Optical and Electronic Expert System for Diagnosing Eye Pathology in Glaucoma

Abstract

For the first time, mathematical models for evaluating biomedical images were obtained using fuzzy set methods on the basis of expert knowledge bases, thus making it possible to carry out complex qualitative diagnostics and increase the reliability and efficiency of diagnosis. A methodology for analyzing biomedical images was formed based on the fuzzy set apparatus, which allowed a fuller assessment of the level of disease for glaucoma patients. Aspects of the practical implementation of the optical–electronic system for biomedical information processing were considered. An algorithm and an optical–electronic system for biomedical image analysis are proposed, and they can be used to increase the informativeness and reliability in the diagnosis of eye pathologies and glaucoma in particular.

1. Introduction

The modern level of knowledge in the field of information technologies allows creating quite effective tools for optimizing the processes of medical diagnosis and treatment, in particular, the diagnosis of glaucoma. However, in order to increase the effectiveness and reliability of support for decision-making about the level of pathology in the diagnosis of glaucoma, it is necessary to create automated systems based on a wide range of modern mathematical and optimization methods, systems theory and system analysis, in particular, the use of the fuzzy set method. Today, this problem in medical practice is quite non-trivial, since the factor of subjectivity enters the decision-making process, which leads to a decrease in the reliability of the established diagnosis. An early diagnosis of eye pathologies is the most important stage in the treatment of eye diseases, in particular, fundus, glaucoma, etc. At the same time, inaccurate vision test results can lead to the appointment of inappropriate treatment, and instead of helping and restoring vision, it will only worsen it.

When experts form a reference sample of images of fundi, conflicts may arise due to ambiguities in the images. Practice has shown that even the same expert can differently assess whether the same image displays glaucoma or not at different times (after a week, a month, etc.). It is natural that different experts often have different opinions about the presence of glaucoma in images of fundi. Therefore, when forming a knowledge base using an expert system, it is necessary to provide procedures for assessing the convergence and reproducibility of the results of creating a reference sample [1,2,3].

The result of the work on an optical–electronic expert system is a conclusion about the presence of glaucoma of a certain type with an indication of its probability. The latter requires the creation of a representative reference sample of images of a necessary volume [4,5,6].

A feature of the considered expert system is that, along with the knowledge of experts accumulated in it, a database is created based on the results of measuring quantitative features through automated image processing. Next, a conclusion is formed based on the assessment of the probability of the considered image exhibiting a type of glaucoma belonging to a list of possible types [2,7,8,9].

Since conclusions based on the results of drug research using expert systems are formed based on the results of computer image processing, it is necessary to consider the factors affecting the accuracy of the measurements performed in the system [10,11,12,13].

For the considered task of automating the analysis of fundi, in the first stage, image improvement procedures are performed; these are associated with the suppression of image-distorting factors (filtering of obstacles, elimination of lighting irregularities, etc.). In the description stage, the characteristic features of an object are calculated; on this basis, in the third stage, the object is assigned to a class. The key to these three stages is the description stage. The recognition result depends on the choice of features and their informativeness (the ability to attribute an object to a class based on the value of the features). We can distinguish two groups of factors that influence the recognition result; the first group is that of the properties of the object itself (images of fundi are very diverse), while the second group is that of the image formation conditions (sensor noise, uneven illumination of the object, etc.) [14,15].

The purpose of this work is to develop a conceptual model of an optical–electronic expert system for the diagnosis of glaucoma using computer processing methods, as well as to analyze the influences of factors on the results of fundus image recognition [16,17,18].

2. Methods

The proposed approach to the recognition of images of fundi is based on the use of the knowledge of specialists in the field of ophthalmology and consists of creating an expert system for the diagnosis of glaucoma. The basis of the system is a reference sample of digital images, the description of which is stored in the knowledge base. An important component of the system is the analytical subsystem, which includes many rules by which decisions are made (Figure 1) [19,20,21,22].

There are factors that have a dominant influence on the correctness of image recognition. As a result of the research conducted here, several factors that had the most significant impacts on the accuracy of the measurement results were identified, and they were divided into three groups based on the type of source (instrumental, methodical, subjective user errors).

For the considered system, instrumental factors can be classified into two groups; the first is that of factors that are due to physical processes in the equipment used, while the second is that of factors that are due to the influence of external conditions. The first group of instrumental factors includes the noise of the image sensor, color distortions of the camera, brightness distortions, diffraction effects of the optical system, uneven spectral characteristics of the illuminator in the ophthalmoscope, uneven illumination of the drug in the field of view of the camera, etc. The factors of the second group include factors determined by the external conditions of the system’s application [23,24,25].

So, for example, an image registered in the system can be affected by factors such as the presence of bright external lighting (sunlight), which can decrease the contrast of the image. In addition, the external factors include surface vibration (this can lead to image distortion when using large exposures) [26,27].

