APPLICATION OF NUMERICAL AND FUNCTIONAL SERIES IN IMAGE ANALYSIS AND SHAPE RECOGNITION AT ALMALYK MINING AND METALLURGICAL COMPLEX

Аннотация

Numerical and functional series play a pivotal role in modeling chemical processes and advancing image processing within chemical engineering. This study explores their application in theAlmalyk Mining and Metallurgical Complex (AMMC) "Smart Mine" strategy, with a focus on shape recognition in binary images. Taylor series are employed to approximate shape boundaries in noisy images, Fourier descriptors model closed contours, and Zernike moments enhance shape classification. Through practical examples, a Python implementation, and a comprehensive literature review, this study demonstrates the effectiveness of these methodsin ore classification and qualitycontrol. Keywords:Numerical series, Functional series, Taylor series, Fourier descriptors, Zernike moments, Image analysis, Shape recognition, Almalyk Mining and Metallurgical Complex, Smart Mine, Ore classification, Quality control, Image processing, Chemical engineering, Hough transform, Python implementation Аннотация:Числовые и функциональные ряды играют ключевую роль в моделировании химических процессов и развитии обработки изображений в химической инженерии. Данное исследование рассматривает их применение в рамках стратегии «Умная шахта» Алмалыкского горно-металлургического комбината (АГМК) с акцентом на распознавание форм в бинарных изображениях. Ряды Тейлора используются для аппроксимации границ форм в зашумленных изображениях, дескрипторы Фурье моделируют замкнутые контуры, а моменты Цернике улучшают классификацию форм. На основе практических примеров, реализации на языке Python и всестороннего обзора литературы данное исследование демонстрирует эффективность этих методов в классификациируды иконтролекачества. Ключевые слова: числовые ряды, функциональные ряды, ряды Тейлора, дескрипторы Фурье, моменты Цернике, анализ изображений, распознавание форм, Алмалыкский горно-металлургический комбинат, Умная шахта, классификация руды, контроль качества, обработка изображений, химическая инженерия, преобразование Хафа, реализациянаPython. Annotatsiya:Sonliva funksional qatorlar kimyoviy jarayonlarni modellashtirishda va kimyoviy muhandislikda tasvirlarni qayta ishlashni rivojlantirishda muhim rol o‘ynaydi. Ushbu tadqiqot ularning Almalik kon-metallurgiya kombinati (AMMC) “Aqlli kon” strategiyasida, xususan, ikkilik tasvirlarda shakl tanishda qo‘llanilishini o‘rganadi. Teylor qatorlari shovqinli tasvirlarda shakl chegaralarini taxmin qilish uchun ishlatiladi, Furye deskriptorlari yopiq konturlarni page1318 INTERNATIONAL JOURNAL OF ARTIFICIAL INTELLIGENCE ISSN:2692-5206,ImpactFactor:12,23 AmericanAcademicpublishers,volume05,issue06,2025 Journal: https://www.academicpublishers.org/journals/index.php/ijai modellashtiradi va Zernike momentlari shakl klassifikatsiyasini yaxshilaydi. Amaliy misollar, Python dasturida amalga oshirish va keng qamrovli adabiyotlar sharhi orqali ushbu tadqiqot ushbuusullarning ruda klassifikatsiyasi vasifat nazoratida samaradorligini namoyish etadi. Kalit so‘zlar: raqamli qatorlar, funksional qatorlar, Teylor qatorlari, Furye deskriptorlari, Zernike momentlari, tasvir tahlili, shakl tanish, Almalik kon-metallurgiya kombinati, Aqlli kon, ruda klassifikatsiyasi, sifat nazorati, tasvirlarni qayta ishlash, kimyoviy muhandislik, Hough transformatsiyasi, Python dasturidaamalga oshirish. 1Introduction Image processing is a cornerstone of modern chemical engineering, particularly for automated material analysis and classification. At the Almalyk Mining and Metallurgical Complex (AMMC), the "Smart Mine" strategy leverages advanced image processing algorithms to streamline ore classification, quality control, and process optimization. Numerical and functional series, such as Taylor series and Fourier descriptors, provide efficient frameworks for addressing complex mathematical challenges in these tasks. Additionally, Zernike moments offer robust shape feature detection in noisy environments. This studyaims to: (1) illustrate the application of Taylor series, Fourier descriptors, and Zernike moments in image analysis; (2) present practical examples tailored to AMMC’s operations; and (3) develop aPython-based solution forshape recognition. 2Methods This study employs numerical and functional series, combined with Zernike moments, to tackle image analysis challenges within AMMC’s "Smart Mine" system. The methods are designed to recognize closed contours in binary images, a critical component of ore classification. 2.1TaylorSeries forBoundary Detection Taylor series are used to approximate complex functions, such as trigonometric functions intheHough transform, which isapplied todetect straight lines inimages: Forsmall angles ,thefollowing approximationsare used: ρ = xcosθ+ysinθ θ 2 4 θ θ cosθ ≈ 1− + 32 254 These approximations simplify computations inθnoisyθimages, improving boundary detection sinθ ≈ θ− + forore separation tasks. 6 120 2.2FourierDescriptors forShape Modeling Fourier descriptors model closed contours usingtheformula: N−1 2πnt 1 −j N