From b52efeac667d1bcdde9e85f1c9e5a367aa919e3e Mon Sep 17 00:00:00 2001 From: Maria Byvalkina Date: Fri, 12 Jun 2026 15:40:25 +0300 Subject: [PATCH 1/9] added folder with report --- Mariia_Byvalkina/Mariia_Byvalkina_report.tex | 218 +++++++++++++++++++ 1 file changed, 218 insertions(+) create mode 100644 Mariia_Byvalkina/Mariia_Byvalkina_report.tex diff --git a/Mariia_Byvalkina/Mariia_Byvalkina_report.tex b/Mariia_Byvalkina/Mariia_Byvalkina_report.tex new file mode 100644 index 0000000..4a72af0 --- /dev/null +++ b/Mariia_Byvalkina/Mariia_Byvalkina_report.tex @@ -0,0 +1,218 @@ +\documentclass[a4paper]{article} + +\usepackage[a4paper, top=8mm, bottom=8mm, left=8mm, right=8mm]{geometry} + +\usepackage{polyglossia} +\setdefaultlanguage[babelshorthands=true]{russian} +\setotherlanguage{english} + +\usepackage{fontspec} +\setmainfont{FreeSerif} +\newfontfamily{\russianfonttt}[Scale=0.7]{DejaVuSansMono} + +\usepackage[tiny, compact]{titlesec} + +\usepackage{titling} +\setlength{\droptitle}{-1cm} +\pretitle{\begin{center}\begin{bfseries}\Large} +\posttitle{\par\end{bfseries}\end{center}} +\preauthor{\begin{center}\normalsize} +\postauthor{\par\end{center}\vspace{-1.8cm}} + +\usepackage{hyperref} +\usepackage{bookmark} +\usepackage{csquotes} +\usepackage{enumitem} +\usepackage{amsmath} +\usepackage{graphicx} + +\title{Реализация свёртки изображений на Python} + +\author{Бывалкина Мария Дмитриевна} + +\date{} + +\begin{document} + +\maketitle + +\begin{flushright} + Группа: \emph{\enquote{25.Б43-мм}} + + Кафедра: \emph{системного программирования} + + Научный руководитель: \emph{Пономарев Николай Алексеевич} + + Номер семестра практики: \emph{2} +\end{flushright} + +\section{Введение} + +Обработка изображений является одной из важных задач современного программного обеспечения. Она используется в системах компьютерного зрения, медицинской диагностике, графических редакторах и многих других областях. + +Свёртка является из базовых операций обработки изображений. Данная операция позволяет изменять изображение при помощи специальной матрицы коэффициентов, называемой ядром свёртки. В зависимости от выбранного ядра можно выполнять размытие изображения, повышение резкости, выделение контуров и другие преобразования. + +Математически двумерная свёртка изображения $I$ с ядром $K$ определяется следующим выражением: + +\[ +(I * K)(x,y)= +\sum_{i=-r}^{r} +\sum_{j=-r}^{r} +I(x+i,y+j)\cdot K(i,j), +\] + +где $r$ --- половина размера ядра. + +Целью данной работы является разработка собственной реализации свёртки изображений на языке Python, проверка её корректности и сравнение производительности с существующими библиотечными решениями. + +\section{Постановка задачи} + +Цель практики заключается в реализации алгоритма двумерной свёртки изображений и проведении экспериментального исследования его производительности. + +Для достижения поставленной цели необходимо решить следующие задачи: + +\begin{itemize} + \item реализовать операцию свёртки для полутоновых и цветных изображений; + \item реализовать набор свёрточных ядер; + \item обеспечить корректную обработку границ изображения; + \item разработать тесты для проверки правильности работы алгоритма; + \item провести сравнение производительности собственной реализации с библиотеками OpenCV и Pillow; + \item визуализировать результаты измерений. +\end{itemize} + +\section{Описание реализации} + +Проект реализован на языке Python и построен на основе объектно-ориентированного подхода. Основная функциональность свёртки изображений