Curvature Algorithm Research Articles

Comparison of Topographic Technologies in Anterior Surface Mapping of Keratoconus using Two Display Algorithms and Six Corneal Topography Devices

ABSTRACT Purpose To evaluate anterior surface topographic technologies and display algorithms in mapping keratoconus. Materials and methods A total of 27 eyes of 17 subjects clinically diagnosed with keratoconus were imaged on six topographers: EyeSys, Alcon EyeMap, Keratron, TMS-1, Orbscan and PAR corneal topography system. Axial distance (AD) and instantaneous radius of curvature (IROC) algorithms were generated, and the cone apex was determined manually using a cursor. Intermachine comparisons for cone magnitude (steepest curvature), as well as cone location in radius and meridian were performed for each display algorithm using both AD and IROC. Significance (p < 0.05) was determined using repeated measures analysis of variance (ANOVA) on successive mean values. Maps were also evaluated for processability, defined by the ability to reconstruct a reasonable map for each subject, not map quality. Results There were no significant differences between successive means for cone location in either radial or meridional directions. For AD, Orbscan was greater than both small mire Placido devices (Keratron and TMS-1), which were not different from each other. The small mire devices had significantly greater curvature magnitude than the large mire placido devices (EyeSys, Alcon EyeMap) which were not different from each other. Finally, PAR was significantly lower than the large mire Placido devices. For IROC, the pattern was the same with the exception that the Orbscan was not different than the small mire Placido devices in curvature magnitude. For processing success, the PAR had 100% processability, and all other devices were between 73 and 77%. Conclusion In monitoring keratoconus, evaluation of change over time is fundamental to treatment decisions, making understanding of topographic technology differences in mapping keratoconic corneas extremely important. How to cite this article Markakis GA, Roberts CJ, Harris JW, Lembach RG. Comparison of Topographic Technologies in Anterior Surface Mapping of Keratoconus using Two Display Algorithms and Six Corneal Topography Devices. Int J Kerat Ect Cor Dis 2012;1(3):153-157.

Analysis of sub-micron parameters derived from multi-altitude and multi-spectral AOD measurements acquired during the 2009 PAM-ARCMIP airborne campaign

Abstract A series of Arctic sunphotometry flights were analyzed in terms of their multi-altitude, sub-micron (fine mode) information content. A spectral deconvolution algorithm (SDA) and a fine mode curvature algorithm (FMC) were applied to extract fine mode and coarse mode optical depth as well as the effective radius of the fine mode as a function of altitude. The fine mode optical depth was differentiated as a function of altitude to retrieve vertical profiles of fine mode extinction coefficient. These optical results were compared with volumetric altitude profiles of fine mode particle size distribution acquired by a UHSAS (Ultra High Sensitivity Aerosol Spectrometer). The results showed that layer-averaged extinction cross sections derived from the ratio of fine mode optical depth to integrated UHSAS number density were significantly larger than extinction cross sections derived from the application of Mie theory to the UHSAS particle size distributions. Vertical profiles of extinction coefficients derived from altitude derivatives of the fine mode optical depth profiles showed some correlation with the UHSAS extinction coefficients. Profiles of the fine mode effective radius retrieved from the sunphotometry data were generally of similar magnitude to columnar averages of the UHSAS radii but no significant trend with altitude could be detected. An example was given of a high altitude smoke plume whose presence eliminated any hope of correlating the volumetric sampling information with the sunphotometer profiles. This is simply a statement of the obvious; that the atmospheric state must be stable in order to make such comparisons.

