�

Abstract²This paper presents AFCMAC, an Auto-adaptive

Fuzzy Cerebellar Model Articulation Controller, and its

comparison with the traditional CMAC (Cerebellar Model

Articulation Controller) for horizontal voluntary eye

movements. We evaluated the performance of the AFCMAC

and the traditional CMAC, by using the standard deviation of

binocular fixation disparity of five healthy control and five

dyslexic subjects, during reading a text. The evaluation results

prove a noteworthy performance of the AFCMAC compared to

the traditional CMAC in terms of the number of training

iterations.

I. INTRODUCTION

The Cerebellar Model Articulation Controller (CMAC) ± a feed-forward associative memory neural network ± was originally proposed for robotic arm controller (initially by Albus [1-2]).

In this work, we integrated Fuzzy Logic ± introduced by Zadeh [3-7] ± into the CMAC to propose an Auto-adaptive Fuzzy Cerebellar Model Articulation Controller (AFCMAC), and applied it to oculomotor control system.

Principally, we are interested in the voluntary eye movements while reading a text, like saccades (bringing the eyes from left to right), fixations (fixating word after word), and also vergence movements.

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. Accordingly, vergence eye movements are combined with saccades [8]. That means while reading, in addition to saccades, binocular vision of the text needs persistently adjusting the vergence angle for appropriate fusion of the two retinal images during fixation word after word [9].

The remainder of this paper is structured as follows: section II describes the modular architecture of the AFCMAC. The performance evaluation and comparison results between the AFCMAC and the traditional CMAC are clarified in section III, while section IV provides concluding remarks.

EOKDP�*KDVVHPL�LV�ZLWK�WKH�,5,6�*URXS��&HQWUH�G¶eWXGHV�GH�OD�6HQVRUL-

Motricité, UMR 8194, CNRS, Université Paris Descartes, Paris, France

(e-mail : elham.ghassemi@etu.parisdescartes.fr)

=Rw� .DSRXOD� LV� ZLWK� WKH� ,5,6� *URXS�� &HQWUH� G¶eWXGHV� GH� OD� 6HQVRUL-MotULFLWp��805�������&156��6HUYLFH�G¶RSKWDOPRORJLH��+{SLWDO�(XURSpHQ�Georges Pompidou, Paris, France

(e-mail : zoi.kapoula@egp.aphp.fr)

II. AFCMAC

As the Fig. 1 shows, the inputs pass through an Input Filter module. Each input has a minimum and maximum value. The Input Filter rejects any value beyond the minimum and maximum ranges. Then the filtered inputs pass through a Fuzzification module with trapezoid Fuzzy membership functions.

Fuzzified inputs pass through the Fuzzy neural network of Input-Output Mapping module, which uses the Fuzzy Training module. The Fuzzy Training module takes the desired output for a given input as input-output pairs (training points).

The training process adapts the Fuzzy rules dynamically to achieve the desired results. That means the breakpoints of the Fuzzy membership functions are dynamically calculated to generate the new Fuzzy rules and/or modify the existing rules.

Figure 1. The modular architecture of the AFCMAC

An Auto-adaptive Fuzzy based Cerebellar Model Articulation

Controller for Eye Movement

Elham Ghassemi, IEEE Student Member, and Zoï Kapoula

The Fourth IEEE RAS/EMBS International Conferenceon Biomedical Robotics and BiomechatronicsRoma, Italy. June 24-27, 2012

978-1-4577-1200-5/12/$26.00 ©2012 IEEE 124

The memory layer of the AFCMAC is a Fuzzy rules database. Indeed, each cell of this layer is a Fuzzy rule, which will be dynamically modified to adapt the input-output changes.

From a functional point of view, in the learning phase, if an input-output pair needs:

x a rule which exists in the memory, the rule will be used for this pair.

x a new rule which is not in the memory, the rule will be added to it.

x some modifications over an existing rule, the rule will be modified and saved to the rule database.

Finally, the Fuzzy outputs will be defuzzified while passing through the Defuzzification module.

This modular architecture of the AFCMAC which uses a dynamic adaptation of the rules, offers it a significant performance, discussed in the next section.

III. EVALUATION

We compared the performance of the AFCMAC to the traditional CMAC, over the number of training iterations (training time).

A. Data

The data acquired from [9] is used to evaluate the AFCMAC and the CMAC. For this work, five healthy control and five dyslexic subjects were selected. Their binocular eye movements were measured 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 (which exists when there is a small misalignment of the eyes, while viewing with binocular vision). For each subject, nearly 128 SD values in two viewing distances of 40 cm. and 100 cm. were used.

This parameter gives us a summed estimation of the quality of vergence adjustments during fixations. In fact, the angle of vergence of the two optic axes should be adjusted to the depth of the screen, and also should be maintained in a sustained manner during saccades and fixations, so that a single clear image of each word to be projected onto the fovea [9], where visual acuity is the best.

C. Environment

The AFCMAC and the CMAC were implemented by Microsoft Visual C# .net 2010. DotFuzzy, an open source stand-alone class library for Fuzzy Logic, is used to implement fuzzification and defuzzification processes [10].

