ALGORITHMS AND METHODS FOR CALCULATING THE AREA OF A GASTRIC ULCER DEFECT USING MODERN MATHEMATICAL TECHNIQUES

ISSUE 12 Acceptance of papers December, 2025 Acceptance of papers Published monthly Topics economics, technology, social sciences INNOVATION SCIENCE AND TECHNOLOGY t.me/scupus_IST2100 2https://ist-journal.uz 12/2025 t.me/scupus_IST2100 Sharipov Kongiratbay Avezimbetovich, Doctor of Technical Sciences (DSc), Professor Ahmed Aziz Ismail Doctor of Technical Sciences (DSc), Professor (Egypt) Cham Tat Huei, Doctor of Philosophy (PhD), Professor (Malaysia) Asongu Simplice Doctor of Philosophy in Economics (PhD), Cameroon Abdurakhmanova Gulnora Kalandarovna, Doctor of Economic Sciences (DSc), Professor Lee Chin Doctor of Philosophy in Economics (PhD), (Malaysia) Muhammad Imran Sadiq Doctor of Philosophy in Economics (PhD), Professor, Malaysia Rui Dang Doctor of Chemistry (DSc), Professor, China Zahoor Ahmed Doctor of Philosophy in Economics (PhD), Turkey Shujaat Abbas Doctor of Philosophy in Economics (PhD), Russia Tina A Coffelt Doctor of Philosophy in Educational Sciences (PhD), USA Electronic publication, Issue 12. 152 pages. Approved for publication on December, 2025. EDITOR-IN-CHIEF: Mirzaliyev Sanjar Makhamatjon ugli DEPUTY EDITOR-IN-CHIEF: Makhmudov Nosir Makhmudovich DSc., Prof., Academican DEPUTY EDITOR-IN-CHIEF: Ochilov Bobur Bakhtiyor ugli – Senior lecturer at TSUI THE SCIENTIFIC-POPULAR ELECTRONIC JOURNAL "INNOVATION SCIENCE AND TECHNOLOGY" HAS BEEN REGISTERED UNDER THE NUMBER C-5669633 BY THE AGENCY FOR INFORMATION AND MASS COMMUNICATIONS (AOKA) OF THE REPUBLIC OF UZBEKISTAN, EFFECTIVE FROM OCTOBER 9, 2024. The scientific electronic journal “Innovation Science and Technology” has been included in the list of scientific publications recommended for the publication of main scientific results of dissertations for the award of PhD and DSc degrees in economics and technical sciences, in accordance with the Resolution No. 370 of the Presidium of the Higher Attestation Commission of the Republic of Uzbekistan, dated May 8, 2025. CONTACTS Phone: +998 50 737 87 88 Website: https://ist-journal.uz Email: [email protected] Editorial board: CONTENTS SOCIAL, ECONOMIC, SCIENTIFIC, AND TECHNICAL ACADEMIC JOURNAL12/2025 t.me/scupus_IST2100 3 https://ist-journal.uz CONTENTS THE THEORETICAL FOUNDATIONS OF APPLYING TAX INCENTIVES FOR INVESTMENTS DIRECTED TOWARD HUMAN CAPITAL ................................................................................................................................14 Quliyev Begimqul Melikovich ECONOMETRIC MODELS OF CASHLESS SETTLEMENTS AMONG ECONOMIC ENTITIES ...............................21 Ruzimuradov Shuxrat Xusanovich PROSPECTS FOR THE DEVELOPMENT OF TOURISM BRAND MARKETING IN MODERN CONDITIONS (UAE: DUBAI ON THE EXAMPLE OF A CITY) ..........................................................................................26 Ibodova Dilsora Ibodovna CREDIT DEFAULT SWAPS AS A WAY TO HEDGE AGAINST FORTHCOMING FUTURE UNCERTAINTIES IN THE DEBT MARKET OF UZBEKISTAN .........................................................................................31 Abduganiev Abdulaziz Alisher o‘g‘li SHOULD THE REGULATION OF THE E-COMMERCE MARKET IN THE REPUBLIC OF UZBEKISTAN BE CARRIED OUT BY THE NATIONAL AGENCY FOR PERSPECTIVE PROJECTS OR THE CENTRAL BANK? ...........................................................................................................................................................39 Sadikov Aziz Mirsharapovich MECHANISM FOR IMPLEMENTING ARTIFICIAL INTELLIGENCE TECHNOLOGIES IN THE OPERATIONS OF COMMERCIAL BANKS IN UZBEKISTAN .............................................................................................46 Bakhriddin Berdiyarov INNOVATIVE APPROACHES OF SMALL BUSINESSES IN THE INDUSTRY AND CONSTRUCTION SECTORS AND THEIR IMPACT ON EMPLOYMENT...........................................................................................................53 Ergasheva Nigora Abdigapparovna AI-BASED NORMALIZATION METHODOLOGY FOR COLLECTING AND PROCESSING KPI INDICATORS ......................................................................................................................................................................................56 Shuhratov Mamurjon Shuhrat o‘g‘li REFORMS AND PROSPECTS FOR THE DEVELOPMENT OF THE PARTICIPATORY BUDGETING INITIATIVE IN UZBEKISTAN ......................................................................................................................................................63 Khamidov Khabibullo Hikmatulla ugli PROBLEMS OF THE INWARD PROCESSING CUSTOMS REGIME AND WAYS TO ELIMINATE THEM ..........70 Abdullaev Shakhzodbek FINANCIAL ANALYSIS OF SMALL BUSINESS AND PRIVATE ENTREPRENEURSHIP IN CONSTRUCTION ........................................................................................................................................................................74 Musayeva Shoira Azimovna MEASURES TO ENHANCE THE ROLE AND EFFECTIVENESS OF SMALL BUSINESS IN REGIONAL ECONOMIC DEVELOPMENT ....................................................................................................................................................... 80 Ergashev Jamshid Jamoliddinovich THEORETICAL AND METHODOLOGICAL FOUNDATIONS FOR IMPLEMENTING INNOVATIVE TECHNOLOGIES IN EDUCATION ..............................................................................................................................................84 Alijonova Marjonabonu Jaxongir qizi INDIA’S EXPERIENCE IN ENHANCING PUBLIC WELFARE THROUGH THE DEVELOPMENT OF ENTREPRENEURIAL ACTIVITY .........................................................................................................................................88 Aripov Oybek Abdullayevich GREEN STRUCTURAL TRANSFORMATION IN UZBEKISTAN: GREEN FINANCE AND ECO-INNOVATION FOR SUSTAINABLE INDUSTRIAL AND AGRICULTURAL DEVELOPMENT .............................................................. 93 Egamberdiev Khumoyun AGRICULTURAL MANAGEMENT BASED ON INNOVATIVE TECHNOLOGIES AT THE INTERNATIONAL LEVEL: THE EXAMPLE OF UZBEKISTAN ......................................................................................101 Bustonov Komiljon Kumakovich ANALYSIS OF THE FINANCIAL CONDITION OF ENTERPRISES: ASSESSMENT OF EQUITY EFFICIENCY ....................................................................................................................................................................................110 Umurkul Shukhratovich Fayziev CONTENTS SOCIAL, ECONOMIC, SCIENTIFIC, AND TECHNICAL ACADEMIC JOURNAL 12/2025 t.me/scupus_IST2100 4https://ist-journal.uz IMPROVING THE QUALITY OF ECONOMIC GROWTH THROUGH THE TRANSITION TO THE DIGITAL ECONOMY ....................................................................................................................................................118 Mamadaliev Akmaljon МЕТОДЫ И МЕХАНИЗМЫ ИССЛЕДОВАНИЯ ПОТРЕБИТЕЛЬСКОГО ПОВЕДЕНИЯ НА ТУРИСТСКОМ РЫНКЕ ......................................................................................................................................................124 Нурматова Ситора Шавкатовна ANALYSIS OF INNOVATION ACTIVITIES ............................................................................................................................ 133 Alieva Elnara Ametovna METHODS AND MECHANISMS FOR STUDYING CONSUMER BEHAVIOR IN THE TOURISM MARKET ...........................................................................................................................................................................................139 Nurmatova Sitora Shavkatovna ALGORITHMS AND METHODS FOR CALCULATING THE AREA OF A GASTRIC ULCER DEFECT USING MODERN MATHEMATICAL TECHNIQUES ..........................................................................................................145 Yusupov Ibrohimbek XXX, Abdusamatova Munira Sultonbek qizi SOCIAL, ECONOMIC, SCIENTIFIC, AND TECHNICAL ACADEMIC JOURNAL INNOVATION SCIENCE AND TECHNOLOGY t.me/scupus_IST2100 145 https://ist-journal.uz 12/2025 ALGORITHMS AND METHODS FOR CALCULATING THE AREA OF A GASTRIC ULCER DEFECT USING MODERN MATHEMATICAL TECHNIQUES Yusupov Ibrohimbek XXX Associate Professor, Department of Artificial Intelligence Tashkent University of