Angle-Only Filtering of a Maneuvering Target in 3D.

We consider the state estimation of a maneuvering target in 3D using bearing and elevation measurements from a passive infrared search and track (IRST) sensor. Since the range is not observable, the sensor must perform a maneuver to observe the state of the target. The target moves with a nearly constant turn (NCT) in the XY-plane and nearly constant velocity (NCV) along the Z-axis. The natural choice for the NCT motion is to allow perturbations in speed and angular rate in the stochastic differential equation, as has been pointed out previously for a 2D scenario using range and bearing measurements. The NCT motion in the XY-plane cannot be discretized exactly, whereas the NCV motion along the Z-axis is discretized exactly. We discretize the continuous-time NCT model using the first and second-order Taylor approximations to obtain discrete-time NCT models, and we consider the polar velocity and Cartesian velocity-based states for the NCT model. The dynamic and measurement models are nonlinear in the target state. We use the cubature Kalman filter to estimate the target state. Accuracies of the first and second-order Taylor approximations are compared using the polar velocity-based and Cartesian velocity-based models using Monte Carlo simulations. Numerical results for realistic scenarios considered show that the second-order Taylor approximation provides the best accuracy using the polar velocity or Cartesian velocity-based models.

Automatic estimation of the corneal limbus in videokeratoscopy.

An algorithm for estimating the corneal limbus from videokeratoscopic images is proposed. After the image is transformed to a polar grid, a novel edge-detection procedure, suitable for the detection of the soft edge produced by the limbus, is used to locate the limbus. Outliers due to the eyelids, eyelashes, and videokeratoscopic rings are removed by taking advantage of the approximate circularity of the cornea. An ellipse which minimizes the sum of the squared algebraic errors is fitted to the remaining edge points. Comparisons between the proposed algorithm, a manual computer-based technique and an algorithm which uses conventional edge-detection techniques demonstrate the accuracy of the proposed algorithm.

Analyzing the dynamic wavefront aberrations in the human eye.

The optics of the human eye are not static in steady viewing conditions and exhibit microfluctuations. Previous methods used for analyzing dynamic changes in the eye's optics include simple Fourier-transform-based methods, which have been used in studies of the eye's accommodation response. However, dedicated tools for the analysis of dynamic wavefront aberrations have not been reported. We propose a set of signal processing tools, the combination of which uncovers aspects of the dynamics of eye's optical aberrations which were hidden from conventional analysis techniques. The methodology includes extraction of artifacts from potentially significant eye movements, filtering, optimal parametric signal modeling, and frequency and time-frequency representations. The exposition of the techniques and their advantages over traditional techniques is illustrated for real dynamic eye wavefront aberration measurements.

A refined bootstrap method for estimating the Zernike polynomial model order for corneal surfaces.

Following our previous work on optimal modeling of corneal surfaces with Zernike polynomials, we have developed a refined bootstrap-based procedure which improves the accuracy of the previous method. We show that for normal corneas, the optimal number of Zernike terms usually corresponds to the fourth or fifth radial order expansion of Zernike polynomials. On the other hand, for distorted corneas such as those encountered in keratoconus or in surgically altered cases, the estimated model was found to be up to three radial orders higher than for normal corneas.

Modeling of corneal surfaces with radial polynomials.

We consider analytical modeling of the anterior corneal surface with a set of orthogonal basis functions that are a product of radial polynomials and angular functions. Several candidate basis functions were chosen from the repertoire of functions that are orthogonal in the unit circle and invariant in form with respect to rotation about the origin. In particular, it is shown that a set of functions that is referred herein as Bhatia-Wolf polynomials, represents a better and more robust alternative for modeling corneal elevation data than traditionally used Zernike polynomials. Examples of modeling corneal elevation are given for normal corneas and for abnormal corneas with significant distortion.

Modelling and estimation of multicomponent T(2) distributions.

Estimation of multiple T2 components within single imaging voxels typically proceeds in one of two ways; a nonparametric grid approximation to a continuous distribution is made and a regularized nonnegative least squares algorithm is employed to perform the parameter estimation, or a parametric multicomponent model is assumed with a maximum likelihood estimator for the component estimation. In this work, we present a Bayesian algorithm based on the principle of progressive correction for the latter choice of a discrete multicomponent model. We demonstrate in application to simulated data and two experimental datasets that our Bayesian approach provides robust and accurate estimates of both the T2 model parameters and nonideal flip angles. The second contribution of the paper is to present a Cramér-Rao analysis of T2 component width estimators. To this end, we introduce a parsimonious parametric and continuous model based on a mixture of inverse-gamma distributions. This analysis supports the notion that T2 spread is difficult, if not infeasible, to estimate from relaxometry data acquired with a typical clinical paradigm. These results justify the use of the discrete distribution model.

Performance analysis for magnetic resonance imaging with nonlinear encoding fields.

Nonlinear spatial encoding fields for magnetic resonance imaging (MRI) hold great promise to improve on the linear gradient approaches by, for example, enabling reduced imaging times. Imaging schemes that employ general nonlinear encoding fields are difficult to analyze using traditional measures. In particular, the resolution is spatially varying, characterized by a position-dependent point spread function (PSF). Likewise, the use of nonlinear encoding fields creates an additional spatial dependence on the signal-to-noise ratio (SNR). Although the two properties of resolution and SNR are linked, in this work we focus on the latter. To this end, we examine the pixel variance, which requires a computation that is often not feasible for nonlinear encoding schemes. This paper presents a general formulation for the performance analysis of imaging schemes using arbitrary encoding fields. The analysis leads to the derivation of a practical and computationally efficient performance metric, which is demonstrated through simulation examples.

Adapting magnetic resonance imaging performance using nonlinear encoding fields.

Nonlinear spatial encoding fields for magnetic resonance imaging (MRI) hold great promise to improve on the linear gradient approaches. Unlike the linear techniques, the nonlinear encoding leads to a spatially varying signal-to-noise ratio (SNR). This paper demonstrates the possibility to tailor the encoding fields to focus the high SNR areas to a region of interest. To achieve this, a metric is derived to quantify the spatially dependent performance for arbitrary encoding schemes.

Combining central and peripheral videokeratoscope maps to investigate total corneal topography.

PURPOSE: To extend the area of standard corneal topography maps, one central map is combined with six peripheral maps after correlating them in a custom written computer program. METHODS: The point corresponding to the vertex normal of the central map is found in each of the peripheral maps. Data from the peripheral maps can then be added on to the edges of the central map to create a topography map that extends from limbus to limbus horizontally and vertically. RESULTS: The average size of the combined maps from 15 subjects was 11.3 +/- 0.3 mm horizontally and 10.3 +/- 0.3 mm vertically, compared to 9.2 +/- 0.4 mm horizontally and 7.5 +/- 0.7 mm vertically for the standard single maps. These values represent an increase in surface area of approximately 70%. CONCLUSIONS: The topography of the entire cornea can be represented by combining multiple measurements from a Placido videokeratoscope. Conic fits based on central topography data are a poor representation of the total corneal shape.