First, the methodological factors include the measurement model and mathematical methods of image processing that are implemented in the system software, as well as the discretization and quantization operations that are carried out when forming a digital image.

A group of factors that depend on the user is related to the setting of the ophthalmoscope (the choice of the lens, the position of the condenser, field, and aperture diaphragm, the voltage of the lamp, and light flux correction filters, position of the lens focus). Along with these, this group includes factors related to the selection of the field for research and the positioning of the research object in the field of view of the camera, as well as factors that depend on the user in the interactive mode of image processing (when the processing parameters are specified by the user when implementing the processing in the application software).

Related Work

Many authors have created models for the diagnosis and classification of glaucoma using a variety of research approaches and computer programs. These methods have led to the development of several research models. Most of these models include several layers of performance analysis using deep learning. Many similarities between retinal disease and glaucoma make it difficult to distinguish between them. The authors used such parameters as intraocular pressure, field of vision, excavation diameter to OD diameter ratio, excavation area to OD area ratio, excavation volume to OD volume ratio, excavation area, excavation volume, area neuroretinal belt, volume of the neuroretinal belt, average thickness of the nerve fiber layer along the edge of the disc, cross-sectional area of the nerve fiber layer along the edge of the disc.

In the past, glaucoma could be identified from these digital recordings of retinal images. This strategy has been used in the vast majority of clinical trials, making it the most commonly used technique.

The image classification method was used to analyze the data and organize things into categories. This project required numerical analysis of the image filled correctly. In order to finish the study on time, the information needs to be entered in different groups, such as “normal” and “glaucoma”. They used the U-Net segmentation technique to accurately identify and segment the optic cup in the retinal fundus photographs they examined.

A detailed analysis of the methods used today to diagnose glaucoma is presented in the work of the authors: Kashyap, R.; Nair, R.; Gangadharan, S.M.P.; Botto-Tobar, M.; Farooq, S.; and Rizwan [28].

It should be noted that the CNN technique for the diagnosis of glaucoma involves combining the results of two different types of measurements, namely temporal and geographical data. Because they did it this way, they could use both time and place data. Thanks to these characteristics, it was possible to make a reliable diagnosis of the condition of the eye (on the basis of a static structural system).

3. Recommendations for the Implementation of the Optical–Electronic Expert System for the Proceeding of Images of the Retina of the Eye

To implement the tasks, the architecture of the optical–electronic expert system shown in Figure 2 was implemented.

The user receives the data to be processed as a result of diagnostics based on a modern fundus camera. An interface for entering information and its pre-processing has been developed, which allows you to process images and accurately distinguish pathological zones.

In the future, the received processed image must be recorded in the knowledge base replenishment block, for the sake of correct interpretation when the dynamics of progress or regression of this or that pathology is carried out.

The block of formation of knowledge bases is responsible for the preservation of all previously obtained data and existing standards regarding the norms and pathologies of the fundus of the eye.

4. Realization of Expert System for Diagnosing Glaucoma Based on Fuzzy Logic

A conceptual model of an expert system for diagnosing glaucoma is proposed to reduce the ambiguity of the interpretation of research objects. Factors affecting the correctness of the recognition of complex objects (images of fundi) using an expert system based on methods of computer ophthalmoscopy were considered (

Table 1. Formation of an expert base in the diagnosis of glaucoma.

Severity of Pathology	Intraocular Pressure, mm Hg, X1	Field of Vision, X2	Ratio of Excavation Diameter to OD Diameter, X3	Ratio of Excavation Area to OD Area, X4	Ratio of Excavation Volume to OD Volume, X5	Excavation Area, X6	Excavation Volume, X7	Area of the Neuroretinal Band, X8	Volume of the Neuro- retinal Girdle, X9	Average Thickness of the Nerve Fiber Layer along the Edge of the Disc, X10	Cross-Sectional Area of the Nerve Fiber Layer Along the Edge of the Disc, X11
d1—normal	15–21	60°	0.009–0.635	0–0.42	0–1.1	0–0.95	0–0.295	1.097–2.14	0.165–0.7	0.13–0.4	0.603–2.03
d2—stage I of glaucoma	15–21	50°	0.55–0.8	0.3–0.62	0.2–2.6	0.55–1.77	0.04–0.52	0.79–2.04	0.12–0.53	0.06–0.34	0.26–1.26
d3—stage II of glaucoma	31	45°–35°	0.5–0.92	0.25–0.82	0.2–8	0.7–2.04	0.1–0.74	0.32–2.04	0.07–0.49	0.02–0.22	0.1–1.11
d4—stage III of glaucoma	33	<35°	0.65–1.0	0.4–0.97	1.0–35	0.82–2.47	0.15–1.35	0.217–2.09	0.025–0.262	−0.12–0.26	−0.6–1.5

Explanation of Table 1. To diagnose glaucoma, we take the following indicators into account: X1—intraocular pressure (mm Hg). X2—field of vision. X3—the ratio of the diameter of the excavation to the diameter of the DZN. X4—the ratio of the excavation area to the area of the DZN. X5—the ratio of the volume of the excavation to the volume of the DZN. X6—excavation area. X7—excavation volume. X8—neuroretinal strip area. X9—volume of the neuroretinal strip. X10—the average thickness of the layer of nerve fibers along the edge of the disc. X11—cross-sectional area of the layer of nerve fibers along the edge of the disc.

