedimensional (3D) head volume and computes projections onto an estimated signal subspace. To locate the sources, the user must search the head volume for multiple local peaks in the projection metric. This task is time consuming and subjective. Here, we describe an extension of this approach which we refer to as recursive MUSIC (RMUSIC). This new procedure automatically extracts the locations of the sources through a recursive use of subspace projections. The new method is also able to locate synchronous sources through the use of a spatiotemporal independent topographies (IT) model. This model defines a source as one or more nonrotating dipoles with a single time course. Within this framework, we are able to locate fixed, rotating, and synchronous dipoles. The recursive subspace projection procedure that we introduce here uses the metric of canonical or subspace correlations as a multidimensional form of correlation analysis between the model subspace and the data subspace. By recursively computing subspace correlations, we build up a model for the sources which account for a given set of data. We demonstrate here how RMUSIC can easily extract multiple asynchronous dipolar sources that are difficult to find using the original MUSIC scan. We then demonstrate RMUSIC applied to the more general IT model and show results for combinations of fixed, rotating, and synchronous dipoles. Index Terms—Dipole modeling, electroencephalography, magnetoencephalography, signal subspace methods, source localization. I.