D. Methods

The evaluation was done by using three methods to train the AFCMAC and the CMAC:

x Method 1: The control and dyslexic subjects¶� GDWD�were given to the models randomly at the same time.

x Method 2: This method is divided into two steps. In the first step, the control JURXS¶V data were imported into the models. The models were trained. Afterwards, in the second step, the dyslexic JURXS¶V�data were imported into the trained models.

x Method 3: In this method, unlike the previous method, the models were trained first by the dyslexic VXEMHFWV¶� GDWD, and then the control VXEMHFWV¶ data were imported into the trained models.

E. Results

Table 1 illustrates the comparison between the number of training iterations of the AFCMAC and WKH�&0$&¶s one, by using the first training method in two viewing distances of 40 cm. and 100 cm. The results indicate that the AFCMAC¶V�training iterations are 159% less WKDQ� WKH�&0$&¶V� RQHs at near distance and 158% at far distance.

The results of second training method are presented in Table 2. In the first step (for control group), tKH�$)&0$&¶V�training iterations are 237% less than WKH�&0$&¶V� RQHs at near distance and 242% at far distance.

In the second step (for dyslexic group), the number of training iterations of the AFCMAC decreases 726% FRPSDUHG�WR�WKH�&0$&¶V�RQH in near vision and 641% in far vision.

TABLE I. THE NUMBER OF ITERATIONS NEEDED TO TRAIN THE

AFCMAC AND THE CMAC BY USING THE FIRST TRAINING METHOD

AFCMAC CMAC

Number of training

iterations 449 713

a. Distance = 40 cm.

AFCMAC CMAC

Number of training

iterations 460 725

b. Distance = 100 cm.

TABLE II. THE NUMBER OF ITERATIONS NEEDED TO TRAIN THE

AFCMAC AND THE CMAC BY USING THE SECOND TRAINING METHOD

Step AFCMAC CMAC

1 315 748

2 99 719

a. Distance = 40 cm.

Step AFCMAC CMAC

1 320 773

2 113 724

b. Distance = 100 cm.

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TABLE III. THE NUMBER OF ITERATIONS NEEDED TO TRAIN THE

AFCMAC AND THE CMAC THE BY USING THE THIRD TRAINING METHOD

Step AFCMAC CMAC

1 290 735

2 303 694

a. Distance = 40 cm.

Step AFCMAC CMAC

1 303 730

2 350 703

b. Distance = 100 cm.

Table 3 confirms that in the first step (for dyslexic group) of the third training method, the number of training iterations of the AFCMAC is 253% less than WKH�&0$&¶V�RQH in near vision and 241% in far vision. In the second step (for control group), the $)&0$&¶V� training iterations are 229% less FRPSDUHG�WR�WKH�&0$&¶V�RQHs at near distance and 201% at far distance.

As Table 2 and Table 3 demonstrate, importing the control VXEMHFWV¶� GDWD� SULPDULO\, DQG� WKH� G\VOH[LF¶V� RQHs secondly, into the AFCMAC (applying the second method) is indeed, more efficient than using the third method (in which, there are roughly the same values for two models in each step��� %XW� LW� LV� LQWHUHVWLQJ� WR� VHH� WKDW� WKH� &0$&¶V�efficiency is approximately the same using all three methods.

IV. CONCLUSION

An auto-adaptive CMAC, based on dynamic Fuzzy Logic, called AFCMAC is evaluated in this paper. Its UHPDUNDEOH� SHUIRUPDQFH�� FRPSDUHG� WR� WKH�&0$&¶V� RQH�� LV�resulted by using the dynamic Fuzzy Logic. In fact, for each VXEMHFW��WKH�$)&0$&�OHDUQV�WKH�VXEMHFWV¶�H\H�PRYHPHQWV�± vergence adjustments ± by an auto-adaptive method.

Table 4 presents a brief comparison between the structure of the AFCMAC and the traditional CMAC¶V�RQH.

TABLE IV. A BRIEF COMPARISON BETWEEN THE STRUCTURE OF THE

AFCMAC AND THE CMAC¶S ONE

AFCMAC CMAC

Uses dynamic Fuzzy Logic

and Fuzzy neural network Uses neural network

Memory cells are the Fuzzy

rules

Memory cells are

presented by the neurons

of the neural network

Uses Fuzzy training Uses neural network

training

It is conveniently

interpretable by an expert,

and WKH�H[SHUW¶V�NQRZOHGJH�can be integrated into the

system as the Fuzzy rules

It is not feasible to extract

the structural information

from a trained CMAC, or

to include the H[SHUW¶V�knowledge into it

As the evaluation results illustrate, the time needed to train the AFCMAC at near distance is always less than at far distance. Since Fuzzy Logic is a marvelous tool that reasons as human brain with uncertain and imprecise information, this outcome inspires us to lead a time-effect analysis over all the subjects (control and dyslexic) in two viewing of distances, and realize how it works in biology. Is it the same fact DV�WKH�$)&0$&¶V�prediction? Respond to this, is one of our current activities.

The ultimate idea by proposing the AFCMAC will be applying it to develop an intelligent eye training expert system.

REFERENCES

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[9] S. Jainta and Z. .DSRXOD�� ³Dyslexic children are confronted with unstable binocular fixation while rHDGLQJ´� PLoS ONE, 6(4):e18694, 2011.

[10] www.havana7.com/dotfuzzy

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