Information Technologies E-mail: [email protected] Abdusamatova Munira Sultonbek qizi First-Year Master’s Student, Graduate Faculty Field of Study: Artificial Intelligence Tashkent University of Information Technologies E-mail: [email protected] Abstract: This study proposes a novel integrated methodology for digital processing of endoscopic video signals, combining automated video analysis, segmentation of pathological structures, and accurate calculation of the gastric ulcer surface area. A multi-stage algorithm is developed, incorporating intelligent extraction of clinically significant frames, contour detection of ulcerated regions using combined gradient operators, and construction of an adaptive spline model for subsequent integral area estimation. Experimental results demonstrate that the proposed approach provides stable and reliable accuracy and can be effectively used as an auxiliary tool to enhance the objectivity of endoscopic diagnostics. Key words: endoscopy, digital video processing, spline approximation, segmentation, gastric ulcer, area calculation. Annotatsiya: Ushbu ishda endoskopik video signallarni raqamli qayta ishlashga asoslangan yangi integrallashgan metodika taklif etiladi. Mazkur yondashuv video ma’lumotlarni avtomatik tahlil qilish, patologik tuzilmalarni segmentasiyalash hamda oshqozon yarasi yuzasining aniq maydonini hisoblash jarayonlarini birlashtiradi. Taklif etilgan ko‘p bosqichli algoritm klinik jihatdan ahamiyatli kadrlarni intellektual ajratish, gradient operatorlari kombinatsiyasi asosida zararlangan hudud konturini aniqlash hamda keyingi integral hisob-kitoblarni amalga oshirish uchun moslashuvchan splayn-modelni qurishni o‘z ichiga oladi. O‘tkazilgan tajriba natijalari ushbu metodikaning barqaror va yuqori aniqlikka ega ekanligini ko‘rsatib, uni endoskopik diagnostika obyektivligini oshirishda samarali yordamchi vosita sifatida qo‘llash mumkinligini tasdiqladi. Kalit so‘zlar: endoskopiya, video signallarni raqamli qayta ishlash, splayn-approksimatsiya, segmentatsiya, oshqozon yarasi, maydonni hisoblash. Аннотация: В данной работе предлагается новая интегрированная методика цифровой обработки эндоскопических видеосигналов, объединяющая автоматический анализ видеоданных, сегментацию патологических структур и точное вычисление площади язвенной поверхности желудка. Разработан многоэтапный алгоритм, включающий интеллектуальное извлечение клинически значимых кадров, контурное выделение поражённого участка с использованием комбинированных градиентных операторов, а также построение адаптивной сплайн-модели для последующего интегрального вычисления площади. Проведённые экспериментальные исследования показали, что предложенная методика обеспечивает высокую и устойчивую точность и может эффективно применяться в качестве вспомогательного инструмента для повышения объективности эндоскопической диагностики. Ключевые слова: эндоскопия, цифровая обработка видео, сплайновая аппроксимация, сегментация, язва желудка, вычисление площади. INTRODUCTION In recent years, there has been a steady increase in interest in digital methods for the analysis of biomedical images, driven by the need to enhance the accuracy and reliability of medical diagnosis of various diseases. Among these, pathologies of the gastrointestinal tract occupy a prominent position, as their prevalence continues to rise. One of the most frequently encountered diseases in this group is peptic ulcer disease of the SOCIAL, ECONOMIC, SCIENTIFIC, AND TECHNICAL ACADEMIC JOURNAL INNOVATION SCIENCE AND TECHNOLOGY t.me/scupus_IST2100 146 https://ist-journal.uz 12/2025 gastric mucosa. Disruption of the integrity of the protective mucosal layer leads to the development of erosive changes, inflammatory processes, and the formation of mucosal defects, which, in the absence of timely and adequate therapy, may progress to more severe clinical forms. Both external and internal factors contribute to the development of peptic ulcer disease, including unhealthy dietary habits, consumption of alcoholic and energy drinks, the presence of diabetes mellitus, pancreatitis, as well as chronic liver and kidney diseases. The clinical