AN ALGORITHM FOR PARTITIONING OF RIGHT HEART VENTRICLE MEDIAL AXIS

A right heart ventricle has a complex and irregular shape, this obscures analysis of ventricle surface movements. We are trying to quantitative evaluate morphological changes of right ventricle surface, these changes appear during heart beat cycle, between different age groups, due to heart diseases, and other factors. A method for such evaluation would open new possibilities for insights into heart function, disease course extrapolation and other. We see this as a multistage task, where the first step is partitioning whole surface into smaller, more manageable regions, and the second step is to analyse each region separately. In this paper we present a new algorithm for partitioning the medial axis of right heart ventricle surface. Such partitioning leads to division of surface into smaller regions with clear shape. The proposed algorithm first computes medial axis from sampled ventricle surface. Later, the medial axis is filtered and smoothed, and third, we compute curvature map and use it as weights in Dijkstra's algorithm for curvature guided partitioning. Algorithm provides a way for fully automatic partitioning of medial manifold into separate medial scaffolds and a semi automatic way for additional curvature based division of medial scaffolds.

A three-dimensional sharp interface model for the quantitative simulation of solutal dendritic growth

A three-dimensional (3-D) sharp interface model is developed to simulate the solutal dendritic growth in the low Péclet number regime. The model adopts a previously proposed solutal equilibrium approach to calculate the evolution of the solid/liquid interface. To describe specific crystallographic orientations of 3-D dendritic growth, a weighted mean curvature algorithm incorporated with the anisotropy of surface energy is proposed, allowing the simulation of 3-D dendrites with various orientations in a straightforward manner. The model validation is performed by comparing the simulations with the analytical predictions and experimental data for both single and multi-dendritic growth, which demonstrates the quantitative capabilities of the proposed model. The model efficiently reproduces realistic 3-D multi-equiaxed and columnar dendrites with various orientations and well-developed side branches.

The ice age paleo-channel Ellerbeker Rinne an integrated 3D gravity study

In the framework of a joint field work with partners of the Landesamt fur Landwirtschaft, Umwelt und landliche Raume (LLUR, the former LANU; Flintbek, Germany) and the Leibniz-Institut fur Angewandte Geophysik (LIAG; Hannover, Germany) gravity measurements have been conducted in July 2005 by members of a student course Geophysical field exercise in the area of the Ellerbek paleo-channel near Tangstedt. At approximately 450 stations complete Bouguer anomalies have been calculated. The error of gravity anomaly accounts for 2 x 10(-7) m/s(2) (max.) to -8 x 10(-7) m/s(2) (min.). The gravity field of the region is affected by a strong regional gravity field, which is caused by salt structures. Therefore, a regional field was calculated which based on a regional survey of the State Geodetic Survey. It was subtracted from the Bouguer field and a slightly negative residual field (-1.0 to -1.5 x 10(-5) m/s(2)) resulted in the area of the Ellerbek paleo-channel. It was analysed and interpreted by curvature algorithms, Euler deconvolution and 3D modelling. Euler deconvolution and curvature result in a depth of max. 400 m for this part of the Ellerbek paleo-channel; clusters of Euler source points were also calculated for depths of 130 m and 220 m which points to rather inhomogeneous infill of the channel. The compiled 3D density model was constrained by the seismic profile P3 of LIAG and borehole information. The model explains the positive anomaly north of Tangstedt (> 1.5 x 10(-5) m/s(2)) With a high density body (Geschiebemergel; boulder clay) of 300 kg/m(3) density contrast to the sedimentary infill of the paleo-channel which has its bottom at 200 m depth.

