2004 IEEE Workshop on Machine Learning for Signal Processing

MACHINE LEARNING TECHNIQUES FOR OCULAR ERRORS ANALYSIS

Giampaolo L. Libralao, Osvaldo C. P. de Almeida, Antonio Valerio Netto giampaoldibralon, cesar.pinheiro, antonio.,alerio{Ocientistasassociados.co~.b~}

Associated Scientists Ltd., Sa0 Carlos, Sa0 Paulo, Brazil

Alerandre C. B. Delbem, Andre C. P. Leon F. de Carvalho acbd, andre{Oicmc.usp.br)

Institute of Mathematical and Computer Sciences, University of Sa0 Paulo - USP, Brazil LABlC - Laboratory of Computational Intelligence

Abstract. The conventional techniques for refractive error mea- surements (myopia, hypermetropia, and astigmatism) have been considered inadequate for several optometry researches. In this context, they have investigat.ed alternative methodologies for re- fractive error measurement. A new strategy is the determination of refractive errors from images of the globe of the eye. A process named Hartmann-Shack can obtain these images. The HS images should be analysed in order to extract relevant inforniation for identification of refractive errors. The present paper investigates a technique based on Radial Basis Functions (RBFs), an Artificial Neural Network (ANN), and on Support Vector Machines (SVMs), which automatically performs analysis of images from the globe of the eye and identifies refractive errors. The most relevant data of these images are extracted using Gahor wavelets transform, and then these Machine Learning techniques carry out the image anal- ysis.

Keywords. Refractive Errors; Optometry: Machine Learning; Radial Basis Function (RBF); Support Vector Machine (SVM); Artificial Intelligence; Hartmann-Shack images.

INTRODUCTlON

The human eye may present refractive errors as myopia; hypermetropia and astigmatism. There exist several procedures for diagnosing these diseases, however, they are not efficient enough 1181. The available devices for re- fractive error detection require frequent calibrations. Since the maintaining process is expensive and needs expert technicians, it make difficult to keep

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the device working properly 1201. On the other hand, lrlachine Learning (ML) approaches have shown satisfactory results for a large variety of problems in which conventional methodologies have not been successful. The present pa- per investigates the use of these ML techniques, the RBF networks, and the SVMs for refractive error measurement. SVM is constituted of learning algo- rithms family that have been drawing great attention in the last years 1151. They were developed from 1992 on: by researcher Vladimir Vapnik's team [21] and it is based on the theory of statistical learning, through the principle of Structural Risk Minimization (SRM). SVM can be considered as a learning machine with only one hidden layer, through a supervised aIgorithm.

In this proposal, previous knowledge from refractive diseases composes a set of eye images from the globe of the eye and the corresponding diag- noses. The process for obtaining the eye images is also very important. The proposed approach, based on Hartmann-Shack (HS) technique, uses the HS images and their corresponding diagnoses as previous knowledge used for the ML techniques investigated. The present paper investigates these techniques applied to the OptometryJOphthalmology field, aiming t o contribute to the development of alternative approaches for analysis of ocular problems. New diagnosis procedures using hlL techniques may result in development of more efficient equipment for measurement of refractive errors. In addition, proce- dures capable of automatically analysing images from the globe of the eye might also be used to obtain several other eye diseases.

Shack t,echnique for image acquisition; third section presents a brief review of ANNs and SVhls; fourth section explains the proposed System of Refract.ive Error Measurement (SREM) using the hlL techniques proposed and shows tests and results using the proposed approach, finally, fifth section preseuts the final remarks.

This paper is organized as follows: second section introduces the Hartmann-

DATA ACQUISITION FROM HUMAN EYE

There are several methods for obtaining human eye information; the Ilartmann- Shack (HS) has been cousidered t,he most, promising technique [Si. Images of human eyes are difficult to obtain. Typically, it is assumed that light rays entering t,he eye are focused in front of the retina. If the observed object is sufficiently distant t o be regarded light point, such as a star, the light rays can be considered parallel when t,hey enter the eye and are refracted to form a perfect point image on the retina. In other words, it may be assumed that the source point emits light waves in a single direction. If the source point is sufficient.ly distant, the rays entering the eye have the form of a plane wave. Taking light rays simply as lines and assuming they are plane waves: the wave front reaches perpendicularly the eye. i.e. the light rays are parallel. Inside the eye the waves change into circular waves and are focused into a point in the retina 1181.

