Proceedings of 20121CME International Conference on Complex Medical Engineering

July I - 4, Kobe, Japan

An Auto-adaptive Fuzzy based Inspiration of Cerebellar

Cortex for Dyslexic Ocular Motor Control

Elham Ghassemi IRIS Group, Centre d'Etudes de fa Sensori-Motricite,

UMR 8194, CNRS, Universite Paris Descartes, Paris, France

e lham. ghassem i@etu.parisdescartes.fr

Abstract- This paper presents a novel modeling approach for

dyslexic oculomotor control, called AFCMAC, an Auto-adaptive

Fuzzy CMAC (Cerebellar Model Articulation Controller). We

made some comparisons between the AFCMAC and the CMAC,

over the standard deviation of binocular fixation disparity of ten

dyslexic subjects while reading, in two viewing distances (near

and far). The evaluation results prove the promising

performance of the AFCMAC, over the training time, and also,

the memory requirements, while increasing the number of

subjects.

Index Terms - Cerebellum, CMAC, Dynamic Fuzzy Logic,

Adaptive Oculomotor Control, Vergence Eye Movement

I. INTRODUCTION

The cerebellum contains nearly half of neurons and synaptic connections in the brain. It plays a major role in the learning, the control and the organization of the motor events. The organization of inputs to and outputs from the cerebellum indicates that it compares internal feedback (the intended movement) to external feedback signals (the actual movement) [1]. While repeating the movement, the cerebellum is able to correct ongoing movement deviated from the intended path, and modify motor programs in the central nervous system, so that future movement accomplishes its objective, i.e. motor learning [2].

The cerebral cortex and the cerebellar cortex, each one has a mosaic texture represented by repeated cerebral microcolurnns [3] and cerebellar microzones [4]. Each micro zone of the cerebellum can be compared to a neural network with three layers [5-6].

The Cerebellar Model Articulation Controller (CMAC) is a feed-forward associative memory neural network. Mainly, the CMAC was employed to control robotic arm [7-8]. An intact cerebellum, which is not the case of dyslexia [9-10], is a prerequisite for optimal oculomotor performance. The cerebellum fme-tunes each of the subtypes of eye movements. Therefore, they work together to bring and maintain images of objects of interest on the fovea, where visual acuity is the best [11 ].

One of the main disadvantages of the CMAC is that, its memory requirement increases, when the number of inputs grows. Furthermore, it is not conceivable to extract the structural information from the trained CMAC, or to integrate the expert's knowledge into it.

978-1-4673-1618-7112/$31.00 ©2012 IEEE 165

Zoi'Kapoula IRIS Group, Centre d'Etudes de fa Sensori-Motricite, UMR 8194, CNRS, Service d'ophtafmofogie, H6pitaf

Europeen Georges Pompidou, Paris, France

zoi.kapoula@egp.aphp.fr

These drawbacks lead us to apply Fuzzy Logic, founded by Zadeh [12-16], to the CMAC and propose the AFCMAC (Auto-adaptive Fuzzy CMAC), as described in part II.

The performance evaluation and comparison results between the AFCMAC and the CMAC are elucidated in part III, while part IV provides the closing notes.

II. PROPOSED MODEL

In this section, the structure of the AFCMAC which consists of input/output fuzzification and defuzzification schemes and an auto-adaptive Fuzzy learning module is presented. The AFCMAC uses Mamdani's Fuzzy inference method for fuzzification and defuzzification processes [17]. �l;;�l----------------------------------------------�

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Figure 1. The layered modular architecture of the AFCMAC

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As Fig. 1 illustrates, the modular architecture of the AFCMAC has 3 layers:

• Layer J: First, the Input Filter is used to determine the proper inputs. The filter rejects any input values beyond the acceptable input range. Then, the filtered inputs are given to the Fuzzification module to convert them to the Fuzzy values.

• Layer 2: In this layer, the Input-Output Mapping module takes the fuzzified inputs and uses the Fuzzy Training module to map them to a desired output. Fuzzy Training module uses a Fuzzy rule database and also the desired output values to apply an existing rule, or to generate a new one, if there is no rule in the database corresponding to the given input-output pair. That means to ensure the input-output mapping process, according to the requirements of the system, either the new rules will be generated and added to the database, or the existing rules will be applied.

• Layer 3: Finally, the Defuzzification module takes the Fuzzy values and converts them to the numerical values.