manifestation of the disease is typically characterized by epigastric pain, heartburn, digestive disorders, abdominal bloating, and a sensation of heaviness. In certain cases, concealed or overt gastrointestinal bleeding may occur [1]. Accurate diagnosis requires a comprehensive approach that includes laboratory and instrumental examination methods [2], such as: – clinical and biochemical blood tests to identify signs of inflammation and anemia; – PCR diagnostics of Helicobacter pylori as a highly sensitive method for detecting infection; – analysis of gastric juice; – contrast-enhanced radiographic examination; – ultrasound investigation of the abdominal organs; – endoscopic biopsy to exclude oncopathology; – fecal occult blood testing; – serological tests for hepatitis and HIV. The treatment strategy for peptic ulcer disease is aimed at eradication of the bacterial pathogen, normalization of gastric acidity, and restoration of the protective functions of the gastric mucosa. In most cases, therapy is carried out using conservative methods; however, surgical intervention may be required in the presence of complications. Despite the widespread introduction of endoscopic technologies into clinical practice, objective quantitative assessment of the area of an ulcerative defect remains a challenging task. While obtaining an image of the affected region generally presents no difficulty, determining its size is often performed visually, which is subjective in nature and may lead to diagnostic discrepancies and suboptimal treatment decisions. This problem becomes particularly relevant in cases of atypical ulcers or defects with complex geometry. In this regard, one of the priority directions of modern medical engineering is the development of automated methods for the analysis of endoscopic images and calculation of the area of pathological changes. The application of such algorithms makes it possible to reduce the dependence of diagnostic results on the subjective experience of the specialist and to improve their objectivity and reproducibility [3], [4]. To date, a significant number of mathematical methods have been developed for determining the area of objects with arbitrary shapes. The choice of a specific approach is determined by the geometric characteristics of the region under study. Prior to considering the processes of region-of-interest extraction and its digital processing, it is appropriate to focus on the hardware and software tools used for the acquisition of video and photographic materials. Currently, endoscopic equipment is produced under various brands, including FujiFilm, Aohua, Hikimaging, and others, and is intended for the examination of different human organs such as the ear, nose, and gastrointestinal tract. Within the framework of this study, the endoscopic systems FujiFilm VP-7000 and FujiFilm LL-7000 (Fig. 1), developed by German specialists and designed for the diagnosis of gastrointestinal tract diseases, were used. A significant advantage of the FujiFilm VP-7000 system is its capability for simultaneous video recording and image capture, as well as the availability of functions for adjusting image parameters and an extended set of additional settings, which increases the informational value of the acquired data (Figure 1). Fig. 1 — Endoscopic image of an ulcerative defect of the gastric mucosa. SOCIAL, ECONOMIC, SCIENTIFIC, AND TECHNICAL ACADEMIC JOURNAL INNOVATION SCIENCE AND TECHNOLOGY t.me/scupus_IST2100 147 https://ist-journal.uz 12/2025 LITERATURE REVIEW Contemporary medical literature emphasizes that the development of digital processing methods for biomedical images represents one of the key directions for improving the accuracy and reproducibility of diagnostics of diseases of the digestive system. Studies devoted to intelligent human–machine interfaces and visual information analysis demonstrate the active integration of computer vision algorithms, machine learning techniques, and intelligent video data processing into clinical practice, including their application in decision support for physicians in endoscopy and related fields. A number of studies in the areas of