Техносфера - Цифровая Обработка Изображений

Содержание

Предисловие

Благодарности

Об авторах

ТОМ 1

Введение

1.1

Что такое цифровая обработка изображений?

1.2

Истоки цифровой обработки изображений

1.3

Примеры областей, использующих цифровую обработку изображений

1.3.1

Формирование изображений с помощью гамма лучей

1.3.2

Рентгеновские изображения

1.3.3

Изображения в ультрафиолетовом диапазоне

1.3.4

Изображения в видимом и инфракрасном диапазонах

1.3.5

Изображения в микроволновом диапазоне

1.3.6

Изображения в диапазоне радиоволн

1.3.7

Примеры, иллюстрирующие другие способы формирования изображений

1.4

Основные стадии цифровой обработки изображений

1.5

Компоненты системы обработки изображений

Заключение

Ссылки и литература для дальнейшего изучения

Основы цифрового представления изображений

2.1

Элементы зрительного восприятия

2.1.1

Схема человеческого глаза

2.1.2

Формирование изображения в глазу

2.1.3

Яркостная адаптация и контрастная чувствительность

2.2

Свет и электромагнитный спектр

2.3

Считывание и регистрация изображения

2.3.1

Регистрация изображения с использованием одиночного сенсора

2.3.2

Регистрация изображения с использованием линеек сенсоров

2.3.3

Регистрация изображения с использованием массивов сенсоров

2.3.4

Простая модель формирования изображения

2.4

Дискретизация и квантование изображения

2.4.1

Основные понятия, используемые при дискретизации и квантовании

2.4.2

Представление цифрового изображения

2.4.3

Пространственное и полутоновое разрешения

2.4.4

Картины, возникающие при наложении спектров и при муаре

2.4.5

Увеличение и уменьшение дискретизованных изображений

2.5

Некоторые фундаментальные взаимосвязи между элементами изображения

2.5.1

Соседи отдельного элемента

2.5.2

Соседство, связность, области и границы

2.5.3

Меры расстояния

2.5.4

Поэлементные преобразования изображения

2.6

Линейные и нелинейные преобразования

Заключение

Ссылки и литература для дальнейшего изучения

Проблемы

Пространственные методы улучшения изображения

3.1

Предпосылки

3.2

Некоторые основные преобразования полутонов

3.2.1

Преобразование изображения в негатив

3.2.2

Логарифмическое преобразование

3.2.3

Степенное преобразование

3.2.4

Кусочно-линейные функции преобразований

3.3

Преобразование гистограммы

3.3.1

Эквализация гистограммы

3.3.2

Совмещение (формирование заданной) гистограммы

3.3.3

Локальное улучшение

3.3.4

Использование гистограммных статистик для улучшения изображения

3.4

Улучшение с помощью арифметических/логических операций

3.4.1

Вычитание изображений

3.4.2

Усреднение изображения

3.5

Основы пространственной фильтрации

3.6

Сглаживающие пространственные фильтры

3.6.1

Линейные сглаживающие фильтры

3.6.2

Фильтры, основанные на порядковых статистиках

3.7

Пространственные фильтры повышения резкости

3.7.1

Основы

3.7.2

Использование второй производной для улучшения – лапласиан

3.7.3

Использование первой производной для улучшения – градиент

3.8

Комбинирование методов пространственного улучшения

Заключение

Ссылки и литература для дальнейшего изучения

Проблемы

Частотные методы улучшения изображения

4.1

Предпосылки

4.2

Введение в Фурье-преобразование и частотная область

4.2.1

Одномерные прямое и обратное преобразования

4.2.2

Двумерные прямое и обратное преобразования

4.2.3

Фильтрация в частотной области

4.2.4

Соответствие между фильтрациями в пространственной и частотной областях

4.3

Сглаживающие частотные фильтры

4.3.1

Идеальные фильтры нижних частот

4.3.2

Фильтры Баттерворта нижних частот

4.3.3

Гауссовские фильтры нижних частот

4.3.4

Дополнительные примеры низкочастотной фильтрации

4.4

Частотные фильтры повышения резкости

4.4.1

Идеальные фильтры верхних частот

4.4.2

Фильтры Баттерворта верхних частот

4.4.3

Гауссовские фильтры верхих частот

4.4.4

Лапласиан в частотной области

4.4.5

Нерезкое маскирование, высокочастотная фильтрация и фильтрация усилением верхних частот

