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[Перевод] Сила оттенков серого: компьютерное зрение с нуля

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В обсуждениях компьютерного зрения обычно речь идёт об OpenCV или нейронных сетях глубокого обучения наподобие YOLO. Однако в большинстве случаев для работы с компьютерным зрением требуется понимание базовых алгоритмов, чтобы можно было адаптировать их под свои нужды.

Мне захотелось понять, насколько далеко я смогу зайти, оставив в computer vision только самый минимум: одни лишь 8-битные изображения в градациях серого; никаких сложных структур данных, старый добрый C, немного байтовых массивов и единственный файл заголовка. В конце концов, изображение — это ведь просто прямоугольник из чисел, не так ли?

Этот пост — экскурсия по алгоритмам, лежащим в основе Grayskull — минималистичной библиотеки компьютерного зрения, спроектированной для устройств с ограниченными ресурсами.

Пиксели

Пиксель в градациях серого обычно представлен одним байтом: 0 означает чёрный цвет, 255 — белый, а промежуточные значения представляют различные оттенки серого.

По сути, изображение в градациях серого — это 2D-массив таких пикселей, задаваемый шириной и высотой, однако на языках с более простой структурой памяти наподобие C он часто представляется в виде 1D-массива размером width * height:

// Изображение размером WxH пикселей, хранящееся как плоский массив байтов
struct gs_image { unsigned w, h; uint8_t *data; };

// Вспомогательные функции для считывания/записи значений пикселей с учётом границ
uint8_t gs_get(struct gs_image img, unsigned x, unsigned y) {
  return (x < img.w && y < img.h) ? img.data[y * img.w + x] : 0;
}
void gs_set(struct gs_image img, unsigned x, unsigned y, uint8_t value) {
  if (x < img.w && y < img.h) img.data[y * img.w + x] = value;
}

// Удобный макрос для итеративного обхода всех пикселей
#define gs_for(img, x, y)                \
  for (unsigned y = 0; y < (img).h; y++) \
    for (unsigned x = 0; x < (img).w; x++)

Этот скромный фундамент уже позволяет нам выполнять определённые трюки, например, инвертировать или отзеркаливать изображения:

// Инвертирование изображения (создание негатива): px[x,y] = 255 - px[x,y]
gs_for(img, x, y) gs_set(img, x, y, 255 - gs_get(img, x, y));

// Отзеркаливание изображения: заменяем px[x,y] на px[w-x-1,y]
gs_for(img, x, y) {
for (unsigned y = 0; y < img.h; y++) {
  for (unsigned x = 0; x < img.w/2; x++) { // итеративно обходим только первую половину
    uint8_t tmp = gs_get(img, x, y);
    gs_set(img, x, y, gs_get(img, img.w - x - 1, y));
    gs_set(img, img.w - x - 1, y, tmp);
  }
}
struct gs_rect { unsigned x, y, w, h; }; // Для интересующих нас областей (region of interest, ROI)

// Обрезаем src изображения в dst на основании roi
gs_for(roi, x, y) gs_set(dst, x, y, gs_get(src, roi.x + x, roi.y + y));

// Уменьшаем размер в два раза: усредняем значение пикселя по четырём соседям (2x2)
gs_for(dst, x, y) {
    unsigned sum = 0;
    for (unsigned j = 0; j < 2; j++)
      for (unsigned i = 0; i < 2; i++)
        sum += gs_get(src, x * 2 + i, y * 2 + j);
    gs_set(dst, x, y, sum / 4);
}

Можно выполнять наивное изменение размера по ближайшим соседям, результат будет быстрым, но слишком грубым, или же выполнять билинейную интерполяцию, что медленнее и требует операций с плавающей запятой, зато часто выглядит красивее:

// Изменение размера по ближайшим соседям
void gs_resize_nn(struct gs_image dst, struct gs_image src) {
    gs_for(dst, x, y) {
        unsigned sx = x * src.w / dst.w, sy = y * src.h / dst.h;
        gs_set(dst, x, y, gs_get(src, sx, sy));
    }
}