).

Mathematical equations for classification of the level of pathology are formed from the data in Table 1 (Rotshtein A. Design and Tuning of Fussy IF–THEN Vuly for Medical Didicol Diagnosis).

For d₁,

$${\mu }^{d_1}(x_1÷x_{11})={\mu }^H(x_1)\cdot {\mu }^B(x_2)\cdot {\mu }^H(x_3)\cdot {\mu }^H(x_4)\cdot {\mu }^H(x_5)\cdot$$

$$\cdot {\mu }^H(x_6)\cdot {\mu }^H(x_7)\cdot {\mu }^{BC}(x_8)\cdot {\mu }^{HC}(x_9)\cdot {\mu }^C(x_{10})\cdot {\mu }^C(x_{11})\vee$$

$$\vee {\mu }^{HC}(x_1)\cdot {\mu }^B(x_2)\cdot {\mu }^{HC}(x_3)\cdot {\mu }^{HC}(x_4)\cdot {\mu }^H(x_5)\cdot$$

$$\cdot {\mu }^{HC}(x_6)\cdot {\mu }^{HC}(x_7)\cdot {\mu }^B(x_8)\cdot {\mu }^C(x_9)\cdot {\mu }^{BC}(x_{10})\cdot {\mu }^{BC}(x_{11})\vee$$

$$\vee {\mu }^{HC}(x_1)\cdot {\mu }^B(x_2)\cdot {\mu }^C(x_3)\cdot {\mu }^C(x_4)\cdot {\mu }^H(x_5)\cdot$$

$$\cdot {\mu }^C(x_6)\cdot {\mu }^{HC}(x_7)\cdot {\mu }^B(x_8)\cdot {\mu }^{BC}(x_9)\cdot {\mu }^B(x_{10})\cdot {\mu }^B(x_{11})\vee$$

$$\vee {\mu }^{HC}(x_1)\cdot {\mu }^B(x_2)\cdot {\mu }^{BC}(x_3)\cdot {\mu }^C(x_4)\cdot {\mu }^H(x_5)\cdot$$

$$\cdot {\mu }^C(x_6)\cdot {\mu }^{HC}(x_7)\cdot {\mu }^B(x_8)\cdot {\mu }^B(x_9)\cdot {\mu }^B(x_{10})\cdot {\mu }^B(x_{11})$$

For d₂,

$${\mu }^{d_2}(x_1÷x_{11})={\mu }^H(x_1)\cdot {\mu }^C(x_2)\cdot {\mu }^C(x_3)\cdot {\mu }^{HC}(x_4)\cdot {\mu }^H(x_5)\cdot$$

$$\cdot {\mu }^{HC}(x_6)\cdot {\mu }^H(x_7)\cdot {\mu }^C(x_8)\cdot {\mu }^{HC}(x_9)\cdot {\mu }^{HC}(x_{10})\cdot {\mu }^{HC}(x_{11})\vee$$

$$\vee {\mu }^{HC}(x_1)\cdot {\mu }^C(x_2)\cdot {\mu }^{BC}(x_3)\cdot {\mu }^C(x_4)\cdot {\mu }^H(x_5)\cdot$$

$$\cdot {\mu }^C(x_6)\cdot {\mu }^{HC}(x_7)\cdot {\mu }^{BC}(x_8)\cdot {\mu }^C(x_9)\cdot {\mu }^C(x_{10})\cdot {\mu }^C(x_{11})\vee$$

$$\vee {\mu }^{HC}(x_1)\cdot {\mu }^C(x_2)\cdot {\mu }^{BC}(x_3)\cdot {\mu }^{BC}(x_4)\cdot {\mu }^H(x_5)\cdot$$

$$\cdot {\mu }^{BC}(x_6)\cdot {\mu }^C(x_7)\cdot {\mu }^B(x_8)\cdot {\mu }^{BC}(x_9)\cdot {\mu }^{BC}(x_{10})\cdot {\mu }^{BC}(x_{11})\vee$$

$$\vee {\mu }^{HC}(x_1)\cdot {\mu }^C(x_2)\cdot {\mu }^{BC}(x_3)\cdot {\mu }^{BC}(x_4)\cdot {\mu }^H(x_5)\cdot$$

$$\cdot {\mu }^{BC}(x_6)\cdot {\mu }^C(x_7)\cdot {\mu }^B(x_8)\cdot {\mu }^{BC}(x_9)\cdot {\mu }^B(x_{10})\cdot {\mu }^{BC}(x_{11})$$