инкапсулирована в классе ImageConvolution, который содержит методы для выполнения операции свёртки и различных режимов паддинга. + +Для хранения и обработки изображений используются библиотеки Pillow и NumPy. Представление изображения в виде массива NumPy позволяет эффективно выполнять математические операции над пикселями. + +\subsection{Поддержка цветовых режимов} + +Программа поддерживает работу как с изображениями в оттенках серого, так и с RGB-изображениями. + +Для полутоновых изображений свёртка применяется непосредственно к двумерному массиву яркостей. + +Для цветных изображений обработка выполняется отдельно для каждого цветового канала (красного, зелёного и синего), после чего результаты объединяются в итоговое изображение. + +\subsection{Обработка границ изображения} + +При вычислении свёртки для пикселей, расположенных возле границ изображения, часть элементов ядра выходит за пределы массива. + +Для корректной обработки таких ситуаций реализован механизм дополнения изображения по краям. + +В проекте используются следующие режимы дополнения: + +\begin{itemize} + \item \textbf{zero} --- заполнение отсутствующих значений нулями; + \item \textbf{edge} --- копирование ближайших граничных пикселей; + \item \textbf{reflect} --- зеркальное отражение изображения; +\end{itemize} + +Выбор режима осуществляется пользователем при запуске программы. + +\subsection{Свёрточные ядра} + +Для исследования были реализованы несколько наиболее распространённых фильтров. + +\begin{itemize} + \item \textbf{Blur} --- размытие изображения. + \item \textbf{Sharpen} --- повышение резкости. + \item \textbf{Sobel} --- выделение границ объектов. +\end{itemize} + +Каждое ядро хранится в виде матрицы коэффициентов и может использоваться при выполнении свёртки. + +\subsection{Интерфейс программы} + +Для взаимодействия с пользователем реализован интерфейс командной строки. + +При запуске программы пользователь может указать: + +\begin{itemize} + \item входное изображение; + \item выходной файл; + \item тип фильтра; + \item режим обработки границ; +\end{itemize} + +\section{Тестирование} + +Для проверки корректности реализации были разработаны интеграционные тесты с использованием эталонных изображений. Тесты храняться в файле \verb|tests/test_convolution.py|. + +Тестирование включает следующие категории: + +\begin{itemize} + \item проверка корректности работы различных ядер; + \item проверка обработки полутоновых изображений; + \item проверка обработки RGB-изображений; + \item проверка различных режимов дополнения границ; + \item сравнение результатов с эталонами. +\end{itemize} + +Все тесты были успешно пройдены, что подтверждает корректность разработанного алгоритма. + +\section{Эксперименты} + +Для оценки производительности использовалась библиотека \verb|pytest-benchmark|. + +Сравнивались три реализации: + +\begin{itemize} + \item собственная реализация; + \item Pillow; + \item OpenCV. +\end{itemize} + +Тестирование проводилось на случайно сгенерированных изображениях размером $512 \times 512$ и $1024 \times 1024$ пикселей. + +Использование случайных изображений позволило исключить влияние операций чтения файлов на результаты измерений. + +Измерения выполнялись отдельно для изображений в оттенках серого и для RGB-изображений. + +Для каждого теста вычислялись: + +\begin{itemize} + \item среднее время выполнения; + \item стандартное отклонение; + \item количество операций в секунду. +\end{itemize} + +Результаты представлены на рисунке~\ref{fig:benchmark}. + +\begin{figure}[ht] + \centering + \includegraphics[width=\textwidth]{benchmark.png} + \caption{Сравнение производительности различных реализаций свёртки} + \label{fig:benchmark} +\end{figure} + +Проведённые эксперименты позволяют сделать несколько выводов. + +Во-первых, собственная реализация существенно уступает по скорости библиотечным решениям. В среднем она оказывается в несколько тысяч раз медленнее OpenCV и в несколько сотен раз медленнее Pillow. + +Во-вторых, увеличение размера изображения приводит к росту времени выполнения для всех реализаций. При переходе от размера $512 \times 512$ к размеру $1024 \times 1024$ количество пикселей возрастает в четыре раза, что приводит к соответствующему увеличению времени обработки. + +В-третьих, обработка RGB-изображений требует больше времени по сравнению с полутоновыми изображениями. Это связано с необходимостью выполнять свёртку отдельно для каждого цветового канала. + +Наиболее высокую производительность показала библиотека OpenCV, что объясняется использованием низкоуровневых оптимизаций и реализацией основных алгоритмов на языке C++. + +\section{Заключение} + +В ходе выполнения учебной практики была разработана собственная реализация операции двумерной свёртки изображений на языке Python. + +В результате работы: + +\begin{itemize} + \item реализована поддержка полутоновых и RGB-изображений; + \item реализованы различные режимы обработки границ изображения; + \item реализован набор свёрточных фильтров; + \item разработаны интеграционные для проверки корректности работы; + \item проведено исследование производительности; + \item выполнено сравнение с библиотеками OpenCV и Pillow. +\end{itemize} + +Полученные результаты показали корректность реализованного алгоритма и подтвердили преимущество специализированных библиотек по скорости выполнения. При этом разработанная реализация позволяет наглядно изучить принцип работы свёртки изображений и особенности её применения на практике. + +Репозиторий проекта: \url{https://github.com/MariiaByvalkina/image-convolution-practice} + +\end{document} From 08f34b5d2e18f353a8caee8f44d4daa93c5558f6 Mon Sep 17 00:00:00 2001 From: Maria Byvalkina Date: Fri, 12 Jun 2026 18:38:42 +0300 Subject: [PATCH 2/9] add file with report --- Mariia_Byvalkina/Mariia_Byvalkina_report.tex | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/Mariia_Byvalkina/Mariia_Byvalkina_report.tex b/Mariia_Byvalkina/Mariia_Byvalkina_report.tex index 4a72af0..c5e4f15 100644 --- a/Mariia_Byvalkina/Mariia_Byvalkina_report.tex +++ b/Mariia_Byvalkina/Mariia_Byvalkina_report.tex @@ -177,8 +177,6 @@ \section{Эксперименты} \item количество операций в секунду. \end{itemize} -Результаты представлены на рисунке~\ref{fig:benchmark}. - \begin{figure}[ht] \centering \includegraphics[width=\textwidth]{benchmark.png} @@ -186,6 +184,8 @@ \section{Эксперименты} \label{fig:benchmark} \end{figure} +Результаты представлены на рисунке~\ref{fig:benchmark}. + Проведённые эксперименты позволяют сделать несколько выводов. Во-первых, собственная реализация существенно уступает по скорости библиотечным решениям. В среднем она оказывается в несколько тысяч раз медленнее OpenCV и в несколько сотен раз медленнее Pillow. 