Modelling of solutal dendritic growth in three dimensions

A three-dimensional （3D） model for the simulation of solutal dendritic growth in the low Pclet number region is presented. In the model is adopted a solutal equilibrium approach previously proposed by Zhu and Stefanescu to calculate the evolution of the solid/liquid（SL） interface， which allows the accurate simulation of dendritic growth from the initial unstable stage to the steady-state stage with a good computational efficiency. In this approach， the kinetics of dendritic growth is driven by the difference between the local equilibrium composition， calculated from the local temperature and curvature， and the local actual liquid composition，obtained by solving the solutal transport equation. To describe the specific crystallographic orientation of 3D dendritic growth， a weighted mean curvature （WMC） algorithm， which is incorporated with the anisotropy of surface tension， is proposed to calculate the local SL interface curvature. This approach is convenient to be implemented and to make the transformation for WMC calculation from two to three dimensions. The model is verified by the comparison of our numerical resuets with the analytical ones. The simulated steady-state tip velocity and radius varying with the degree of undercooling of an Al-2wt%Cu alloy are found to be close to the ones predicted by the Lipton-Glicksman-Kurz analytical model. The steady-state morphology of the needle dendrite tip is analyzed. It is found that the tip is nonaxisymmetric and deviates from a paraboloid in the manner of the fourfold symmetry. Finally， the simulated 3D multi-equiaxed dendrites with various crystallographic orientations are presented.

Accurate Automatic Detection of End-Diastole From Left Ventricular Pressure Using Peak Curvature

Precise identification of end-diastole (ED), corresponding to the end of diastole and start of systole, is crucial for accurate assessment of cardiac function. The aims of this study were to develop a new algorithm based on peak curvature (kappa(p)) for detecting ED as a "corner" in left ventricular pressure (LVP) signals, and to compare this approach with "gold-standard" ED obtained by manual annotation (ED(man)) and ED calculated with previously described algorithms that use an LVP first-derivative threshold (dP/dt(0) or dP/dt(100)), the peak LVP second-derivative (d(2)P/dt(2)(p)) or ECG R-wave peak (ECG(R)). Using customized software, all algorithms were applied to data derived from 213 large animal studies spanning a wide range of animal ages (fetus to adult), heart rates, inotropic states, and loading conditions. Differences between ED(man) and each algorithm were then compared after defining an acceptance region for the ED detection based on ED(man) interobserver variability. ED detected with kappa(p) was the most accurate (p < 0.001) and least variable (p < 0.001), with 97% of measurements within the acceptance region and difference from ED(man) of (1.5 +/- 4.2) ms. By contrast, ED was often detected early with dP/dt(0) and dP/dt(100) , and late with d(2)P/dt(2)(p) and ECG(R). These results indicate that the peak curvature algorithm using LVP provides accurate and reliable detection of ED.

Parameter selection methods for axisymmetric flame tomography through Tikhonov regularization

Deconvolution of optically collected axisymmetric flame data is equivalent to solving an ill-posed problem subject to severe error amplification. Tikhonov regularization has recently been shown to be well suited for stabilizing this deconvolution, although the success of this method hinges on choosing a suitable regularization parameter. Incorporating a parameter selection scheme transforms this technique into a reliable automatic algorithm that outperforms unregularized deconvolution of a smoothed data set, which is currently the most popular way to analyze axisymmetric data. We review the discrepancy principle, L-curve curvature, and generalized cross-validation parameter selection schemes and conclude that the L-curve curvature algorithm is best suited to this problem.

A Multiscale Curvature Algorithm for Classifying Discrete Return LiDAR in Forested Environments

One prerequisite to the use of light detection and ranging (LiDAR) across disciplines is differentiating ground from nonground returns. The objective was to automatically and objectively classify points within unclassified LiDAR point clouds, with few model parameters and minimal postprocessing. Presented is an automated method for classifying LiDAR returns as ground or nonground in forested environments occurring in complex terrains. Multiscale curvature classification (MCC) is an iterative multiscale algorithm for classifying LiDAR returns that exceed positive surface curvature thresholds, resulting in all the LiDAR measurements being classified as ground or nonground. The MCC algorithm yields a solution of classified returns that support bare-earth surface interpolation at a resolution commensurate with the sampling frequency of the LiDAR survey. Errors in classified ground returns were assessed using 204 independent validation points consisting of 165 field plot global positioning system locations and 39 National Oceanic and Atmospheric Administration-National Geodetic Survey monuments. Jackknife validation and Monte Carlo simulation were used to assess the quality and error of a bare-earth digital elevation model interpolated from the classified returns. A local indicator of spatial association statistic was used to test for commission errors in the classified ground returns. Results demonstrate that the MCC model minimizes commission errors while retaining a high proportion of ground returns and provides high confidence in the derived ground surface