For d₃,

$${\mu }^{d_3}(x_1÷x_{11})={\mu }^B(x_1)\cdot {\mu }^H(x_2)\cdot {\mu }^C(x_3)\cdot {\mu }^{HC}(x_4)\cdot {\mu }^H(x_5)\cdot$$

$$\cdot {\mu }^{HC}(x_6)\cdot {\mu }^H(x_7)\cdot {\mu }^H(x_8)\cdot {\mu }^{HC}(x_9)\cdot {\mu }^{HC}(x_{10})\cdot {\mu }^{HC}(x_{11})\vee$$

$$\vee {\mu }^B(x_1)\cdot {\mu }^{HC}(x_2)\cdot {\mu }^{BC}(x_3)\cdot {\mu }^C(x_4)\cdot {\mu }^{HC}(x_5)\cdot$$

$$\cdot {\mu }^C(x_6)\cdot {\mu }^{HC}(x_7)\cdot {\mu }^{HC}(x_8)\cdot {\mu }^C(x_9)\cdot {\mu }^C(x_{10})\cdot {\mu }^C(x_{11})\vee$$

$$\vee {\mu }^B(x_1)\cdot {\mu }^C(x_2)\cdot {\mu }^B(x_3)\cdot {\mu }^{BC}(x_4)\cdot {\mu }^{HC}(x_5)\cdot$$

$$\cdot {\mu }^{BC}(x_6)\cdot {\mu }^C(x_7)\cdot {\mu }^C(x_8)\cdot {\mu }^{BC}(x_9)\cdot {\mu }^{BC}(x_{10})\cdot {\mu }^{BC}(x_{11})\vee$$

$$\vee {\mu }^B(x_1)\cdot {\mu }^C(x_2)\cdot {\mu }^B(x_3)\cdot {\mu }^{BC}(x_4)\cdot {\mu }^{HC}(x_5)\cdot$$

$$\cdot {\mu }^{BC}(x_6)\cdot {\mu }^{BC}(x_7)\cdot {\mu }^{BC}(x_8)\cdot {\mu }^{BC}(x_9)\cdot {\mu }^{BC}(x_{10})\cdot {\mu }^{BC}(x_{11})\vee$$

$$\vee {\mu }^B(x_1)\cdot {\mu }^C(x_2)\cdot {\mu }^B(x_3)\cdot {\mu }^{BC}(x_4)\cdot {\mu }^{HC}(x_5)\cdot$$

$$\cdot {\mu }^{BC}(x_6)\cdot {\mu }^{BC}(x_7)\cdot {\mu }^B(x_8)\cdot {\mu }^{BC}(x_9)\cdot {\mu }^{BC}(x_{10})\cdot {\mu }^{BC}(x_{11})$$

For d₄,

$${\mu }^{d_4}(x_1÷x_{11})={\mu }^B(x_1)\cdot {\mu }^H(x_2)\cdot {\mu }^{BC}(x_3)\cdot {\mu }^C(x_4)\cdot {\mu }^H(x_5)\cdot$$

$$\cdot {\mu }^{HC}(x_6)\cdot {\mu }^H(x_7)\cdot {\mu }^H(x_8)\cdot {\mu }^H(x_9)\cdot {\mu }^H(x_{10})\cdot {\mu }^H(x_{11})\vee$$

$$\vee {\mu }^B(x_1)\cdot {\mu }^H(x_2)\cdot {\mu }^B(x_3)\cdot {\mu }^{BC}(x_4)\cdot {\mu }^{HC}(x_5)\cdot$$

$$\cdot {\mu }^C(x_6)\cdot {\mu }^{HC}(x_7)\cdot {\mu }^{HC}(x_8)\cdot {\mu }^{HC}(x_9)\cdot {\mu }^{HC}(x_{10})\cdot {\mu }^{HC}(x_{11})\vee$$

$$\vee {\mu }^B(x_1)\cdot {\mu }^H(x_2)\cdot {\mu }^B(x_3)\cdot {\mu }^B(x_4)\cdot {\mu }^C(x_5)\cdot$$

$$\cdot {\mu }^{BC}(x_6)\cdot {\mu }^C(x_7)\cdot {\mu }^C(x_8)\cdot {\mu }^C(x_9)\cdot {\mu }^C(x_{10})\cdot {\mu }^C(x_{11})\vee$$

