Advanced techniques for the human eye study: ocular aberrometry

Lectures about the course module "Advanced techniques for the human eye study: ocular aberrometry".

Neural networks and statistical analysis for classification of corneal videokeratography maps based on Zernike coefficients: a quantitative comparison

PURPOSE: The main goal of this study was to develop and compare two different techniques for classification of specific types of corneal shapes when Zernike coefficients are used as inputs. A feed-forward artificial Neural Network (NN) and discriminant analysis (DA) techniques were used. METHODS: The inputs both for the NN and DA were the first 15 standard Zernike coefficients for 80 previously classified corneal elevation data files from an Eyesys System 2000 Videokeratograph (VK), installed at the Departamento de Oftalmologia of the Escola Paulista de Medicina, São Paulo. The NN had 5 output neurons which were associated with 5 typical corneal shapes: keratoconus, with-the-rule astigmatism, against-the-rule astigmatism, "regular" or "normal" shape and post-PRK. RESULTS: The NN and DA responses were statistically analyzed in terms of precision ([true positive+true negative]/total number of cases). Mean overall results for all cases for the NN and DA techniques were, respectively, 94% and 84.8%. CONCLUSION: Although we used a relatively small database, results obtained in the present study indicate that Zernike polynomials as descriptors of corneal shape may be a reliable parameter as input data for diagnostic automation of VK maps, using either NN or DA.

Reconhecimento de contorno de edifício em imagens de alta resolução usando os momentos complexos de Zernike

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

A parallel implementation of 3D Zernike moment analysis

Zernike polynomials are a well known set of functions that find many applications in image or pattern characterization because they allow to construct shape descriptors that are invariant against translations, rotations or scale changes. The concepts behind them can be extended to higher dimension spaces, making them also fit to describe volumetric data. They have been less used than their properties might suggest due to their high computational cost. We present a parallel implementation of 3D Zernike moments analysis, written in C with CUDA extensions, which makes it practical to employ Zernike descriptors in interactive applications, yielding a performance of several frames per second in voxel datasets about 2003 in size. In our contribution, we describe the challenges of implementing 3D Zernike analysis in a general-purpose GPU. These include how to deal with numerical inaccuracies, due to the high precision demands of the algorithm, or how to deal with the high volume of input data so that it does not become a bottleneck for the system.

Fast human pose estimation using 3D Zernike descriptors

Markerless video-based human pose estimation algorithms face a high-dimensional problem that is frequently broken down into several lower-dimensional ones by estimating the pose of each limb separately. However, in order to do so they need to reliably locate the torso, for which they typically rely on time coherence and tracking algorithms. Their losing track usually results in catastrophic failure of the process, requiring human intervention and thus precluding their usage in real-time applications. We propose a very fast rough pose estimation scheme based on global shape descriptors built on 3D Zernike moments. Using an articulated model that we configure in many poses, a large database of descriptor/pose pairs can be computed off-line. Thus, the only steps that must be done on-line are the extraction of the descriptors for each input volume and a search against the database to get the most likely poses. While the result of such process is not a fine pose estimation, it can be useful to help more sophisticated algorithms to regain track or make more educated guesses when creating new particles in particle-filter-based tracking schemes. We have achieved a performance of about ten fps on a single computer using a database of about one million entries.

Robust fitting of Zernike polynomials to noisy point clouds defined over connected domains of arbitrary shape

A new method for fitting a series of Zernike polynomials to point clouds defined over connected domains of arbitrary shape defined within the unit circle is presented in this work. The method is based on the application of machine learning fitting techniques by constructing an extended training set in order to ensure the smooth variation of local curvature over the whole domain. Therefore this technique is best suited for fitting points corresponding to ophthalmic lenses surfaces, particularly progressive power ones, in non-regular domains. We have tested our method by fitting numerical and real surfaces reaching an accuracy of 1 micron in elevation and 0.1 D in local curvature in agreement with the customary tolerances in the ophthalmic manufacturing industry.

X-ray mosaic nanotomography of large microorganisms.

Full-field X-ray microscopy is a valuable tool for 3D observation of biological systems. In the soft X-ray domain organelles can be visualized in individual cells while hard X-ray microscopes excel in imaging of larger complex biological tissue. The field of view of these instruments is typically 10(3) times the spatial resolution. We exploit the assets of the hard X-ray sub-micrometer imaging and extend the standard approach by widening the effective field of view to match the size of the sample. We show that global tomography of biological systems exceeding several times the field of view is feasible also at the nanoscale with moderate radiation dose. We address the performance issues and limitations of the TOMCAT full-field microscope and more generally for Zernike phase contrast imaging. Two biologically relevant systems were investigated. The first being the largest known bacteria (Thiomargarita namibiensis), the second is a small myriapod species (Pauropoda sp.). Both examples illustrate the capacity of the unique, structured condenser based broad-band full-field microscope to access the 3D structural details of biological systems at the nanoscale while avoiding complicated sample preparation, or even keeping the sample environment close to the natural state.

