Visual acuity of vision tested by fuzzy logic: An application in ophthalmology as a step towards a telemedicine project
Introduction
In the world we live in, the knowledge and the information that we use are imperfect. Indeed, they appear blemished with uncertainty and imprecision. The human mind appears to be very efficient in the analysis and the reasoning of this type of information. Data processing and Artificial Intelligence in particular try to reproduce human reasoning. Classic mathematical tools such as classic logic and the theory of the probabilities are not often sufficient to deal with the logical values “true” and “false”, or information taking the imprecise character of data into account. In our survey (tests of visual acuity), we were confronted to this type of problematic where it is not possible to come up with the right answers. This is the reason why we preferred a tool which takes into account this imprecision, ignorance, and approximation in the decision systems: the theory of the fuzzy sets.
One can also remark that physicians are more and more solicited to improve the quality of their medical examinations and to increase the number of their patients. It therefore becomes indispensable to develop new tools to allow them to reach their new objectives without undermining the quality of their work. Telemedicine via the Internet is now one of these tools.
Indeed, with the rapid development of Internet technologies, remotely accessing and operating medical applications, anytime, anywhere, is becoming increasingly possible. The Internet is now used both as a connection and as a reference tool for commercial, personal, educational and virtual laboratory purposes [1]. So virtual medical advice may be planned for the future, using an Internet link and a fuzzy logic algorithm to replace the “doctor–patient” direct relations. In this paper, we present a first application in that direction, using a simple deployment over the web, and we show the benefits of this association.
In this type of application, uncertainty can arise at various levels. It can occur at the lower levels in the raw sensor input, and remains all the way through the intermediate (treatment of information) and higher levels (transmission of the information and decision level). Ideally, at any level where decisions are made on the basis of previous processing steps, virtual medical advice must have sufficient flexibility for the representation of uncertainty at any of these levels. Studying the various causes of imprecision, ranging from the observed phenomena to the algorithms artefacts is a very complex problem. So we decided not to treat the imprecision induced at each step of the virtual medical advice, but to consider the global uncertainty present at the end of the process to increase the reliability of the advice (precision/uncertainty duality [2]). This study's framework is conventional, and has been used successfully for medical diagnosis [3]. So we specifically address the representation of uncertainty in the decision process (visual acuity estimation) through the use of a fuzzy algorithm, in order to replace a medical consultation.
The study presented here concerns an aid to ophthalmologic exams and more especially the measurement of the visual acuity of the patients. The object of ophthalmology is to detect eye diseases as well as to correct eye trouble. It requires a certain number of examinations for the verification of the vision of the colours, of the vision of contrast, and the visual field of the patient's stereoscopic vision.
A certain number of these examinations can be carried out without the physician's actual presence, with the help of the application we present. People concerned by these types of tests are very numerous, especially drivers who will have to control their visual acuity in the context of the new French highway code. We can imagine that telemedicine sites could be optical stores, motoring schools, medical centers,… In the future, one can also imagine making this test available in private homes, using the Internet. This new organization will reduce the cost of multiple eye-testings, for a simple control test does not require the physician's presence, except when the test is negative and therefore requires a further examination, which is very important for the French public health services. It should be observed that remote tests are legal only if they are validated by ophthalmologists. Two methods can be considered: the expert method and the automatic method.
In the expert method, the examination is assisted by the physician located in a medical center and contacted by the patient. He communicates with him directly via the Internet. The physician sends to the patient's station some test pictures, the messages and the questions, and the patient immediately answers him. Thus, the physician has the results of the complete medical examination and can make his diagnosis.
In the automatic method, the examination is carried out directly by a fully automated system, which means that the verification is automatic and computer assisted. The patient answers the questions asked by the system, which then processes the results and asks new questions, if necessary.
So the project presented here is only a small part of a complex system that should include several applications, like, for example, the evaluation of the vision of the colours, the vision of contrast, the visual field or the patient's stereoscopic vision.
Our work on the automatic measurement of visual acuity is presented in this paper, and a system is under development by a research team of physicians, engineers, professors and students. In Section 2 we will recall some definitions of visual acuity and we will present the existing eye-testing methods used by physicians. We will also present the client server architecture developed for our survey (the Internet application is not developed yet and will be later considered). In Section 3, we will then sum up the interest of the fuzzy sets theory for the modelization of the uncertainty and the application of this theory to the medical process. In Section 4 we will describe the algorithm used to read the patient's answers and Section 5 discusses this algorithm within the frame of the possibility theory. In Section 6, we will present some results obtained with this method. Finally, conclusions are drawn in Section 7.
Section snippets
Fuzzy sets and measurement of fuzziness
The process of selecting the necessary information to present a decision rule must lead here to the correct estimate of visual acuity. The present work presents an application of the theory of fuzzy sets to evaluate this number, replacing a human reasoning (the physician's). The terms fuzziness index [9] and entropy [10] provide the measurement of fuzziness in a set and are used to define the degree of uncertainty of the present medical advice. These data make it possible to define an index of
Algorithm of management of the patient's answers
The developed algorithm is based on a logic of management of the answers which has to achieve the reduction of the zone of uncertainty after every test. For every new displayed picture, the patient gives a seen answer or a not seen answer that can or cannot correspond to the reality. As long as these answers are strict, we do not take the patient's doubt into account. The calculation is based on the fact that if the patient recognizes an object of a certain size, one assumes that he can also
Interpretation of the algorithm with the possibility theory
The proposed algorithm results from a heuristic survey of the problem to be treated. In order to be able to complete the research in this domain, it is necessary to define the theoretical foundations that underlie this algorithm. We tried, therefore, to make an interpretation of it with the theory which seemed the most adapted to the problem treated: the possibility theory.
The whole continuous set R of the sizes of x letters must be classified in two classes of . These two
Results and discussion
The results are easier to analyze by the ophthalmologist if we display along the x-axis the patient's visual acuity instead of the size of the letters. It should be noted that the acuity is inversely proportional to the size of the letters. This is why, in practice, we indicate the values of acuity on the horizontal axis and the degree of membership μA(x) on the vertical axis.
We now present an example in which a patient makes intentional mistakes. The working conditions are the following:
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screen
Conclusion
In the present work, we have shown a possible application to measure visual acuity by fuzzy logic.
The results present the quality of the proposed algorithm. By comparison with the conventional methods of eye testing, this fuzzy approach limits the effects of false answers and the number of tests (the fuzzy method always converges in about 10 tests, where the conventional method converges in more numerous tests (>10)). Whether these false answers are intentional or not, the membership function μA
Acknowledgements
The authors would like thank to S. Target for his advice, Pr. J.C. Hache's department of ophthalmology in the Centre Hospitalier Régional de Lille for its assistance and ASNAV (ASsociation NAtionale pour la Vue). We also want to thank the anonymous reviewers for their helpful remarks.
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