$$\vee {\mu }^B(x_1)\cdot {\mu }^H(x_2)\cdot {\mu }^B(x_3)\cdot {\mu }^B(x_4)\cdot {\mu }^{BC}(x_5)\cdot$$

$$\cdot {\mu }^B(x_6)\cdot {\mu }^{BC}(x_7)\cdot {\mu }^{BC}(x_8)\cdot {\mu }^C(x_9)\cdot {\mu }^{BC}(x_{10})\cdot {\mu }^{BC}(x_{11})\vee$$

$$\vee {\mu }^B(x_1)\cdot {\mu }^H(x_2)\cdot {\mu }^B(x_3)\cdot {\mu }^B(x_4)\cdot {\mu }^B(x_5)\cdot$$

$$\cdot {\mu }^B(x_6)\cdot {\mu }^B(x_7)\cdot {\mu }^B(x_8)\cdot {\mu }^C(x_9)\cdot {\mu }^{BC}(x_{10})\cdot {\mu }^{BC}(x_{11})$$

5. Algorithmic Software Implementation for Processing Biomedical Images

During the analysis of the characteristics of a fundus, the reliability of the final assessment of the images therein should be increased by using expert methods. The proposed approach to the recognition of images of fundi is based on the use of the knowledge of specialists in the field of ophthalmology and consists of creating an expert system for the diagnosis of glaucoma. The basis of this system is a reference sample of digital images, the description of which is stored in a knowledge base. An important component of the system is the analytical subsystem, which includes many rules by which decisions are made.

To obtain a diagnosis with the help of an expert database, we suggest using elements of fuzzy logic. We built a model on the basis of actual data (Table 1).

Using an algorithm from a processing method based on the fuzzy logic apparatus, we obtain the following.

When entering the data from Table 1, we obtain the following (Figure 3).

When saving the data, i.e., entering the lower and upper values, we can enter the patient’s data.

Having obtained the result, we can conclude that the patient has glaucoma of the third degree (Figure 4).

6. Physical Modeling of the Optical–Electronic System for Researching Pathologies of Fundi

Physical modeling of the optical–electronic system for researching pathologies of fundi performed for the formation of an optical–electronic system for entering biomedical information.

The optical–electronic system for obtaining images of the retina of an eye is related to medicine, namely, to devices for examining fundi, and it can be used in ophthalmology to conduct medical and biological research and, specifically, to fix images of retinas. The optical channel is realized as follows.

The radiation flow coming from the radiating surface of the source to the remote illuminating surface can be calculated as follows (1):

$$\Phi =L\cdot S_{soursce}\cdot S_{sq}\cdot {\displaystyle \frac{\cos {\beta }_1\cdot \cos {\beta }_2}{l^2}},$$

(1)

where L is the brightness of the emitting surface; S_source is the area of the radiating surface; S_sq is the area of the illuminating surface; β₁ is the angle between the direction of radiation propagation and the normal to the radiating surface; β₂ is the angle between the direction of radiation propagation and the normal to the illuminating surface; and l is the distance between the surfaces.

If the lighting system directs radiation into the eye through a pupil area with an area Ssource, then this area can be considered as a light-emitting surface, the brightness of which L_laser due to the transition of light rays from the air to the eye is related to the brightness of the source—the LED L_diode—according to the following Expressions (1) and (2):

$$L_{laser}=n_{eye}^2\cdot L_{diode},$$

(2)

where N_eye is the average refractive index of eye tissues.

Taking Expression (2) and the transmission coefficient of the optical system of the eye τ_eye into account, Expression (1) for the light flux falling on the retina can then be written in the following form:

$$F={\tau }_{eye}\cdot n_{eye}^2\cdot L_{diode}\cdot S_{source}^{\prime }\cdot S_{{eye}^{\prime }}\cdot {\displaystyle \frac{\cos {\beta }_1\cdot \cos {\beta }_2}{l_{eye}^2}}$$

(3)

where S_eye′ is the area of the retina; and l_eye is the distance between the pupil and the retina.

When the light flux spreads along the optical axis of the eye, which is assumed to be perpendicular to the planes of the pupil and retina (β₁ = β₂ = 0), the illumination of the retina will be

$$E_{okɑ}={\displaystyle \frac{F}{S_{sq}}}={\displaystyle \frac{{\tau }_{eye}\cdot n_{eye}^2\cdot L_{diode}\cdot S_{source}^{\prime }}{l_{eye}^2}}$$

(4)

Expression (4) is true for the illumination of a retinal point lying on the optical axis of the eye. However, since the fundus is a sphere and due to the multiple reflections of light rays inside the eye, it can be assumed that the illumination of the entire retina is uniform and is determined by Expression (4).