4.5

Гомоморфная фильтрация

4.6

Реализация

4.6.1

Некоторые дополнительные свойства двумерного преобразования Фурье

4.6.2

Вычисление обратного преобразования Фурье с помощью алгоритма прямого преобразования

4.6.3

Еще о периодичности: необходимость заполнения

4.6.4

Теоремы о свертке и корреляции

4.6.5

Список свойств двумерного преобразования Фурье

4.6.6

Быстрое преобразование Фурье

4.6.7

Несколько замечаний касательно конструирования фильтров

Заключение

Ссылки

Проблемы

Восстановление изображений

5.1

Модель процесса искажения/восстановления изображения

5.2

Модели шума

5.2.1

Пространственные и частотные свойства шума

5.2.2

Функции плотности вероятностей некоторых важных видов шума

5.2.3

Периодический шум

5.2.4

Оценивание параметров шума

5.3

Восстановление в случае наличия только шума – пространственная фильтрация

5.3.1

Усредняющие фильтры

5.3.2

Фильтры, основанные на порядковых статистиках

5.3.3

Адаптивные фильтры

5.4

Ослабление периодического шума с помощью фильтрации в частотной области

5.4.1

Режекторные фильтры

5.4.2

Полосовые фильтры

5.4.3

Узкополосные режекторные фильтры

5.4.4

Оптимальная узкополосная режекторная фильтрация

5.5

Линейные пространственно-инвариантные искажения

5.6

Оценивание искажающей функции

5.6.1

Оценивание путем визуального анализа изображения

5.6.2

Оценивание путем экспериментирования

5.6.3

Оценивание путем моделирования

5.7

Обратная фильтрация

5.8

Фильтрация по минимуму среднеквадратической ошибки (Винеровская)