gastroenterology and hepatology indicate that the transition to quantitative assessment of pathological changes significantly increases the informative value of examinations and enables more objective monitoring of treatment dynamics. In research focused on the therapy of viral hepatitis, particular attention is paid to the use of biochemical and molecular markers, as well as to strict quantitative criteria for evaluating treatment effectiveness, which illustrates the overall trend toward standardization and formalization of clinical indicators. A similar approach appears relevant for endoscopic visualization of ulcerative defects, where the shift from subjective visual evaluation to mathematically grounded computation of lesion area makes it possible to reduce inter-observer variability and enhance diagnostic objectivity. The theoretical foundation for the development of algorithms for quantitative estimation of ulcer surface area is provided by classical works in the fields of spline functions and numerical integration. Studies on spline approximation methods demonstrate the high efficiency of piecewise polynomial models for describing complex curvilinear contours, which is particularly important when dealing with biological objects characterized by irregular geometry. The use of spline functions ensures smoothness of the approximating curve, robustness to noise, and the feasibility of subsequent application of numerical integration methods for calculating the areas of figures with arbitrary shapes. An additional contribution to the advancement of this research direction is made by studies on signal processing in piecewise polynomial bases. These works show that the selection of an appropriate basis and numerical schemes can significantly reduce computational errors and adapt algorithms to the characteristics of real measurement data. In the context of endoscopic image analysis, this enables the development of integrated methods that combine preliminary segmentation of the ulcerative defect, its spline approximation, and subsequent numerical integration, thereby ensuring more accurate and reproducible determination of the pathological area. RESEARCH METHODOLOGY 1. Rectangle Method The rectangle method is one of the simplest approaches to approximate numerical integration and is based on partitioning the region under study into elementary rectangles. The area of the figure is determined as the sum of the areas of all such rectangles. Despite its ease of implementation and low computational complexity, this method is characterized by relatively high error, especially when approximating complex curvilinear contours, which is typical for biological objects. 2. Trapezoidal Method The trapezoidal method represents a more accurate technique of numerical integration compared with the rectangle method. Within this approach, the segment between adjacent nodes is approximated by a trapezoid, allowing a more adequate representation of contour shape variation. The trapezoidal method provides improved computational accuracy while maintaining moderate computational complexity and is widely applied in the processing of medical images. 3. Numerical Integration Method Using Spline Interpolation To increase the accuracy of ulcer defect shape reconstruction, spline-based interpolation was employed in this study. Spline interpolation makes it possible to construct a smooth approximating curve passing through the given experimental points. As a result, the contour of the ulcerative lesion is described by a continuous function, to which numerical integration is subsequently applied in order to determine the area of the region. 