// Билинейное изменение размера
GS_API void gs_resize(struct gs_image dst, struct gs_image src) {
  gs_for(dst, x, y) {
    float sx = ((float)x + 0.5f) * src.w / dst.w, sy = ((float)y + 0.5f) * src.h / dst.h;
    sx = GS_MAX(0.0f, GS_MIN(sx, src.w - 1.0f)), sy = GS_MAX(0.0f, GS_MIN(sy, src.h - 1.0f));
    unsigned sx_int = (unsigned)sx, sy_int = (unsigned)sy;
    unsigned sx1 = GS_MIN(sx_int + 1, src.w - 1), sy1 = GS_MIN(sy_int + 1, src.h - 1);
    float dx = sx - sx_int, dy = sy - sy_int;
    uint8_t c00 = gs_get(src, sx_int, sy_int), c01 = gs_get(src, sx1, sy_int),
            c10 = gs_get(src, sx_int, sy1), c11 = gs_get(src, sx1, sy1);
    uint8_t p = (c00 * (1 - dx) * (1 - dy)) + (c01 * dx * (1 - dy)) + (c10 * (1 - dx) * dy) + (c11 * dx * dy);
    gs_set(dst, x, y, p);
  }
}
Resize: bilinear and nearest neighbour

Так исходное изображение (слева) выглядит после билинейного изменения размера (посередине) и изменения размера по ближайшим соседям (справа).

Обработка изображений

Теперь, когда мы можем манипулировать отдельными пикселями, можно приступать к более серьёзной обработке изображений.

Полезным инструментом здесь будут свёрточные фильтры. Фильтр — это маленький 2D-массив (ядро), применяемый к каждому пикселю изображения. Новое значение пикселя вычисляется как взвешенная сумма соседних пикселей, где веса определяются ядром.

void gs_filter(struct gs_image dst, struct gs_image src, struct gs_image kernel, unsigned norm) {
    gs_for(dst, x, y) {
        int sum = 0;
        gs_for(kernel, i, j) {
            sum += gs_get(src, x + i - kernel.w / 2, y + j - kernel.h / 2) * (int8_t)gs_get(kernel, i, j);
        }
        gs_set(dst, x, y, sum / norm);
    }
}

Эту методику можно использовать для размытия, повышения резкости, распознавания краёв и многих других эффектов. Вот примеры одних из самых распространённых ядер. Учтите, что они определяются, как 8-битные integer со знаком:

// box blur 3x3, все пиксели имеют одинаковый вес
struct gs_image gs_blur_box = {3, 3, (uint8_t *)(int8_t[]){1, 1, 1, 1, 1, 1, 1, 1, 1}};
// гауссово размытие 3x3, центральные пиксели имеют больший вес
struct gs_image gs_blur_gaussian = {3, 3, (uint8_t *)(int8_t[]){1, 2, 1, 2, 4, 2, 1, 2, 1}};
// повышение резкости и усиление краёв
struct gs_image gs_sharpen = {3, 3, (uint8_t *)(int8_t[]){0, -1, 0, -1, 5, -1, 0, -1, 0}};
// тиснение, изображение становится более "3D"
struct gs_image gs_emboss = {3, 3, (uint8_t *)(int8_t[]){-2, -1, 0, -1, 1, 1, 0, 1, 2}};

Аналогично, можно применить фильтры Собеля, которые полезны, если мы хотим распознавать на изображениях края:

struct gs_image gs_sobel_x = {3, 3, (uint8_t *)(int8_t[]){-1, 0, 1, -2, 0, 2, -1, 0, 1}};
struct gs_image gs_sobel_y = {3, 3, (uint8_t *)(int8_t[]){1, 2, 1, 0, 0, 0, -1, -2, -1}};

void gs_sobel(struct gs_image dst, struct gs_image src) {
    struct gs_image gx = {src.w, src.h, malloc(src.w * src.h)};
    struct gs_image gy = {src.w, src.h, malloc(src.w * src.h)};
    gs_filter(gx, src, gs_sobel_x, 1);
    gs_filter(gy, src, gs_sobel_y, 1);
    gs_for(dst, x, y) {
        int mag = sqrt(gs_get(gx, x, y) * gs_get(gx, x, y) + gs_get(gy, x, y) * gs_get(gy, x, y));
        gs_set(dst, x, y, GS_MIN(mag, 255));
    }
    free(gx.data);
    free(gy.data);
}