Statistical treatment of grain-size curves and empirical distributions: densities as compositions?

The preceding two editions of CoDaWork included talks on the possible considerationof densities as infinite compositions: Egozcue and D´ıaz-Barrero (2003) extended theEuclidean structure of the simplex to a Hilbert space structure of the set of densitieswithin a bounded interval, and van den Boogaart (2005) generalized this to the setof densities bounded by an arbitrary reference density. From the many variations ofthe Hilbert structures available, we work with three cases. For bounded variables, abasis derived from Legendre polynomials is used. For variables with a lower bound, westandardize them with respect to an exponential distribution and express their densitiesas coordinates in a basis derived from Laguerre polynomials. Finally, for unboundedvariables, a normal distribution is used as reference, and coordinates are obtained withrespect to a Hermite-polynomials-based basis.To get the coordinates, several approaches can be considered. A numerical accuracyproblem occurs if one estimates the coordinates directly by using discretized scalarproducts. Thus we propose to use a weighted linear regression approach, where all k-order polynomials are used as predictand variables and weights are proportional to thereference density. Finally, for the case of 2-order Hermite polinomials (normal reference)and 1-order Laguerre polinomials (exponential), one can also derive the coordinatesfrom their relationships to the classical mean and variance.Apart of these theoretical issues, this contribution focuses on the application of thistheory to two main problems in sedimentary geology: the comparison of several grainsize distributions, and the comparison among different rocks of the empirical distribution of a property measured on a batch of individual grains from the same rock orsediment, like their composition

Measuring higher order optical aberrations of the human eye: techniques and applications

In the present paper we discuss the development of "wave-front", an instrument for determining the lower and higher optical aberrations of the human eye. We also discuss the advantages that such instrumentation and techniques might bring to the ophthalmology professional of the 21st century. By shining a small light spot on the retina of subjects and observing the light that is reflected back from within the eye, we are able to quantitatively determine the amount of lower order aberrations (astigmatism, myopia, hyperopia) and higher order aberrations (coma, spherical aberration, etc.). We have measured artificial eyes with calibrated ametropia ranging from +5 to -5 D, with and without 2 D astigmatism with axis at 45º and 90º. We used a device known as the Hartmann-Shack (HS) sensor, originally developed for measuring the optical aberrations of optical instruments and general refracting surfaces in astronomical telescopes. The HS sensor sends information to a computer software for decomposition of wave-front aberrations into a set of Zernike polynomials. These polynomials have special mathematical properties and are more suitable in this case than the traditional Seidel polynomials. We have demonstrated that this technique is more precise than conventional autorefraction, with a root mean square error (RMSE) of less than 0.1 µm for a 4-mm diameter pupil. In terms of dioptric power this represents an RMSE error of less than 0.04 D and 5º for the axis. This precision is sufficient for customized corneal ablations, among other applications.

Performance Study of an Improved Legendre Moment Descriptor as Region-Based Shape Descriptor

This paper reports a novel region-based shape descriptor based on orthogonal Legendre moments. The preprocessing steps for invariance improvement of the proposed Improved Legendre Moment Descriptor (ILMD) are discussed. The performance of the ILMD is compared to the MPEG-7 approved region shape descriptor, angular radial transformation descriptor (ARTD), and the widely used Zernike moment descriptor (ZMD). Set B of the MPEG-7 CE-1 contour database and all the datasets of the MPEG-7 CE-2 region database were used for experimental validation. The average normalized modified retrieval rate (ANMRR) and precision- recall pair were employed for benchmarking the performance of the candidate descriptors. The ILMD has lower ANMRR values than ARTD for most of the datasets, and ARTD has a lower value compared to ZMD. This indicates that overall performance of the ILMD is better than that of ARTD and ZMD. This result is confirmed by the precision-recall test where ILMD was found to have better precision rates for most of the datasets tested. Besides retrieval accuracy, ILMD is more compact than ARTD and ZMD. The descriptor proposed is useful as a generic shape descriptor for content-based image retrieval (CBIR) applications

Statistical treatment of grain-size curves and empirical distributions: densities as compositions?

The preceding two editions of CoDaWork included talks on the possible consideration of densities as infinite compositions: Egozcue and D´ıaz-Barrero (2003) extended the Euclidean structure of the simplex to a Hilbert space structure of the set of densities within a bounded interval, and van den Boogaart (2005) generalized this to the set of densities bounded by an arbitrary reference density. From the many variations of the Hilbert structures available, we work with three cases. For bounded variables, a basis derived from Legendre polynomials is used. For variables with a lower bound, we standardize them with respect to an exponential distribution and express their densities as coordinates in a basis derived from Laguerre polynomials. Finally, for unbounded variables, a normal distribution is used as reference, and coordinates are obtained with respect to a Hermite-polynomials-based basis. To get the coordinates, several approaches can be considered. A numerical accuracy problem occurs if one estimates the coordinates directly by using discretized scalar products. Thus we propose to use a weighted linear regression approach, where all k- order polynomials are used as predictand variables and weights are proportional to the reference density. Finally, for the case of 2-order Hermite polinomials (normal reference) and 1-order Laguerre polinomials (exponential), one can also derive the coordinates from their relationships to the classical mean and variance. Apart of these theoretical issues, this contribution focuses on the application of this theory to two main problems in sedimentary geology: the comparison of several grain size distributions, and the comparison among different rocks of the empirical distribution of a property measured on a batch of individual grains from the same rock or sediment, like their composition