Creating high-fidelity images – a convolution approach to gridding airborne data using a SINC kernel

Airborne geophysical data sampled at a constant time-interval along lines and with a nominal spatial-separation across lines are quasi-periodic and are therefore amenable to interpolation onto a regular grid by convolving the original line data with a 2D SINC kernel. This method has advantages over commonly used minimum curvature or bidirectional gridding algorithms because it better maintains the spatial fidelity of the original data as per the sampling theorem. Unlike splines, the SINC function does not suffer from over- interpolation, although ringing can be problematic. Lastly, the smooth SINC kernel places no lower bound on cell sizes, except computation time. The method first uses a 1D SINC interpolation to resample the along-line data. An SVD matrix inversion is then used to move each line from its true to its nominal location before interpolating the inter-line areas of the grid with the 2D kernel. Ringing and aliasing are mitigated by employing a window function to dampen the effects of the ideal RECT function in the wavenumber domain. Through judicious selection of the along- and across-line maximum wavenumbers, the SINC kernel can improve the continuity of lineaments trending obliquelyto the flight lines.

GPS-derived Geoid using Artificial Neural Network and Least Squares Collocation

The geoidal undulations are needed for determining the orthometric heights from the Global Positioning System GPS-derived ellipsoidal heights. There are several methods for geoidal undulation determination. The paper presents a method employing the Artificial Neural Network (ANN) approximation together with the Least Squares Collocation (LSC). The surface obtained by the ANN approximation is used as a trend surface in the least squares collocation. In numerical examples four surfaces were compared: the global geopotential model (EGM96), the European gravimetric quasigeoid 1997 (EGG97), the surface approximated with minimum curvature splines in tension algorithm and the ANN surface approximation. The effectiveness of the ANN surface approximation depends on the number of control points. If the number of well-distributed control points is sufficiently large, the results are better than those obtained by the minimum curvature algorithm and comparable to those obtained by the EGG97 model.

GPS-derived Geoid using Artificial Neural Network and Least Squares Collocation

The geoidal undulations are needed for determining the orthometric heights from the Global Positioning System GPS-derived ellipsoidal heights. There are several methods for geoidal undulation determination. The paper presents a method employing the Artificial Neural Network (ANN) approximation together with the Least Squares Collocation (LSC). The surface obtained by the ANN approximation is used as a trend surface in the least squares collocation. In numerical examples four surfaces were compared: the global geopotential model (EGM96), the European gravimetric quasigeoid 1997 (EGG97), the surface approximated with minimum curvature splines in tension algorithm and the ANN surface approximation. The effectiveness of the ANN surface approximation depends on the number of control points. If the number of well-distributed control points is sufficiently large, the results are better than those obtained by the minimum curvature algorithm and comparable to those obtained by the EGG97 model.

Direct descent curvature optimal control with a modification algorithm and its application to nonlinear process

This paper presents a direct descent second order or direct descent curvature algorithm with some modifications for the optimal control computations. This algorithm is compared with Hamiltonian methods in the literature. The proposed algorithm has generated numerically robust solutions with respect to conjugate points. The weighting matrix updating scheme was developed to improve the second-order optimal control algorithm, tested the performance of the algorithm, and shown on the benchmark and industrial process. The time-varying optimal feedback (TVOFB) gains are also generated along the trajectory as byproducts. If the trajectory deviates from the optimal trajectory for any reason (i.e., changing of system parameters, step disturbance into the plant, changing of initial conditions), it is held on the optimal trajectory by means of the optimal feedback. Simulations have been given for controlling the Van der Pol and bioreactor system, which are nonlinear benchmark systems.