Вот примеры таких фильтров; обратите внимание, как некоторые из них устраняют шум или выделяют края:

Filters: blur, sharpen, emboss, sobel

Первое изображение — это оригинал, далее идут box filter и фильтр гауссова размытия. Затем идёт фильтр повышения резкости, фильтр тиснения и, наконец, фильтр Собеля, выделяющий края.

Пороговые значения

Чтобы «видеть» объекты на изображении, нам нужно разделить его на передний и задний планы, а затем работать с передними сегментами, пытаясь найти находить интересующие нас объекты.

Гораздо проще это делать, если каждый пиксель полностью чёрный или полностью белый. Такое преобразование из градаций серого в чёрно-белые данные называется thresholding (бинаризацией).

В простейшем случае мы можем считать все пиксели со значениями больше 127 белыми, а ниже — чёрными. Это thresholding с фиксированным уровнем. Разумеется, если изображение тёмное, то такое значение thresholding окажется слишком высоким и многие значимые детали будут утеряны. Как же выбрать пороговое значение точнее?

// Применяем фиксированное пороговое значение и бинаризируем изображение
GS_API void gs_threshold(struct gs_image img, uint8_t thresh) {
  for (unsigned i = 0; i < img.w * img.h; i++) img.data[i] = (img.data[i] > thresh) ? 255 : 0;
}

Одно из решений заключается в вычислении распределения яркости как гистограммы. Мы знаем, что на изображении в градациях серого есть 255 уникальных значений, поэтому можем итеративно обойти все пиксели и посчитать, какие из них имеют то или иное значение. Проанализировав получившуюся гистограмму, мы получим представление, какое значение пикселя лучше всего подойдёт в качестве порогового.

Это можно сделать при помощи способа Оцу. Он автоматически определяет оптимальное пороговое значение, проверяя каждое возможное значение (от 0 до 255). Для каждого значения он разбивает пиксели изображения на два класса (фон и передний план), а затем вычисляет их межклассовую дисперсию. Пороговым значением, максимизирующим эту дисперсию, будет то, которое создаёт наилучшее разделение между двумя классами. Такой способ довольно неплохо работает для изображений с хорошей контрастностью:

// пытаемся найти наилучшее пороговое значение для разделения "переднего" и "заднего" плана
uint8_t gs_otsu_threshold(struct gs_image img) {
  unsigned hist[256] = {0}, wb = 0, wf = 0, threshold = 0;
  // вычисляем количество пикселей с каждым значением яркости
  for (unsigned i = 0; i < img.w * img.h; i++) hist[img.data[i]]++;
  float sum = 0, sumB = 0, varMax = -1.0;
  for (unsigned i = 0; i < 256; i++) sum += (float)i * hist[i];
  // пытаемся найти пороговое значение, максимизирующее межклассовую дисперсию
  for (unsigned t = 0; t < 256; t++) {
    wb += hist[t];
    if (wb == 0) continue;
    wf = (img.w * img.h) - wb;
    if (wf == 0) break;
    sumB += (float)t * hist[t];
    float mB = (float)sumB / wb;
    float mF = (float)(sum - sumB) / wf;
    float varBetween = (float)wb * (float)wf * (mB - mF) * (mB - mF);
    if (varBetween > varMax) varMax = varBetween, threshold = t;
  }
  return threshold;
}

Однако в реальной жизни условия освещения часто неравномерны. В таких случаях единое глобальное пороговое значение может не подойти, и ни одно из потенциальных 255 пороговых значений не обеспечит хорошего результата.