A complex network-based approach for boundary shape analysis

This paper introduces a novel methodology to shape boundary characterization, where a shape is modeled into a small-world complex network. It uses degree and joint degree measurements in a dynamic evolution network to compose a set of shape descriptors. The proposed shape characterization method has all efficient power of shape characterization, it is robust, noise tolerant, scale invariant and rotation invariant. A leaf plant classification experiment is presented on three image databases in order to evaluate the method and compare it with other descriptors in the literature (Fourier descriptors, Curvature, Zernike moments and multiscale fractal dimension). (C) 2008 Elsevier Ltd. All rights reserved.

Road and Traffic Signs Recognition using Vector Machines

Intelligent Transportation System (ITS) is a system that builds a safe, effective and integrated transportation environment based on advanced technologies. Road signs detection and recognition is an important part of ITS, which offer ways to collect the real time traffic data for processing at a central facility.This project is to implement a road sign recognition model based on AI and image analysis technologies, which applies a machine learning method, Support Vector Machines, to recognize road signs. We focus on recognizing seven categories of road sign shapes and five categories of speed limit signs. Two kinds of features, binary image and Zernike moments, are used for representing the data to the SVM for training and test. We compared and analyzed the performances of SVM recognition model using different features and different kernels. Moreover, the performances using different recognition models, SVM and Fuzzy ARTMAP, are observed.

Traffic and Road Sign Recognition

This thesis presents a system to recognise and classify road and traffic signs for the purpose of developing an inventory of them which could assist the highway engineers’ tasks of updating and maintaining them. It uses images taken by a camera from a moving vehicle. The system is based on three major stages: colour segmentation, recognition, and classification. Four colour segmentation algorithms are developed and tested. They are a shadow and highlight invariant, a dynamic threshold, a modification of de la Escalera’s algorithm and a Fuzzy colour segmentation algorithm. All algorithms are tested using hundreds of images and the shadow-highlight invariant algorithm is eventually chosen as the best performer. This is because it is immune to shadows and highlights. It is also robust as it was tested in different lighting conditions, weather conditions, and times of the day. Approximately 97% successful segmentation rate was achieved using this algorithm.Recognition of traffic signs is carried out using a fuzzy shape recogniser. Based on four shape measures - the rectangularity, triangularity, ellipticity, and octagonality, fuzzy rules were developed to determine the shape of the sign. Among these shape measures octangonality has been introduced in this research. The final decision of the recogniser is based on the combination of both the colour and shape of the sign. The recogniser was tested in a variety of testing conditions giving an overall performance of approximately 88%.Classification was undertaken using a Support Vector Machine (SVM) classifier. The classification is carried out in two stages: rim’s shape classification followed by the classification of interior of the sign. The classifier was trained and tested using binary images in addition to five different types of moments which are Geometric moments, Zernike moments, Legendre moments, Orthogonal Fourier-Mellin Moments, and Binary Haar features. The performance of the SVM was tested using different features, kernels, SVM types, SVM parameters, and moment’s orders. The average classification rate achieved is about 97%. Binary images show the best testing results followed by Legendre moments. Linear kernel gives the best testing results followed by RBF. C-SVM shows very good performance, but ?-SVM gives better results in some case.

The aggregation process in tetraethoxysilane-derived sonogels as an analogy to the critical phenomenon

The structural evolution in silica sols prepared from tetraethoxysilane (TEOS) sonohydrolysis was studied 'in situ' using small-angle x-ray scattering (SAXS). The structure of the gelling system can be reasonably well described by a correlation function given by gamma(r) similar to (1/R(2))(1/r) exp(- r/xi), where xi is the structure correlation length and R is a chain persistence length, as an analogy to the Ornstein-Zernike theory in describing critical phenomenon. This approach is also expected for the scattering from some linear and branched molecules as polydisperse coils of linear chains and random f-functional branched polycondensates. The characteristic length. grows following an approximate power law with time t as xi similar to t(1) (with the exponent quite close to 1) while R remains undetermined but with a constant value, except at the beginning of the process in which the growth of. is slower and R increases by only about 15% with respect to the value of the initial sol. The structural evolution with time is compatible with an aggregation process by a phase separation by coarsening. The mechanism of growth seems to be faster than those typically observed for pure diffusion controlled cluster-cluster aggregation. This suggests that physical forces (hydrothermal forces) could be actuating together with diffusion in the gelling process of this system. The data apparently do not support a spinodal decomposition mechanism, at least when starting from the initial stable acid sol studied here.