The reverse process may also be considered, i.e. suppose some of the light

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from a point on the retinal image reflects back out from the eye. If the eye is perfect, the emerging wavefront mill be a plane wave and the rays will be parallel to each other. However, if the eye displays some kind of anomaly the emerging wavefront will be distorted away from the perfect shape of a plane wave. Naturally, the reflected light will he very dim. Nevertheless, anyone who has ever had their Rash photographs ruined by a red eye knows that it is possible to capture photographically the light reflected back out from the eye if the Rash is bright enough. A system apparatus to capture this reflected wavefront is described in the following.

A point light source is created in the retina and the wave front of emerging light from the eye is analysed by an array of fine lenses. This micro-lenslet array divides the wave front into several individual beams, each one focused into a CCD (Charge-Coupled Device) sensor [18]. In a normal eyel t,he re- flected plane wave is perfectly focused into a grid of image points. An image is generated with all the points coming from the array of lenses and with the spacing among such points equal to the spacing among lenses in the micro-lenslet array.

Note that for a perfect plane wave, the direction of light propagation is the same for all light rays. However, in an anomalous wave, the direction of light propagation varies. This process can be used to determine the shape of the wave front propagation by analysing locations of the points registered by the CCD sensor. The light rays reflected by an imperfect eye are not parallel. As a consequence, the rays reaching the niicralenslet array generate an image with disordered points. For an analysis of image with disordered points, rates assessing the disorder can be calculated relatively to the reflection of a perfect globe of eye. Then these rates may he used to determine the type of anomaly.

The shape of the anomalous wave front, known as wave front aberration function, provides the fundamental measurement to evaluate the optical qual- ity of the eye. This function is the core of the optical theory proposed by [SI that allows the analysis of the image formed in the retina by some object in order to evaluate the eye capacity to perform several tasks.

MACHINE LEARNING TECHNIQUES

Machine Learning is an area involving computational intelligence that de- velops methods capable to extract concepts (knowledge) from data samples [Ill. In general, RIL algorithms allow that a machine learn how to classify data (samples) using a process named training. After the training phase, the machine is capable to interpret new samples and properly classify them. hlL algorithms are in general inspired on other science fields [16]: biolog- ical systems (as ANN and Genetic Algorithms), cognitive processes (Case Based Reasoning), symbolic learning (Decision Trees), and statistical the- ries (Support Vector Machines). There are basically thsee paradigms for the learning process of ML algorithms: supervised, non-supervised and based on reinforcement.

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Artificial Neural Networks (ANNs) are based on brain behaviour and can automatically perform tasks that imitate the brain reasoning and learning from large information sets. In real world problems, ANNs are generally used to separate data into classes, such as: false and true, samples of healthy patients and patients with diseases. This technique requires large amounts of data (samples) as input. Samples perform as previous knowledge from which an ANN learns how to correctly classify them [12].

Broomhead and Lowe was proposed the RBF (Radial Basis Function) network in 1988 121. In general, they are used in approximation of mathe- matical functions and pattern recognition. Typically, RBF possesses a single hidden layer whose neurons use radial base activation functions, which are in general Gaussian. REiF are trained by hybrid methods composed of a non- supervised and a supervised stage. The latter determines the number of ra- dial functions and their parameters for a non-supervised method. The former calculates the neuron weights using a linear model as delta rule. In general, k-mean algorithm is used for the first stage. On the other hand, second stage uses a linear approach to calculate the neuron weights. RBF networks have presented relevant performance for pattern recognition (11. Suppose a data group consisting of three classes, while a MLP (MultiLayer Perceptron) 1141 (131 separates these classes generating hyper planes, a RBF classify them in clusters, using hyper-ellipsoids to divide the space of patterns. The space division by hyper-ellipsoids improves precision of the pattern classification process.