Videokeratoscopes for dioptric power measurement during surgery

Purpose To evaluate 2 versions of a computerized surgical videokeratoscope that measures a central region of the cornea of approximately 4.0 to 6.0 mm in diameter to provide information on dioptric power and astigmatism. Setting Grupo de Optica Oftalmica Universidade de São Paulo, and Departamento de Oftalmologia da Escola Paulista de Medicina, São Paulo, Brazil. Methods The first videokeratoscope system with 10 Placido rings is based on a 15 000 fiber-optic illuminated disk attached to the objective lens of a surgical microscope. With this system, the light intensity can be adjusted during surgery for better contrast of the Placido image. The second system with 14 Placido rings is based on a neon light source behind the Placido disk. With both systems, a 480 × 640 pixel resolution charge-coupled device camera and an IBM-compatible personal computer frame grabber were used. Image processing was used for boundary detection of the rings. An axial curvature algorithm based on the spherical surfaces was used to calculate the dioptric power for each examination. Measurements of 4 real spherical surfaces and 4 simulated aspheric surfaces (ellipsotoric surfaces with different apical radii and different shape factors) were performed. Results Twenty corneas of 10 healthy volunteers were measured on both videokeratoscope systems and an EyeSys System 2000 corneal topographer. The root- mean-square error for the spherical and simulated aspheric surfaces was, respectively, less than 0.20 diopter (D) and 1.30 D for the 10-disk videokeratoscope system and less than 0.16 D and 1.40 D for the 14-disk system. The mean deviation in corneal measurements with both systems was 0.09 mm for the radius of curvature, 0.51 D for dioptric power, and 5 degrees for cylinder. Conclusion The results indicate that the 2 surgical videokeratoscopes are sufficiently precise to aid the anterior segment surgeon in reducing residual astigmatism in cataract surgery and keratoplasty.

Boundary defect recognition using neural networks

This research presents schemes for automated visual inspection for boundary defects and classification using neural networks. An efficient method for representing circular boundaries is proposed utilizing a curvature and circular fitting algorithm. For classification, two types of neural network modelling schemes are established. First, a multi-layer perceptron is discussed for defect classification problems. Second, a Hopfield network is modelled to be used for continuous-type variables by a minimizing energy function. Extensive tests are conducted on the casting parts, then the results of neural networks are compared with those of traditional pattern classifiers.

Tangential vs Sagittal Videokeratographs in the “Early” Detection of Keratoconus

To illustrate the difference between tangential and sagittal videokeratographs in the "early" (subclinical) detection of keratoconus. The clinically normal fellow eye of a patient with unilateral keratoconus was studied with a topographer, which can display both a sagittal and a tangential map on the same page using the same color scale. The tangential map depicted a pattern more consistent with keratoconus and provided a maximum power of 51 diopters compared with the 46 diopters of the sagittal map. Tangential videokeratographs, derived from instantaneous radius of curvature algorithms, may be more useful than sagittal displays for detecting subtle corneal topographic abnormalities.

The lunar crust: Global structure and signature of major basins

New lunar gravity and topography data from the Clementine Mission provide a global Bouguer anomaly map corrected for the gravitational attraction of mare fill in mascon basins. Most of the gravity signal remaining after corrections for the attraction of topography and mare fill can be attributed to variations in depth to the lunar Moho and therefore crustal thickness. The large range of global crustal thickness (∼20–120 km) is indicative of major spatial variations in melting of the lunar exterior and/or significant impact‐related redistribution. The 61‐km average crustal thickness, constrained by a depth‐to‐Moho measured during the Apollo 12 and 14 missions, is preferentially distributed toward the farside, accounting for much of the offset in center‐of‐figure from the center‐of‐mass. While the average farside thickness is 12 km greater than the nearside, the distribution is nonuniform, with dramatic thinning beneath the farside, South Pole‐Aitken basin. With the global crustal thickness map as a constraint, regional inversions of gravity and topography resolve the crustal structure of major mascon basins to half wavelengths of 150 km. In order to yield crustal thickness maps with the maximum horizontal resolution permitted by the data, the downward continuation of the Bouguer gravity is stabilized by a three‐dimensional, minimum‐slope and curvature algorithm. Both mare and non‐mare basins are characterized by a central upwarped moho that is surrounded by rings of thickened crust lying mainly within the basin rims. The inferred relief at this density interface suggests a deep structural component to the surficial features of multiring lunar impact basins. For large (&gt;300 km diameter) basins, moho relief appears uncorrelated with diameter, but is negatively correlated with basin age. In several cases, it appears that the multiring structures were out of isostatic equilibrium prior to mare emplacement, suggesting that the lithosphere was strong enough to maintain their state of stress to the present.