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z5a%BY5Aa)%PjsUm-@=RE!YH&u5=>3Uxk{(Rd4^MKX=&z*vc<2*HPAE)E99OY9-t)W zBfW{ghuIG*^0&p8>uK=O0#b%?xqBxkS|;N~i||zz@v9(u2p*lnSJ}?5BCl|9r%asl zA2lhrJSj;Q{ekZ&5CpR5{{3G!zGn0FyT8sJD*D&Ig5m4Go(m4ezYc@=X8d!9;o0OH YGVWhoDLi8(zL&eU@7 Date: Fri, 12 Jun 2026 18:41:26 +0300 Subject: [PATCH 4/9] added Mariia Byvalkina report --- main.tex | 3 +++ 1 file changed, 3 insertions(+) diff --git a/main.tex b/main.tex index ce49627..324229c 100644 --- a/main.tex +++ b/main.tex @@ -40,5 +40,8 @@ \includepdf[pages=-, addtotoc={1, section, 1, {Гаврилов Максим Юрьевич, Программирование микроконтроллеров RISC-V}, gavrilov_maxim}] {Maxim_Gavrilov/Maxim_Gavrilov_report.pdf} +\includepdf[pages=-, + addtotoc={1, section, 1, {Бывалкина Мария Дмитриевна, Свертка изображений}, mariia_byvalkina}] +{Mariia_Byvalkina/Mariia_Byvalkina_report.pdf} \end{document} \end{document} From 83750a3cfec5a7066c8dc5edac4b5b565bdc737b Mon Sep 17 00:00:00 2001 From: Maria Byvalkina Date: Tue, 16 Jun 2026 00:59:02 +0300 Subject: [PATCH 5/9] corrected the comments --- Mariia_Byvalkina/Mariia_Byvalkina_report.tex | 33 ++++---------------- 1 file changed, 6 insertions(+), 27 deletions(-) diff --git a/Mariia_Byvalkina/Mariia_Byvalkina_report.tex b/Mariia_Byvalkina/Mariia_Byvalkina_report.tex index c5e4f15..dfc97f1 100644 --- a/Mariia_Byvalkina/Mariia_Byvalkina_report.tex +++ b/Mariia_Byvalkina/Mariia_Byvalkina_report.tex @@ -53,14 +53,12 @@ \section{Введение} Свёртка является из базовых операций обработки изображений. Данная операция позволяет изменять изображение при помощи специальной матрицы коэффициентов, называемой ядром свёртки. В зависимости от выбранного ядра можно выполнять размытие изображения, повышение резкости, выделение контуров и другие преобразования. Математически двумерная свёртка изображения $I$ с ядром $K$ определяется следующим выражением: - \[ (I * K)(x,y)= \sum_{i=-r}^{r} \sum_{j=-r}^{r} I(x+i,y+j)\cdot K(i,j), \] - где $r$ --- половина размера ядра. Целью данной работы является разработка собственной реализации свёртки изображений на языке Python, проверка её корректности и сравнение производительности с существующими библиотечными решениями. @@ -70,7 +68,6 @@ \section{Постановка задачи} Цель практики заключается в реализации алгоритма двумерной свёртки изображений и проведении экспериментального исследования его производительности. Для достижения поставленной цели необходимо решить следующие задачи: - \begin{itemize} \item реализовать операцию свёртки для полутоновых и цветных изображений; \item реализовать набор свёрточных ядер; @@ -89,19 +86,14 @@ \section{Описание реализации} \subsection{Поддержка цветовых режимов} Программа поддерживает работу как с изображениями в оттенках серого, так и с RGB-изображениями. - Для полутоновых изображений свёртка применяется непосредственно к двумерному массиву яркостей. - Для цветных изображений обработка выполняется отдельно для каждого цветового канала (красного, зелёного и синего), после чего результаты объединяются в итоговое изображение. \subsection{Обработка границ изображения} -При вычислении свёртки для пикселей, расположенных возле границ изображения, часть элементов ядра выходит за пределы массива. - -Для корректной обработки таких ситуаций реализован механизм дополнения изображения по краям. +При вычислении свёртки для пикселей, расположенных возле границ изображения, часть элементов ядра выходит за пределы массива. Для корректной обработки таких ситуаций реализован механизм дополнения изображения по краям. В проекте используются следующие режимы дополнения: - \begin{itemize} \item \textbf{zero} --- заполнение отсутствующих значений нулями; \item \textbf{edge} --- копирование ближайших граничных пикселей; @@ -113,7 +105,6 @@ \subsection{Обработка границ изображения} \subsection{Свёрточные ядра} Для