A uniformly illuminated retina, diffusely reflecting the light stream falling on it, represents a secondary light source, the brightness of which will be equal to

$$L_{eye}={\displaystyle \frac{\rho \cdot E_{eye}}{\pi }}={\displaystyle \frac{\rho \cdot {\tau }_{eye}\cdot n_{eye}^2\cdot L_{diode}\cdot S_{source}^{\prime }}{\pi \cdot l_{eye}^2}}$$

(5)

where ρ is the diffusion reflection coefficient.

Illumination of the retinal image takes place on the photomatrix, which is built with the following optical system:

$$E^{\prime }={\displaystyle \frac{{\tau }_{os}\cdot \pi \cdot L_c}{4}}\cdot {\left({\displaystyle \frac{n^{\prime }}{n}}\right)}^2\cdot {\left({\displaystyle \frac{D}{f^{\prime }}}\right)}^2\cdot {\displaystyle \frac{{\beta }_p^2}{{({\beta }_p-\beta )}^2}}$$

(6)

where τ_os is the transmission coefficient of the optical system; n′ is the refractive index of the medium in the image space (n′ = 1); n is the index of refraction of the medium in the space of objects (n = noka); D is the diameter of the entrance pupil of the optical system; f′ is the focal length of the optical system; β_p is the linear increase in the optical system in the pupils; and β is the linear increase in the optical system.

Substituting (5) into (6) and assuming a linear increase in the pupils β_p = 1, for the illumination of the retinal image on the photomatrix, we obtain

$$E^{\prime }={\displaystyle \frac{{\tau }_{oc}\cdot {\tau }_{okɑ}\cdot \rho \cdot L_{c𝜕}\cdot S_{𝜕\mathcal{ж}}^{\prime }}{4\cdot l_{okɑ}^2}}\cdot {\left({\displaystyle \frac{D}{f^{\prime }}}\right)}^2\cdot {\displaystyle \frac{1}{{(1-\beta )}^2}}$$

(7)

Let us assume that τ_eye = 0.5, τ_os = 0.9, ρ = 0.2, l_eye = 24, and diameter = 24 mm. The maximum brightness of the light source that can be transmitted when directly observed is 7500 cd/m². So that patients would not feel discomfort, as an illuminator, we chose an LED; Lsd = 7000 cd/m². Let us also assume that the projection of the source onto the pupil of the eye occupies 50% of its area. In this case, with a pupil diameter of 6 mm, S_d.pup = 14.13 mm. To perceive the image, we used the 6.6 Megapixel CMOS photomatrix NOII4SM6600A, the main indicators of which are as follows:

Dimensional capacity	2210 × 3002
Optical format, inches	1
Range of spectral sensitivity, nm, hm	400…1000
Apparent sensitivity, V/(lx/s)	2.01
Dark signal, mV/s	3.37

The required linear increase β in the optical system can be determined by the ratio that corresponds to the condition under which the retinal image occupies the largest part of the photomatrix area:

$$\beta ={\displaystyle \frac{H_{phm}}{D_c}}$$

(8)

where H_phm is the height of the photomatrix; and D_retina is the diameter of the retina.

The optical matrix format of 1 inch corresponds to the size of 12.8 × 9.6 mm. The diameter of the human retina is 22 mm. Then,

$$\beta ={\displaystyle \frac{9.6}{22}}=0.436$$

By substituting numerical values for the definition in Expression (7), we obtain

$$E^{\prime }={\displaystyle \frac{0.9\cdot 0.5\cdot 0.2\cdot 7000\cdot 14.13}{4\cdot {24}^2}}\cdot {\left({\displaystyle \frac{D}{f^{\prime }}}\right)}^2\cdot {\displaystyle \frac{1}{{(1-0.436)}^2}}=12.146\cdot {\left({\displaystyle \frac{D}{f^{\prime }}}\right)}^2$$

(9)

To carry out further calculations, we will determine the illumination of the photomatrix E′ at which the value of the useful output signal will be comparable to the dark one. The minimum illumination of the image at which it is indistinguishable from the background noise is found using the sensitivity of the photomatrix and the value of the dark signal:

$$E_0={\displaystyle \frac{3.37\cdot {10}^{-3}}{2.01}}=1.677\cdot {10}^{-3}$$

To obtain a good image of the retina, the illumination of the photomatrix must be at least 10 times higher than this value. Therefore,

$$E^{\prime }=0.01677 \left(\mathrm{Lx}\right)$$

Then, using Expression (9) for the geometric luminous intensity of the optical system, we have

$${\left({\displaystyle \frac{D}{f^{\prime }}}\right)}^2={\displaystyle \frac{0.01677}{12.146}}=1.38\cdot {10}^{-3}$$

(10)