III. EVALUATION

To evaluate the performance of the AFCMAC, we are focused on the horizontal voluntary eye movements during reading, like saccades (bringing the eyes from left to right), fixations (fixating word after word), and also vergence.

Pure vergence movements are the slow eye movements that we make when, we change our binocular fixation between targets differing in distance but not in direction relative to the head. Usually, we change our fixation between targets that differ in both distance and direction. Therefore, vergence eye movements are combined with saccades [18].

That means while reading, in addition to saccades, binocular vision of the text needs continuously adjusting the vergence angle for appropriate fusion of the two retinal images during fixation word after word [19].

A. Data

For this work, ten dyslexic subjects were chosen from study by [19]. Their binocular eye movements were recorded by the Chronos Vision Eye-Tracking device, while reading a French text, in a seated position with the head-fixed.

B. Parameter

We are interested in the parameter of the Standard Deviation (SD) of fixation disparity. Fixation disparity is the difference between the convergence angle under binocular viewing and the angle subtended by the target at the centers of rotation. For each subject, almost 128 SD values in two viewing distances of 40 cm. and 100 cm. were used.

This parameter provides us a summed assessment of the quality of vergence adjustments during fixations. Because without active and fme-tuned vergence adjustments, the fusion process might fail and reading might be troubled [20-21].

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C. Environment

The AFCMAC and the CMAC were implemented by Microsoft Visual C# .net. To develop fuzzification and defuzzification modules, DotFuzzy was used [22].

D. Method

In order to evaluate the trammg performance of the AFCMAC we compared it to the CMAC. To do this, the relationship between the number of subjects and

• the training iterations (which presents the training time ),

• the memory requirements,

were found, when the number of input data was varying from 128 to 1280 (128 SD values for each subject).

In the fust step, the models are trained by using the fust subject's data and the training iterations and the memory requirements were computed. In the second step, the models take the first and the second subject's data and so on. That means in the step n, the models take from the fust to the nIh

subject's data at the same time, and after each step, the models are initialized.

E. Results

J) Training iteration Fig. 2 shows the training iteration's curves of the

AFCMAC compared to the CMAC's ones, when the number of input data increases, for two viewing distances of 40 cm. (Fig. 2.i) and 100 cm. (Fig. 2.ii).

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Figure 2. The training iteration's curves versus the number of input data for two models in two viewing distances of 40 cm. (i.) and 100 cm. (ii.)

As revealed this figure, there is a significant difference between the training performance of the AFCMAC and the CMAC, in both of two viewing distances. When the number of subjects increases, the number of training iterations of the CMAC grows and converges to 1000, whereas, the AFCMAC's one is notably steady, particularly, after the third step.

It is interesting to note that, according to our recent study [23], the number of iterations of the AFCMAC was 290 for five dyslexic subjects at near distance, and here, with other ten dyslexic subjects, it remains closely the same.

This considerable performance of the AFCMAC is resulted by using the dynamic Fuzzy Logic training method.

2) Memory consumption The memory consumption comparison, on a scale of 0 to

10, between the AFCMAC and the CMAC, in two viewing distances is shown in Fig. 3.

As Fig. 3.i demonstrates, the memory resources needed for the CMAC increase and converge to 10, when the number of input data grows. But the memory usage by the AFCMAC has a tendency to remain unchanged, even after a single jump. This memory consumption, which is nearly 250% less than the CMAC's one, is stemmed from the efficiency of the auto­adaptive Fuzzy rule adjustment method, in the AFCMAC.

The same analysis over the SD values of dyslexic subjects at far distance (Fig. 3.ii), confirms these outcomes.

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Figure 3. The memory consumption's curves versus the number of input data for two models in two viewing distances of 40 cm. (i.) and 100 cm. (ii.)

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IV. CONCLUSION

In this study, the AFCMAC, an Auto-adaptive Fuzzy CMAC, which is an inspiration of cerebellar cortex function for oculomotor control, is proposed. Specially, we focused on the horizontal voluntary eye movements of dyslexic SUbjects.

The advantages of the proposed model compared to the CMAC can be summarized as follows:

• it uses dynamic Fuzzy Logic training method to create and adjust the Fuzzy rules.

• its training time is much lower, and above all, it stays stable by increasing the number of subjects.

• it can be easily construed by a human expert.

• it needs a much lower memory.

These prominent gains encourage us to develop an intelligent expert system based on the AFCMAC for dyslexic eye training.

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[22] www.havana7.com/dotfuzzy

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