Asymmetrical spectral curvature algorithms: oceanic-constituents sensitivities

The asymmetrical spectral curvature algorithm for Morel case 1 waters has been characterized by application of the semianalytical radiance model of ocean color to post-Coastal Zone Color Scanner (CZCS) sensor bands. Results of the study suggest that the [L (490)/L (443)][L (490)/L (555)] asymmetrical spectral curvature algorithm has a higher pigment-retrieval sensitivity than does the [L (490)/L (443)][L (490)/L (510)] curvature algorithm that was initially identified for pigment recovery. When this [L (490)/L (443)][L (490)/L (555)] algorithm was highlighted for study, it was found to (a) xhibit pigment-retrieval sensitivity that is intermediate to the [L (443)/L (555)] and the [L (510)/L (555)] CZCS-type radiance-ratio algorithms, (b) have less sensitivity to nonabsorbing particulate backscatter (NAB) than the [L (443)/L (555)] radiance ratio, (c) display remarkable insensitivity to the absorption of dissolved organic material (DOM), and (d) possess a NAB invariance point at an algorithm value of ∼1.8 (corresponding to a pigment concentration of ∼0.35 mg/M(3)). At this invariance point the [L (490)/L (443)][L (490)/L (555)] algorithm is insensitive to a wide concentration range of coccolith-like backscatterers in addition to being insensitive to DOM. The dual DOM and NAB insensitivity of the algorithm at a specific curvature value and chlorophyllous-pigment concentration suggests that such invariance points should be further studied for possible use in (1) the validation of other chlorophyllouspigment algorithms or model inversions and (2) the computation of other inherent optical properties.

Hydraulic radius and transport in reconstructed model three-dimensional porous media

Methods for reconstructing three-dimensional porous media from two-dimensional cross sections are evaluated in terms of the transport properties of the reconstructed systems. Two-dimensional slices are selected at random from model three-dimensional microstructures, based on penetrable spheres, and processed to create a reconstructed representation of the original system. Permeability, conductivity, and a critial pore diameter are computed for the original and reconstructed microstructures to assess the validity of the reconstruction technique. A surface curvature algorithm is utilized to further modify the reconstructed systems by matching the hydraulic radius of the reconstructed three-dimensional system to that of the two-dimensional slice. While having only minor effects on conductivity, this modification significantly improves the agreement between permeabilities and critical diameters of the original and reconstructed systems for porosities in the range of 25–40%. For lower porosities, critical pore diameter is unaffected by the curvature modification so that little improvement between original and reconstructed permeabilities is obtained by matching hydraulic radii.

Ocean color spectral variability studies using solar-induced chlorophyll fluorescence

It is suggested that chlorophyll-induced ocean color spectral variability can be studied using only a passive airborne spectroradiometer instrument, with solar-induced chlorophyll fluorescence used as the standard against which all correlations are performed. The intraspectral correlation (ISC) method is demonstrated with results obtained during an airborne mapping mission in the New York Bight. The curvature algorithm is applied to the solar-induced chlorophyll fluorescence at about 690 nm, and good agreement is found with results obtained using active-passive correlation spectroscopy. The ISC method has application to spectral variability and resulting chlorophyll concentration measurement in different environmental conditions and in different water types.