In order to use the entire field of the optical system, the entrance pupil must be aligned with the plane of the eye pupil. In this case, the field aperture will be the frame of the photomatrix, and with the linear magnification selected in accordance with Expression (8), the image of the entire retina will be formed on the photomatrix. The diameter of the entrance pupil of the optical system D is chosen to be equal to 3 mm. As a result, the area of the entrance pupil of the optical system is equal to 7.065 mm², which is 25% of the area of the pupil of the eye with a pupil diameter of 6 mm. Then, from Expression (10), for the focal length of the optical system, we obtain

$$f^{\prime }=\sqrt{{\displaystyle \frac{9}{1.38\cdot {10}^{-3}}}}=80.76 \left(\mathrm{mm}\right)$$

When calculating the focal length of the optical system, the linear increase in the pupils β_p was taken to be equal to 1. This corresponds to the case when the distance −z_p from the front focus of the optical system to the input pupil is equal to the front focal length of the optical system:

$$-z_p=-f=-80.76 \left(\mathrm{mm}\right)$$

The distance from the front focus to the retina is equal to

$$-z=-z_p-l_{okɑ}=-80.76-24=-104.76 \left(\mathrm{mm}\right)$$

The distance z′ from the back focus to the retinal image formed in the photomatrix plane is determined using the linear magnification of the optical system β:

$$z^{\prime }=\beta \cdot f^{\prime }=0.436\cdot 80.76=35.21 \left(\mathrm{mm}\right)$$

7. Evaluation of Metrological Indicators

For most medical and biological studies, the degree of probability of an error-free forecast equal to 95% is considered sufficient, and the number of cases of the general population in which deviations from the patterns established during a sample study may be observed should not exceed 5%. In a number of studies related, for example, to the use of highly toxic substances, vaccines, and surgical treatments, as a result of which serious diseases, complications, and fatal consequences are possible, the degree of probability p = 99.1% is used, i.e., in no more than in 1% of cases of the general population, deviations from the regularities established in the sample population are possible.

The given degree of probability (p) of an error-free forecast corresponds to a certain value of the criterion t substituted into the formula, which also depends on the number of observations.

When n > 30, the degree of probability of an error-free forecast (p = 99.1%) corresponds to the value of t = 3, and when p = 97.2%, this corresponds to a value of t = 2.

When n < 30, the value of t at the appropriate degree of probability of an error-free forecast is determined according to a special table (N.A. Plokhinsky).

We determined the error of representativeness (mp) and the confidence limits of the relative indicator of the general population (R_gen) in relation to the table of results obtained through diagnosis by an ophthalmologist and with the help of an expert database (See

Table 2. Comparison of the diagnoses obtained using different methods (p < 0.05).

Diagnosis by an Ophthalmologist			The Diagnosis was Obtained with the Help of an Expert Base
The Number of Patients with a Certain Stage	Stages of Glaucoma	Percentage of the Total Quantity, %	The Number of Patients with a Certain Stage	Stages of Glaucoma	Percentage of the Total Quantity, %
54	I	43	51	I	40
18	II	14	15	II	12
54	III	43	60	III	48

).

A group of glaucoma patients consisting of 126 people aged 50–65 years but with different stages was used.

The representativeness error of the relative indicators was determined according to the diagnoses of an ophthalmologist.

$$m_{1{\displaystyle \mathrm{B}}}=\sqrt{{\displaystyle \frac{43\times (100-43)}{42}}}=7.64\%$$

$$m_{2{\displaystyle \mathrm{B}}}=\sqrt{{\displaystyle \frac{14\times (100-14)}{42}}}=5.35\%$$

$$m_{3{\displaystyle \mathrm{B}}}=\sqrt{{\displaystyle \frac{43\times (100-43)}{42}}}=7.64\%$$

The error of representativeness of the relative indicators was determined according to the diagnoses obtained with the help of the expert database.

$$m_{1\mathrm{c}}=\sqrt{{\displaystyle \frac{40\times (100-40)}{42}}}=7.56\%$$

$$m_{2\mathrm{c}}=\sqrt{{\displaystyle \frac{12\times (100-12)}{42}}}=5.01\%$$

$$m_{3c}=\sqrt{{\displaystyle \frac{48\times (100-48)}{42}}}=7.71\%$$

The confidence limits of the average values of the general population (R_gen) were calculated as follows:

-

It was necessary to set the degree of probability of an error-free forecast (p = 95%).

-

At a given degree of probability and with a number of observations of more than 30, the value of the criterion t was equal to 2 (t = 2).

Then, ${\mathrm{P}}_{1{\displaystyle \mathrm{B}}}$ = P_choice ± tm = 43% ± 2 × 7.64 = 43% ± 15.28%.

Then, ${\mathrm{P}}_{2{\displaystyle \mathrm{B}}}$ = P_choice ± tm = 14% ± 2 × 5.35 = 14% ± 10.70%.