Для решения этой проблемы можно использовать адаптивный thresholding. Мы не будем использовать одно пороговое значение для всего изображения, а станем вычислять локальный порог для каждого пикселя на основании средней яркости соседних пикселей. Благодаря этому можно лучше учитывать разные условия освещения в изображении:

gs_for(src, x, y) {
  unsigned sum = 0, count = 0;
  for (int dy = -radius; dy <= (int)radius; dy++) {
    for (int dx = -radius; dx <= (int)radius; dx++) {
      int sy = (int)y + dy, sx = (int)x + dx;
      if (sy >= 0 && sy < (int)src.h && sx >= 0 && sx < (int)src.w) {
        sum += gs_get(src, sx, sy);
        count++;
      }
    }
  }
  int threshold = sum / count - c;
  gs_set(dst, x, y, (gs_get(src, x, y) > threshold) ? 255 : 0);
}

Посмотрим, как разные способы вычисления thresholding выглядят на одном и том же изображении:

Thresholding: fixed, Otsu, adaptive

Первое изображение — оригинал, за ним идут thresholding с фиксированным уровнем (80), способ Оцу и адаптивный thresholding. Обратите внимание, что адаптивный thresholding сохраняет больше деталей и в ярких, и в тёмных областях изображения, а у способа Оцу возникают проблемы с неравномерным освещением.

Морфологические операции

Из-за особенностей работы датчиков изображения в камерах снимки часто содержат шум.

Это означает, что после thresholding в изображении будут встречаться случайные отдельные пиксели, не относящиеся к какому-то объекту, небольшие отверстия в объектах или небольшие разрывы между частями объектов. Всё это сбивает с толку алгоритмы распознавания объектов, однако очистке двоичного изображения могут способствовать морфологические операции.

Две наиболее распространённые операции — это erosion (морфологическое сужение) и dilation (расширение). Сужение убирает пиксели на границах объектов (уменьшая их размеры), а расширение добавляет пиксели к их границам (увеличивая объекты).

Также существует opening (erosion с последующим dilation) и closing (dilation с последующим erosion). Opening полезно для удаления маленьких объектов или шума, а closing — для заполнения небольших отверстий в объектах.

void gs_erode(struct gs_image dst, struct gs_image src, unsigned radius) {
  gs_for(dst, x, y) {
    uint8_t min_val = 255;
    for (int dy = -radius; dy <= (int)radius; dy++) {
      for (int dx = -radius; dx <= (int)radius; dx++) {
        int sy = (int)y + dy, sx = (int)x + dx;
        if (sy >= 0 && sy < (int)src.h && sx >= 0 && sx < (int)src.w) {
          uint8_t val = gs_get(src, sx, sy);
          if (val < min_val) min_val = val;
        }
      }
    }
    gs_set(dst, x, y, min_val);
  }
}
void gs_dilate(struct gs_image dst, struct gs_image src, unsigned radius) {
  gs_for(dst, x, y) {
    uint8_t max_val = 0;
    for (int dy = -radius; dy <= (int)radius; dy++) {
      for (int dx = -radius; dx <= (int)radius; dx++) {
        int sy = (int)y + dy, sx = (int)x + dx;
        if (sy >= 0 && sy < (int)src.h && sx >= 0 && sx < (int)src.w) {
          uint8_t val = gs_get(src, sx, sy);
          if (val > max_val) max_val = val;
        }
      }
    }
    gs_set(dst, x, y, max_val);
  }
}

Вот пример того, как морфологические операции могут подчистить довольно непонятное изображение с метками ArUco:

Aruco markers: original, thresholded, eroded, dilated

Первое изображение — оригинал, за которым следует изображение с thresholding (способ Оцу). Далее идут erosion с последующим dilation. Маркеры чёрные, поэтому это может показаться странным, но так как морфологические операции работают с белыми пикселями, мы, по сути, выполняем closing, но для чёрных пикселей. Также можно предварительно инвертировать изображение, а затем выполнять opening и обратное инвертирование.

В конце все маркеры уменьшаются до их исходных размеров и все их легко можно распознать по форме и размеру.