исследования были реализованы несколько наиболее распространённых фильтров. - \begin{itemize} \item \textbf{Blur} --- размытие изображения. \item \textbf{Sharpen} --- повышение резкости. @@ -127,7 +118,6 @@ \subsection{Интерфейс программы} Для взаимодействия с пользователем реализован интерфейс командной строки. При запуске программы пользователь может указать: - \begin{itemize} \item входное изображение; \item выходной файл; @@ -137,10 +127,9 @@ \subsection{Интерфейс программы} \section{Тестирование} -Для проверки корректности реализации были разработаны интеграционные тесты с использованием эталонных изображений. Тесты храняться в файле \verb|tests/test_convolution.py|. +Для проверки корректности реализации были разработаны интеграционные тесты с использованием эталонных изображений. Эталонные изображения были заранее сделаны с помощью OpenCV. Тесты храняться в файле \verb|tests/test_convolution.py|. Тестирование включает следующие категории: - \begin{itemize} \item проверка корректности работы различных ядер; \item проверка обработки полутоновых изображений; @@ -153,24 +142,19 @@ \section{Тестирование} \section{Эксперименты} +Эксперименты проводились на ПК со следующими характеристиками: +\textit{ОС} EndeavourOS Linux, \textit{процессор} Intel Core i5-12450H, \textit{ОЗУ} 16ГБ. Для оценки производительности использовалась библиотека \verb|pytest-benchmark|. Сравнивались три реализации: - \begin{itemize} \item собственная реализация; \item Pillow; \item OpenCV. \end{itemize} -Тестирование проводилось на случайно сгенерированных изображениях размером $512 \times 512$ и $1024 \times 1024$ пикселей. - -Использование случайных изображений позволило исключить влияние операций чтения файлов на результаты измерений. - -Измерения выполнялись отдельно для изображений в оттенках серого и для RGB-изображений. - +Тестирование проводилось на случайно сгенерированных изображениях размером $512 \times 512$ и $1024 \times 1024$ пикселей. Использование случайных изображений позволило исключить влияние операций чтения файлов на результаты измерений. Измерения выполнялись отдельно для изображений в оттенках серого и для RGB-изображений. Для каждого теста вычислялись: - \begin{itemize} \item среднее время выполнения; \item стандартное отклонение; @@ -179,7 +163,7 @@ \section{Эксперименты} \begin{figure}[ht] \centering - \includegraphics[width=\textwidth]{benchmark.png} + \includegraphics[width=0.5\textwidth]{benchmark.pdf} \caption{Сравнение производительности различных реализаций свёртки} \label{fig:benchmark} \end{figure} @@ -187,13 +171,9 @@ \section{Эксперименты} Результаты представлены на рисунке~\ref{fig:benchmark}. Проведённые эксперименты позволяют сделать несколько выводов. - Во-первых, собственная реализация существенно уступает по скорости библиотечным решениям. В среднем она оказывается в несколько тысяч раз медленнее OpenCV и в несколько сотен раз медленнее Pillow. - Во-вторых, увеличение размера изображения приводит к росту времени выполнения для всех реализаций. При переходе от размера $512 \times 512$ к размеру $1024 \times 1024$ количество пикселей возрастает в четыре раза, что приводит к соответствующему увеличению времени обработки. - В-третьих, обработка RGB-изображений требует больше времени по сравнению с полутоновыми изображениями. Это связано с необходимостью выполнять свёртку отдельно для каждого цветового канала. - Наиболее высокую производительность показала библиотека OpenCV, что объясняется использованием низкоуровневых оптимизаций и реализацией основных алгоритмов на языке C++. \section{Заключение} @@ -201,7 +181,6 @@ \section{Заключение} В ходе выполнения учебной практики была разработана собственная реализация операции двумерной свёртки изображений на языке Python. 