4. Area Determination Using the Rectangle Method For approximate calculation of the area enclosed by the upper and lower contours, the rectangle method based on numerical integration was utilized. The computation was performed by determining the difference between the areas corresponding to the upper and lower boundaries of the region under investigation. The area according to the rectangle method was calculated using the following expression [4]: SOCIAL, ECONOMIC, SCIENTIFIC, AND TECHNICAL ACADEMIC JOURNAL INNOVATION SCIENCE AND TECHNOLOGY t.me/scupus_IST2100 148 https://ist-journal.uz 12/2025 (1) where n denotes the number of partitions of the studied interval, and y₁ and y₂ represent the values of the upper and lower boundary functions, respectively. As the number of partitions increases, the overall computational error decreases; however, the computational load simultaneously increases. It should be noted that under conditions of arbitrary distribution of experimental points, the rectangle method does not always provide sufficient accuracy in the processing of biomedical images, which necessitates the use of more advanced numerical methods. ANALYSIS AND RESULTS Area Determination Using the Trapezoidal Method In order to improve computational accuracy, the trapezoidal method was additionally applied in the present study, as it allows more correct consideration of contour shape variations between adjacent discretization nodes. Within this approach, segments of the curve are approximated by trapezoidal elements, providing a more adequate representation of the actual geometry of the region. The area of the affected zone in this case was determined using the following formula [5], [6]: Numerical Integration Based on Spline Interpolation To achieve the most accurate determination of the ulcer defect area, spline interpolation of the boundary points was applied in this study. After approximating the ulcer contour with a smooth continuous function, numerical integration was performed, which made it possible to significantly reduce the influence of the discreteness of the initial data and to improve the overall computational accuracy. The use of spline interpolation is particularly effective in the analysis of biological objects, as the shape of an ulcerative lesion is typically characterized by complex and irregular geometry. At the next stage, the video recording of the endoscopic examination was divided into individual frames, after which an algorithm for automated extraction of the gastric ulcer lesion area was implemented, thereby generating the initial data for subsequent quantitative analysis (Figure 2). Fig. 2 — Algorithm for detection and segmentation of the region exhibiting features of a pathological process. SOCIAL, ECONOMIC, SCIENTIFIC, AND TECHNICAL ACADEMIC JOURNAL INNOVATION SCIENCE AND TECHNOLOGY t.me/scupus_IST2100 149 https://ist-journal.uz 12/2025 Fig. 3 — Stages of extraction of the ulcer defect of the gastric mucosa. Table 1. Coordinates of the ulcer defect of the gastric mucosa. ixᵢ yᵢ xⱼ yⱼ 1 307 247 307 247 2276 252 342 258 3261 268 352 272 4 251 288 365 285 5 255 322 367 311 6274 348 352 340 7 300 358 333 355 Table 2. Comparative analysis of the results of calculating the area of the ulcer defect of the gastric mucosa. Region of Calculation Rectangle Method, S₁ Trapezoidal Method, S₂ Difference |S₁ − S₂| Upper boundary 38914 39117 203 Lower boundary 29114 29223 109 Final area 9800 9894 94 The values S1S_1S1 and S2S_2S2 characterize the number of discrete points falling within the region bounded by the upper and lower contours of the ulcerative defect, as illustrated in Figure 2. To convert the obtained results into real physical dimensions, a scaling ratio was applied, according to which five discrete points correspond to 1 mm. The results of the performed calculations demonstrated that the method based on numerical integration using the trapezoidal scheme with spline interpolation provides higher accuracy in determining the area of the ulcerative defect compared to the rectangular method. This confirms the feasibility of applying the proposed approach for the quantitative assessment of pathological changes and indicates its potential to enhance the objectivity and reproducibility of endoscopic diagnostics. CONCLUSION AND RECOMMENDATIONS The present study introduces an integrated digital methodology designed for the automatic extraction of gastric ulcer images from endoscopic video recordings, the precise delineation of pathological boundaries, and the highly accurate computation of ulcer surface area. The proposed multi-stage algorithm enables the identification