SVMs make the approach of problems in two different possible mays. In the first, classification mistakes are not considered, in other words, patterns that do not fit the typical values of their class will deviate the separation hyperplane so that this pattern is classified as correct. In the second, extra variables are established, so that patterns that do not fit the typical values of their group can be inconsiderate, depending on the amount of extra ones that is used, reducing, thus, the probability of classification mistake. SVhl accomplishes a non-linear data analysis in a high dimension space where a great hyperplane can be built; allowing the separation of positive and negative classes or using the machine for regression.

The high generalization capacity obtained by SVh4s is result of t,he use of the statistical learning theory, principle presented in the decade of 60 and 70 by [ Z l ] . However, the main practical applications are recent and date from the nineties. SVMs have been applied to the solution of several problems, like pattern recognition and people’s faces detect.ion in the images, in which obtained good performance.

METHODOLOGY AND RESULTS

The proposed Refractive Error Measurement System (REMS) 1201 possesses four modules:

1. Image Acquisition h4odule. The acquisition of the ophthalmic images

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by HS technique was carried out by [lS] Optometry group using equip ment named Aberrometer,

2. Image Pre-processing Module. The ophthalmic images are generated in a format that does not. alloiv their direct use by ML techniques. First the image data is normalized. Then, the image is filtered to eliminate noise that may affect the feature extraction process. This process is carried out by algorithms of image processing based on the histogram analysis method that uses space and geometric information depending on application domain,

3. Feature Extraction Module. 'This module aims the extraction of the main feature of an image in order to reduce the amount of input data for the analysis module. The extraction proc.ess uses a technique named Gabor vavelet transform [lo],

4. Analysis Module. This module analyses patterns provided by feature extraction module. An RBF ANN and a SVM mere used to implement the analysis module.

Once the images are obtained, these are filtered by a pre-processing proce- dure, which eliminates image imperfections introduced during the acquisition process. The preprocessing technique is based on Histogram Analysis that uses geonictric and space information of the application domain 1171. The image database of eyes is composed of one hundred pa,tients, six images for each patient, three images of the right eye and three of the left eye; which re- sults in six hundred images. Each image is associated to three measurements (spherical (S): cylindrical (C) and axis of astigmatism (A)) , which are used to determine refractive diseases.

The measurements of the original data set, mere divided into classes, with a fixed interval between nieasiireinent values, based on the resolution of a commercial auto-refractor. For spherical measurements (S), nine classes were created, varying from -1.75 Dioptric (D) to +0.25 D, with a step of 0.25 D. For c,vlindrical nieasurements (C), six classes were created, varying from 0.0 D to 1.25 D, with a step of 0.25 D. Finally: for astigmatism axis angle mea- surements: 25 classes were created, varying from 0 to 180 degrees, with a step of 5 degrees. For astigmatisni axis angle measurements, 37 classes were first created but since some of these classes had few exemplars, which made the t.raining of hlL techniques difficult, only 25 classes, the ones which had enough exemplars: were considered. Table 1 shows the distribution among classes for t,he cylindrical measurenients. I t is possible to note that the crite- rion adopt,ed does not allow superposition of classes, since it is based on the resolution of a coinmercial auto-refractor.

The resolution of a commercial autrrrefractor is of 0.25 D for spherical (myopia and hypermetropia) and cylindrical (astigmatism), and 5 degree in the axis of cylindrical (astigniatism). The data used in the experiments has the same resolution. Thus, the proposed methodology is not more precise

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T4BLE 1: QUANTITY OF EXEhlPLARS FOR hlEASUREhlENT c C Measurement Quantity of exemplars Distribution among classes (%)

0.00 30 7.04% 0.25 229 53,76% 0.50 113 26,52% 0.75 31 7,28% 1.00 15 3,52% 1.25 8 l;SS%

than a commercial auto-refractor. Negative values of spherical correspond to myopia; for instance, -1.50 D means that the patient has 1.50 D of myopia. Positive values of spherical indicate hypermetropia. The used database pos- sesses the following measurement spectrum: spherical, from -1.75 D to +0.25 D; cylindrical, from 0.0 D to 1.25 D, and astigmatism, from 0 to 180 degree.

