Screening subclinical keratoconus with Placido-based corneal indices

Purpose: To assess in a sample of normal, keratoconic and keratoconus suspect eyes the performance of a set of new topographic indices computed directly from the digitized images of the Placido rings. Methods: This comparative study comprised a total of 124 eyes of 106 patients from the ophthalmic clinics Vissum Alicante and Vissum Almería (Spain), in three groups: control group (50 eyes), keratoconus group (50 eyes) and keratoconus suspect group (24 eyes). In all cases, a comprehensive examination was performed including the corneal topography with a Placido-based CSO topography system. Clinical outcomes were compared among groups, along with the discriminating performance of the proposed irregularity indices. Results: Significant differences at level 0.05 were found on the values of the indices among groups by means of Mann-Witney-Wilcoxon non-parametric test and Fisher’s exact test. Additional statistical methods, such as receiver operating characteristic analysis and K- fold cross-validation, confirmed the capability of the indices to discriminate between the three groups. Conclusions: Direct analysis of the digitized images of the Placido mires projected on the cornea is a valid and effective tool for detection of corneal irregularities. Although based only on the data from the anterior surface of the cornea, the new indices performed well even when applied to the keratoconus suspect eyes. They have the advantage of simplicity of calculation combined with high sensitivity in corneal irregularity detection, and thus can be used as supplementary criteria for diagnosing and grading keratoconus that can be added to the current keratometric classifications. Keywords: Corneal irregularities; subclinical keratoconus; irregularity index; diagnosis; corneal topography; Placido disk

Placido-based indices of corneal irregularity

Purpose: To construct a set of metrics computed from the raw keratoscopic data collected by any Placido corneal topographer. These indices that measure the irregularity of the anterior corneal surface are computed directly from the image of the mires reflected on the cornea, which is the most primary data possible. Besides the high sensitivity and specificity, this approach allows bypassing the surface or curvature reconstruction step that is currently performed by the software of any commercial Placido topographer. Methods: Several basic indices are proposed in order to detect irregularities on the anterior surface of the cornea, via analyzing some geometric and mathematical properties of the mires. These individual primary indices are built in a natural and intuitive way directly from the displacement of the digitized images of the rings reflected on the cornea. Additionally, compound indices are proposed (such as the generalized linear model or the classification trees) by combining some of the so-called primary indices to improve their efficiency. The computed metrics were developed and tested for the CSO topography system (CSO, Firenze,Italy), but the methodology proposed here extends easily to any other commercial Placido disks topographer. Results: The primary indices allow to discriminate, with excellent accuracy, between normal eyes and eyes with keratoconic corneas. Sensitivity and specificity of the primary indices is analyzed by using the ROC (receiver operating characteristic) curve methodology. Some combined indices are presented, and raise the efficiency to optimal. Conclusions: All the primary indices proposed exhibit very good performance at discriminating between normal and irregular corneas. The combined indices accuracy is optimal, so avoiding their use in clinical practice as corneal markers of disease. All these indices are fast to compute and can be easily implemented in any corneal topography system. Keywords: Corneal irregularities keratoconus irregularity index diagnosis corneal topography Placido disk

Optimal sampling patterns for Zernike polynomials

A pattern of interpolation nodes on the disk is studied, for which the inter- polation problem is theoretically unisolvent, and which renders a minimal numerical condition for the collocation matrix when the standard basis of Zernike polynomials is used. It is shown that these nodes have an excellent performance also from several alternative points of view, providing a numer- ically stable surface reconstruction, starting from both the elevation and the slope data. Sampling at these nodes allows for a more precise recovery of the coefficients in the Zernike expansion of a wavefront or of an optical surface. Keywords: Interpolation Numerical condition Zernike polynomials Lebesgue constant

A Comparison of Machine-Learning Methods to Select Socioeconomic Indicators in Cultural Landscapes

Cultural landscapes are regarded to be complex socioecological systems that originated as a result of the interaction between humanity and nature across time. Cultural landscapes present complex-system properties, including nonlinear dynamics among their components. There is a close relationship between socioeconomy and landscape in cultural landscapes, so that changes in the socioeconomic dynamic have an effect on the structure and functionality of the landscape. Several numerical analyses have been carried out to study this relationship, with linear regression models being widely used. However, cultural landscapes comprise a considerable amount of elements and processes, whose interactions might not be properly captured by a linear model. In recent years, machine-learning techniques have increasingly been applied to the field of ecology to solve regression tasks. These techniques provide sound methods and algorithms for dealing with complex systems under uncertainty. The term ‘machine learning’ includes a wide variety of methods to learn models from data. In this paper, we study the relationship between socioeconomy and cultural landscape (in Andalusia, Spain) at two different spatial scales aiming at comparing different regression models from a predictive-accuracy point of view, including model trees and neural or Bayesian networks