5.9

Фильтрация методом наименьших квадратов с ограничениями

5.10

Фильтр геометрического среднего

5.11

Геометрические преобразования

5.11.1

Пространственные преобразования

5.11.2

Интерполяция уровней яркости

Заключение

Ссылки и литература для дальнейшего изучения

Проблемы

Обработка цветных изображений

6.1

Основы теории цвета

6.2

Цветовые модели

6.2.1

Цветовая модель RGB

6.2.2

Цветовые модели CMY и CMYK

6.2.3

Цветовая модель HSI

6.3

Обработка изображения в псевдоцветах

6.3.1

Квантование по интенсивности

6.3.2

Преобразования серой шкалы в цвет

6.4

Основы полноцветного преобразования изображения

6.5

Цветовые преобразования

6.5.1

Формулировка

6.5.2

Цветовые дополнения

6.5.3

Цветовое квантование

6.5.4

Цветовая и тональная коррекции

6.5.5

Обработка гистограммы

6.6

Сглаживание и повышение резкости

6.6.1

Сглаживание цветного изображения

6.6.2

Повышение резкости цветного изображения

6.7

Цветовая сегментация

6.7.1

Сегментация в цветовом пространстве HSI

6.7.2

Сегментация в векторном пространстве RGB

6.7.3

Обнаружение цветовых контуров

6.8

Шум на цветных изображениях

6.9

Сжатие цветных изображений

Заключение

Ссылки и литература для дальнейшего изучения

Проблемы

ТОМ 2

Вэйвлеты и обработка в режиме мультиразрешения

7.1

Предпосылки

7.1.1

Пирамиды изображений

7.1.2

Подполосное кодирование

7.1.3

Преобразование Хаара

7.2

Разложения в ряд мультиразрешений

7.2.1

Последовательные разложения

7.2.2

Функции масштабирования

7.2.3

Вэйвлет-функции

7.3

Одномерные вэйвлет-преобразования

7.3.1

Последовательные вэйвлет-разложения

7.3.2

Дискретное вэйвлет-преобразование

7.3.3

Непрерывное вэйвлет-преобразование

7.4

Быстрое вэйвлет-преобразование

7.5

Двумерное вэйвлет-преобразование

7.6

Вэйвлет-пакеты

Заключение

Ссылки и литература для дальнейшего изучения

Проблемы

Сжатие изображений

8.1

Основы

8.1.1

Кодовая избыточность

8.1.2

Межэлементная избыточность

8.1.3

Психофизическая избыточность

8.1.4

Критерий точности

8.2

Модели сжатия изображений

8.2.1

Кодирование и декодирование источника

8.2.2

Кодирование и декодирование канала

8.3

Элементы теории информации

8.3.1

Измерение информации

8.3.2

Канал передачи информации

8.3.3

Фундаментальные теоремы кодирования

8.3.4

Используя теорию информации

8.4

Сжатие без потерь

8.4.1

Коды переменной длинны

8.4.2

Алгоритм кодирования LZW

8.4.3

Кодирование битовых плоскостей

8.4.4

Кодирование с предсказанием без потерь

8.5

Сжатие с потерями

8.5.1

Кодирование с предсказанием с потерями

8.5.2

Трансформационное кодирование

8.5.3

Вэйвлет-кодирование

8.6

Стандарты сжатия изображений

8.6.1

Стандарты сжатия двоичных изображений

8.6.2

Стандарты сжатия полутоновых неподвижных изображений

8.6.3

Стандарты сжатия видеопоследовательностей

Заключение

Ссылки и литература для дальнейшего изучения

Проблемы

Морфологическая обработка изображений

9.1

Вступление

9.1.1

Некоторые основные понятия из теории множеств

9.1.2

Логические операции, относящиеся к двоичным изображениям

9.2

Дилатация и эрозия

9.2.1

Дилатация

9.2.2

Эрозия

9.3

Раскрывание и закрывание

9.4

Случайное преобразование

9.5

Некоторые основные морфологические алгоритмы

9.5.1

Выделение границ

9.5.2

Заполнение областей

9.5.3

Выделение связных компонентов

9.5.4

Выпуклая оболочка

9.5.5

Утоньшение

9.5.6

Утолщение

9.5.7

Построение скелета

9.5.8

Усечение

9.5.9

Сводка морфологических операций на бинарных изображениях

9.6

Расширение на полутоновые изображения

9.6.1

Дилатация

9.6.2

Эрозия

9.6.3

Раскрывание и закрывание

9.6.4

Некоторые приложения полутоновой морфологии

Заключение

Ссылки и литература для дальнейшего изучения

Проблемы

10.

Сегментация изображений

10.1

Обнаружение разрывов

10.1.1

Обнаружение точек

10.1.2

Обнаружение линий

10.1.3

Обнаружение перепадов

10.2

Связывание контуров и обнаружение границ

10.2.1

Локальная обработка

10.2.2

Глобальная обработка с помощью преобразования Хафа

10.2.3

Глобальная обработка с помощью методов теории графов

10.3

Пороговая обработка

10.3.1

Обоснование

10.3.2

Роль освещения

10.3.3

Обработка с глобальным порогом

10.3.4

Обработка с адаптивным порогом

10.3.5

Обработка с оптимальными глобальным и адаптивным порогами

10.3.6

Использование параметров границ для исправления гистограммы и локальной пороговой обработки

10.3.7

Пороги, основанные на нескольких переменных

10.4

Сегментация на основе областей

10.4.1

Основная формулировка

10.4.2

Выращивание областей

10.4.3

Разделение и слияние областей

10.5

Сегментация по морфологическим водоразделам

10.5.1

Основные концепции

10.5.2

Построение перегородки

10.5.3

Алгоритм сегментации по водоразделу

10.5.4

Использование маркеров

10.6

Использование движения при сегментации

10.6.1

Пространственные методы

10.6.2

Частотные методы

Заключение

Ссылки и литература для дальнейшего изучения

Проблемы

11.

Представление и описание

11.1

Представление

11.1.1

Цепные коды

11.1.2

Приближение полигонами

11.1.3

Сигнатуры

11.1.4

Сегменты границ

11.1.5

Скелеты областей

11.2

Дескрипторы границ

11.2.1

Некоторые простые дескрипторы

11.2.2

Номера очертаний

11.2.3

Фурье дескрипторы

11.2.4

Статистические моменты

11.3

Дескрипторы областей

11.3.1

Некоторые простые дескрипторы

11.3.2

Топологические дескрипторы

11.3.3

Текстура

11.3.4

Моменты двумерных функций

11.4

Использование главных компонент для описания

11.5

Реляционные дескрипторы

Заключение

Ссылки и литература для дальнейшего изучения

Проблемы

12.

Распознавание объектов

12.1

Образы и классы образов

12.2

Распознавание, основанное на методах теории принятия решений

12.1.1

Согласование

12.1.2

Статистически-оптимальные классификаторы

12.1.3

Нейронные сети

12.3

Структурные методы

12.3.1

Численное сравнение формы

12.3.2

Согласование последовательностей

12.3.3

Синтаксическое распознавание последовательностей

12.3.4

Синтаксическое распознавание деревьев

Заключение

Ссылки и литература для дальнейшего изучения

Проблемы

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