Then, ${\mathrm{P}}_{3{\displaystyle \mathrm{B}}}$ = P_choice ± tm = 43% ± 2 × 7.64 = 43% ± 15.28%.

Then, P_1c = P_choice ± tm = 40% ± 2 × 7.56 = 40% ± 15.12%.

Then, P_2c = P_choice ± tm = 12% ± 2 × 5.01 = 12% ± 10.02%.

Then, P_3c = P_choice ± tm = 48% ± 2 × 7.71 = 48% ± 15.42%.

Taking the results of the calculation of the confidence limits of the average value of the general population (R_gen) into account, we established with the probability of an error-free forecast (p = 95%) that the frequency of detection of stage I glaucoma at the age of 50–65 years was in the range from 27.72% to 58.28% of cases (diagnosis by an ophthalmologist) and from 24.88% to 55.12% (diagnosis obtained using an expert database). The frequency of detection of stage II glaucoma at the age of 50–65 years ranged from 3.30% to 24.70% of cases (diagnosis by an ophthalmologist) and from 1.98% to 22.02% (diagnosis obtained with an expert database). The frequency of detection of stage III glaucoma at the age of 50–65 years ranged from 27.72% to 58.28% of cases (diagnosis by an ophthalmologist) and from 32.58% to 63.42% (diagnosis obtained with an expert database).

The main purpose of this study is to diagnose glaucoma and to assess whether the disease has affected people. The model can generate either positive or negative results depending on whether the glaucoma disease impact assessment is achieved.

The ability of a model to correctly predict the behavior of a subset is known as its accuracy. Efficiency is calculated using it during the classification process. Its purpose is to give a rough idea of how often both positive and negative changes are needed. In the classification of glaucoma fundus images, it was demonstrated that the training and testing of the proposed model was more accurate than previous models. The results of this study are shown in

Table 3. An analysis of the effectiveness of the accuracy, on the base [28].

№	Models	Training	Testing
1	VGG-19	97.73	95.54
2	Inception ResNet	94.86	91.64
3	ResNet 152v2	97.56	93.21
4	DenseNet169	97.14	95.45
5	U-Net	98.11	96.37
6	CNN	98.82	96.90
7	Proposed Model Fuzzy Logic	99.1	97.2

.

When evaluating a model, its F-measure, accuracy, precision, and specificity are all considered. Inception additional deep learning models, such as ResNet, ResNet 152v4, DenseNet-169, and VGG-19, CNN are now being utilized to analyze Proposed Model Fuzzy Logic classification findings.

For example, in glaucoma fundus image classification, training and testing using the proposed model turned out to be more accurate than other models previously. The results of this study are shown in Figure 5 and Table 3.

Compared to previous methods, this increased training accuracy from an average of 1.09 percent to 3.96 percent. Compared to other considered models, the tests are 97.2 percent accurate, which means a performance gain of 0.3 to 5.56 percent.

In the future, the received data will be processed by blocks of fuzzy logic, which will make it possible, having in its resource the data of the knowledge base and the received image of a specific patient, to conduct an analysis and give a result about this or that disease. This will enable the doctor to make a correct conclusion about the condition of the fundus during the diagnosis of glaucoma.

8. Conclusions

This paper proposes a deep method based on fuzzy sets for glaucoma assessment and prediction. The glaucoma dataset was used to train a glaucoma image analysis learning model. To detect glaucoma, the images were classified using a deep convolutional neural network.

These images of the fundus retina were used to determine whether the patient had glaucoma. The resulting image data were compared to the baseline images of the dataset. The model was used to extract features from segmented images for data processing.

For the first time, mathematical models were obtained for the evaluation of biomedical images using fuzzy set methods on the basis of expert knowledge bases, which made it possible to carry out complex qualitative diagnostics and increase the reliability and efficiency of diagnosis. A methodology for analyzing biomedical images based on the fuzzy set apparatus was formed, which allowed a fuller assessment of the level of disease for glaucoma.

Aspects of the practical implementation of an optical–electronic system of biomedical information processing were considered. An algorithm and an optical–electronic system for biomedical image analysis were proposed, and they were used to increase the informativeness and reliability of the diagnosis of eye pathologies—in particular, glaucoma. Compared to previous methods, this increased training accuracy from an average of 1.09 percent to 3.96 percent. Compared to other considered models, the tests are 97.2 percent accurate, which means a performance gain of 0.3 to 5.56 percent.

On the basis of the developed model and algorithms, a hardware and software implementation was created, and experimental and medical studies of the obtained system indicators were conducted.

Examples of practical applications of the developed optical–electronic system for the analysis of eye pathologies are given. The main practical result is that the expediency and reliability of such an optical–electronic system were practically confirmed.

The results of this study can be generalized to a variety of imaging modalities. The proposed method of transfer of learning has an additional advantage, as it can be applied in various areas of medicine and biology.