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z$r%$S+oK~b5tj=E0jAe!+CcJh;;hcdwsC+Ew`G9vi&g&njq-u1iR5Jk`b341 zvli1hcqCzi*6e>*Z#(-3;TwhIP{t2VUoz88Iq9kK(p;5HsgN0ZNK)wfx0D2tu*pHLqBPTnZ_BEWQ*)+dIb$` zA&qoPKvThoiHJsy5QKbW`Rr);LnBu}Q;Et|zzu|$kHbTYAgxwMCdV#6_@g6-4g#76 z&pkq#l3X^}^Km-TX*-%is~4qJzj)}SVHFQDmZ-D5|?N|TmG0vbo7Pe9Ys%0@ub zla;Weaat{wr9v7l;{`OV&V*%fI<2T3N{$@F*r!#h6twQ3pLHzIT3*aYOHv`9UZj&s zH7C*yrCKGHi&{&rKqWYO1MQ;mrqpO?60%RL(TV#*s}PMhC7v5ZB-xlkOr`+hz22uXb$wsfZ0;WXHbdz z4Z~O14o;yUD{I#dPN5c!Bg{gyX13>pVu|uoYH?stz{g=W5z#mYG&NaX`!YCkq9ddk z#Pw5&=QVhJgbOG^T9sIS9G(b;a}#{Liso2OO^;xL{GiVwnno$oKfFpMPh|A7jzLbN z7U?~wp+_+RpTTat Date: Tue, 16 Jun 2026 12:37:03 +0300 Subject: [PATCH 8/9] made a correction to the section about testing --- Mariia_Byvalkina/Mariia_Byvalkina_report.tex | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/Mariia_Byvalkina/Mariia_Byvalkina_report.tex b/Mariia_Byvalkina/Mariia_Byvalkina_report.tex index dfc97f1..7df2ea8 100644 --- a/Mariia_Byvalkina/Mariia_Byvalkina_report.tex +++ b/Mariia_Byvalkina/Mariia_Byvalkina_report.tex @@ -127,7 +127,7 @@ \subsection{Интерфейс программы} \section{Тестирование} -Для проверки корректности реализации были разработаны интеграционные тесты с использованием эталонных изображений. Эталонные изображения были заранее сделаны с помощью OpenCV. Тесты храняться в файле \verb|tests/test_convolution.py|. +Для проверки корректности реализации были разработаны интеграционные тесты с использованием эталонных изображений. В качестве эталонов использовались заранее сохранённые результаты работы программы для набора тестовых изображений и фильтров. При выполнении тестов вновь полученные результаты автоматически сравнивались с эталонными изображениями. Тесты храняться в файле \verb|tests/test_convolution.py|. Тестирование включает следующие категории: \begin{itemize} From 3d9ac08e6b7134b8618b87589b2e69a10027398e Mon Sep 17 00:00:00 2001 From: Maria Byvalkina Date: Tue, 16 Jun 2026 12:52:48 +0300 Subject: [PATCH 9/9] several change --- Mariia_Byvalkina/Mariia_Byvalkina_report.tex | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/Mariia_Byvalkina/Mariia_Byvalkina_report.tex b/Mariia_Byvalkina/Mariia_Byvalkina_report.tex index 7df2ea8..73677d3 100644 --- a/Mariia_Byvalkina/Mariia_Byvalkina_report.tex +++ b/Mariia_Byvalkina/Mariia_Byvalkina_report.tex @@ -127,7 +127,7 @@ \subsection{Интерфейс программы} \section{Тестирование} -Для проверки корректности реализации были разработаны интеграционные тесты с использованием эталонных изображений. В качестве эталонов использовались заранее сохранённые результаты работы программы для набора тестовых изображений и фильтров. При выполнении тестов вновь полученные результаты автоматически сравнивались с эталонными изображениями. Тесты храняться в файле \verb|tests/test_convolution.py|. +Для проверки корректности реализации были разработаны интеграционные тесты с использованием эталонных изображений. В качестве эталонов использовались заранее сохранённые результаты работы программы для набора тестовых изображений и фильтров. При выполнении тестов вновь полученные результаты автоматически сравнивались c эталонными изображениями. Тесты храняться в файле \verb|tests/test_convolution.py|. Тестирование включает следующие категории: \begin{itemize}