The Role of Cultural Landscapes in the Delivery of Provisioning Ecosystem Services in Protected Areas

The aim of this paper is to assess and highlight the significance of cultural landscapes in protected areas, considering both biodiversity and the delivery of provisioning ecosystem services. In order to do that, we analyzed 26 protected areas in Andalusia (Spain), all of them Natural or National Parks, regarding some of their ecosystem services (agriculture, livestock grazing, microclimate regulation, environmental education and tourism) and diversity of the four terrestrial vertebrate classes: amphibians, reptiles, mammals, and birds. A cluster analysis was also run in order to group the 26 protected areas according to their dominant landscape. The results show that protected areas dominated by dehesa (a heterogeneous system containing different states of ecological maturity), or having strong presence of olive groves, present a larger area of delivery of provisioning ecosystem services, on average. These cultural landscapes play an essential role not only for biodiversity conservation but also as providers of provisioning ecosystem services

Computation of 2D Fourier transforms and diffraction integrals using Gaussian radial basis functions

We implement an efficient method of computation of two dimensional Fourier-type integrals based on approximation of the integrand by Gaussian radial basis functions, which constitute a standard tool in approximation theory. As a result, we obtain a rapidly converging series expansion for the integrals, allowing for their accurate calculation. We apply this idea to the evaluation of diffraction integrals, used for the computation of the through-focus characteristics of an optical system. We implement this method and compare it performance in terms of complexity, accuracy and execution time with several alternative approaches, especially with the extended Nijboer-Zernike theory, which is also outlined in the text for the reader’s convenience. The proposed method yields a reliable and fast scheme for simultaneous evaluation of such kind of integrals for several values of the defocus parameter, as required in the characterization of the through-focus optics. Keywords: 2D Fourier transform, Diffraction integrals, Radial Basis Functions, Extended Nijboer–Zernike theory, Through-focus characteristics of an optical system

Computational aspects of the through-focus characteristics of the human eye

Calculating through-focus characteristics of the human eye from a single objective measurement of wavefront aberration can be accomplished through a range of methods that are inherently computationally cumbersome. A simple yet accurate and computationally effcient method is developed, which combines the philosophy of the extended Nijboer-Zernike approach with the radial basis function based approximation of the complex pupil function. The main advantage of the proposed technique is that the increase of the computational cost for a vector valued defocus parameter is practically negligible in comparison to the corresponding scalar valued defocus parameter

Cost-Sensitive Variable Selection for Multi-Class Imbalanced Datasets Using Bayesian Networks

Multi-class classification in imbalanced datasets is a challenging problem. In these cases, common validation metrics (such as accuracy or recall) are often not suitable. In many of these problems, often real-world problems related to health, some classification errors may be tolerated, whereas others are to be avoided completely. Therefore, a cost-sensitive variable selection procedure for building a Bayesian network classifier is proposed. In it, a flexible validation metric (cost/loss function) encoding the impact of the different classification errors is employed. Thus, the model is learned to optimize the a priori specified cost function. The proposed approach was applied to forecasting an air quality index using current levels of air pollutants and climatic variables from a highly imbalanced dataset. For this problem, the method yielded better results than other standard validation metrics in the less frequent class states. The possibility of fine-tuning the objective validation function can improve the prediction quality in imbalanced data or when asymmetric misclassification costs have to be considered

Procedimiento de reconstrucción de la topografía corneal a partir de datos altímetros o de curvatura

Número de publicación: ES2392619 A1 (12.12.2012) También publicado como: ES2392619 B1 (22.10.2013) Número de Solicitud: Consulta de Expedientes OEPM (C.E.O.) P201000842(08.06.2010)Procedimiento de reconstrucción de la topografía corneal a partir de datos altimétricos o de curvatura. La invención consiste en un método de reconstrucción de la superficie de la cara anterior de la córnea, a partir de los datos medidos en un conjunto discreto de puntos por medio de un topógrafo corneal o equipo equivalente. Se trata de un procedimiento que obtiene una expresión analítica de la superficie, combinando un ajuste por polinomios de Zernike o con esfera de mejor ajuste, con una reconstrucción por funciones de base radial gaussianas. Se logra obtener una descripción detallada de la superficie corneal, permitiendo un diagnóstico más fiable de patologías, o la implementación de tratamientos customizados. Este procedimiento es fácilmente implementable en cualquier topógrafo corneal, tomógrafo de coherencia óptica, equipos de lámpara de hendidura y equivalentes, de los existentes en el mercado, como sustituto del método estándar basado en polinomios de Zernike.Universidad de Almerí