Before the image analysis, features of each image are extracted using the Gabor wavelet transform [3] [lo]. This technique allows an image to be represent,ed by it,s relevant features storing the majority of the image information. Then, the Analysis Module uses only the features extracted by Gabor as inputs for the proposed techniques, RBF and SVhf, reducing largely the amount of information processed. Gabor has shown appropriate results for extraction of the most, relevant features from images, as i t is capable of minimize data noise in the space and frequency domains (41. Moreover, this technique has been used in several applications of image processing such as: determination of a wavelets set that provide a complete representation of an iinage 181, recovery of images based on their texture [IO] and based on their content (CBIR - Content-based Image Retrieval), people identification by recognition of iris image [ 5 ] , and recognit,ion of fingerprint,s [7] and human faces from pictures [GI.

It is also important to highlight t,hat were developed three different SVM and RBF sub-modules, to analyse independently each measure (S, C and A ) . The first submodule to interpret the S data, another C data and last one, A data. In this way, the Analysis Module is composed by three SVhIs and three RBFs.

SNNS (Stuttgart Neural Network Simulator) [22] was used to training the proposed RBF. This simulator was developed by University of Stuttgart in Germany and it is free software that works on a Linux operational system. For training the random resampling method was applied, that means, the data set (426 examples after leaving the patterns that presented measure- ment problems apart) was divided into 10 different random partitions. This increases the statistical significance of results. These IO partitions were ran- dom generated aiming to have a uniform distribution of each measurement analyzed, S, C or A. For RBFs, the partitions were subdivided into three subsets, one for training a i th 60% of the examples, other for validation, with 20% of exemplars and another for tests, with also 20% of exemplars.

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For SVMs, the partitions mere subdivided into two subsets, one for train- ing and validation with 80% of the examples, and another for tests, with 20% of exemplars. The results of t.he techniques combined were presented to a final classifier responsible to generated the final result of each module devel- oped. The simulator used for SVMs was SVMTorch [19], known by efficiency with great amount of data.

For the training, the spectrum of measurements S, C and A were divided into intervals with equal range. Each spectrum interval is considered as a class from a classification problem, 9 classes were created for spherical: 6 for cylindrical, and 25 for astigmatism.

The obtained results are summarized in Tables 2 and 3: respectively for RBFs and SVMs. The second column of the table presents the amount of samples in each test set for ex11 kind of measurement (S: C: and A). The columns titled “Measurement” to the average rates (in percentage) and standard deviation (also in percentage) of the generated error for the mea- surement analysis S, C and A . The measurement error variation should be taken into account (to S and C it is 0.25 D, and to A it is 5 degree). It means that any measurement either S or C: having its true value equal to 0.5 D; is computed as correct if the value attributed h:, the classifier is 0.5 D, 0.25 D or 0.75 D. For A , if the true value equals 30 degree, it can he con- puted as correct, if the result attributed by the classifier is 30; 25 or 35 degree.

‘TABLE 2: R.E~ULTS USING RBF NETWORKS

hleasurement Total of Exemplars Average Error Standard Deviation

S 82 27.06% 2.08% C 83 21.18% 1.53% A 70 81.18% 2.10%

TABLE 3: RESULTS USING SVhfs Measurement

Total of Exemplars Average Error Standard Deviation S 82 18.29% 1.12% C 83 9.64% 100% A 70 70.00% 1.64%

In the samples available for t,est, the majority of classes do not possesses the same quantity of samples, i.e. the classes are not balanced, which may re- sult in inadequate classifications. In order to certificate whether the obtained results are affected by class unbalaiice, a new set of tests were performed using classes that were artificially balanced. That is, classes with few memurements were augmented repeating data of t.he same class. The obtained results using artificial balancing are shoyn in Tables 4 and 5 , respectively for KBFs and SVhls.

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TABLE 4: RESULTS USING RBF NETWORKS WITH ARTIFICIALLY BALANCED CLASSES

Measurement Total of Exemplars Average Error Standard Deviation

S 82 26.67% 2.90% C 83 29.17% 3.53% A 70 25.00% 2.40%

TABLE 5: RESULTS USING SVhIS WITH ARTIFICIALLY BALANCED CLASSES

Measurement Total of Exemplars Average Error Standard Deviation

S 82 13.33% 1.64% C 83 20.83% 2.09% A 70 0.00% 2.12%

For measurements A, the errors based on error propagation criteria mere largely reduced using the artificially balanced classes, while the measurements S and C were not largely affected. This result suggests the relevance of using the artificial balance. Moreover, it indicates the importance of producing image databases with balanced spectrum in order to facilitate the training and, consequent,lg, a better performance of the Analysis Module, mainly if t,here are a great number of classes. This factor should be taken into account at the moment of building the image database for tests.

FINAL REMARKS

This article shows the application of two Machine Learning kchniques, RBF and SVM, to .the Optometry/Ophthalmology field. The aim is to provide a base of t,ools using computational intelligence for the development of fu- ture researches related to the analysis of ocular problems. The proposed methodology is founded on image database obtained by the Hart.mann:Shack (HS) technique developed by the Optometry group of the Indiana University (USA).

The proposed system (REh4S) possesses four modules: (1) Image Acqui- sition: (2) Image Pre-processing, (3) Feature Extraction, and (4) Analysis. The NS technique is used i n t,he image acquisition. The second module uses conventional pre-processing algorithms. The Gabor wavelet transform per- forms the feature extraction. The proposed techniques carry out the analysis. The Analysis Module approach affects directly the SREM, i.e. performance of this module is critical.

The results obtained mere relevant and may encourage future researches investigating new approaches for the analysis module. Nevertheless, the tests presented in this work show that the quality of the database is crucial for the

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analysis performance. Besides the image database used in the tests are not adequate. The main relevant data problems found were: few samples, small meaurement spect.rum, few samples per class, and unbalanced classes.

In spite of the limitations of database used, as it has not been acquired taking important points into account (balancing, number of examples per class and absence of ambiguities) for its use in an analysis module based on hlL techniques. The RBF neural net,u,ork and SVhl behavior demonstrated that the same ones could answer well enough to the adversities OF database obtained by a real system. In medicine area: it is usually hard t o obtain an appropriate spectrum where all of the classes have enough amounts of examples so that one can obtain an excellent performance in the analysis module.

Observing the easiness of SVh4 or even the RBF network in relating their outputs to inputs, it is possible to verify a great opportunity at the moment that one wants to reproduce the results obtained wit,h complex and high cost system, in low cost computational ones. I t would be possible, for instance, to detect and diagnose an ocular disease using a complex system or methodolog\. and later, use M L algorithms to relate images or informet,ion arrays: coming from specific sensors, to this disease.

In this way, a database with images from the globe of the eye without these problems may improve significantly the proposed approach. Thus, the elaboration of nem HS image data sets with proper features and also the investigation of ot,her hZL a,pproaches may provide a large improvement in the performance of methods using HS images.

ACKNOWLEDGEMENTS

The authors are grateful to Professor PhD. Larry Thibos from the School of Optometry, Indiana University (USA), for his support and for the supplied HS image database; and to Professor PhD. Maria Cristina F. de Oliveira and PhD. Joac Batista E. S. Net,o from University OF Sa0 Paulo for their contributions in t,he image processing area. IVe also acknowledge the support from FAPESP, the State of Sao Paulo Research Funding Agency (Grants: 00/04779-2, 01/09540-0, 02/08038-2).

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