Пятна и контуры

Получив чистое двоичное изображение, можно приступать к распознаванию объектов на нём. Классический способ решения этой задачи — нахождение соединённых компонентов (пятен, blob).

Blob — группа соединённых белых пикселей (255), образующих объект. Для разметки связанных пикселей проще всего находить blob при помощи алгоритма заливки (flood-fill) или поиска в глубину (depth-first search, DFS):

void gs_flood_fill(struct gs_image img, unsigned x, unsigned y, uint8_t target, uint8_t replacement) {
  if (x >= img.w || y >= img.h) return;
  if (gs_get(img, x, y) != target || gs_get(img, x, y) == replacement) return;
  gs_set(img, x, y, replacement);
  gs_flood_fill(img, x + 1, y, target, replacement);
  gs_flood_fill(img, x - 1, y, target, replacement);
  gs_flood_fill(img, x, y + 1, target, replacement);
  gs_flood_fill(img, x, y - 1, target, replacement);
}

Разумеется, при обработке большинства реальных изображений это мгновенно увеличит стек до огромных величин. Поэтому предпочтителен итеративный подход с очередью или стеком.

Однако это всё равно не самый оптимальный способ поиска blob. Более эффективный способ — это алгоритм, состоящий из двух проходов, сканирующий изображение дважды: сначала он присваивает предварительные метки и записывает соответствия между ними, а затем выполняет второе сканирование для ресолвинга этих соответствий и присвоения каждому blob окончательной уникальной метки.

Будет здорово, если мы сможем использовать один и тот же тип gs_image для меток, но в большинстве случаев для этого потребуется больше, чем 256 меток (особенно для временных промежуточных меток). Поэтому для хранения меток нужен отдельный массив integer большего размера:

typedef uint16_t gs_label; // наверно, 64 тысяч будет достаточно?

struct gs_blob {
  gs_label label; // какую метку имеет blob?
  unsigned area; // сколько белых пикселей находится в blob?
  struct gs_rect box; // ограничивающий прямоугольник
  struct gs_point centroid; // центр "масс"
};
unsigned gs_blobs(struct gs_image img, gs_label *labels, struct gs_blob *blobs, unsigned nblobs) { ... }

Прежде, чем двигаться дальше, давайте поговорим о связанности. Существует два распространённых типа связанности пикселей: 4-connectivity и 8-connectivity. В 4-connectivity пиксель соединён с четырьмя непосредственными соседями (сверху, снизу, слева, справа). В 8-connectivity пиксель связан со всеми восемью окружающими его пикселями (те же, плюс по диагонали). То есть, в случае 8-connectivity показанный ниже пример будет одним blob, а в случае 4-connectivity — двумя отдельными blob:

......
.#..#.
.##.#.
.###..
......

В нашей реализации для простоты будет использоваться 4-connectivity. Рассмотрим следующее изображение:

.........
.###..#..
.###.##..
.#####..#
.......##

Начнём сканировать его строка за строкой. Если найден белый пиксель, проверяем соседей слева и справа:

  • Если оба чёрные (0), то присваиваем пикселю новую метку, считая, что это будет новый blob.

  • Если один из них белый, присваиваем его метку текущему пикселю, так как это продолжение уже имеющегося известного blob.

  • Если оба белые, но имеют разные метки, то присваиваем наименьшую из меток текущему пикселю и записываем соответствие между двумя метками в особую структуру данных (как объединение-поиск).

После первого прохода массив меток будет выглядеть так:

.........
.111..2..
.111.32..
.11111..4
.......55

Таблица соответствия будет выглядеть так: 1 <-> 3, 3 <-> 2, 4 <-> 5.

Во втором проходе мы разрешаем соответствия и присваиваем каждому пикселю окончательные метки. Массив окончательных меток будет выглядеть так:

.........
.111..1..
.111.11..
.11111..4
.......44

На втором проходе также можно вычислять такие свойства blob, как площадь, ограничивающий прямоугольник и центр масс. Площадь самого большого blob составляет 14 пикселей, его ограничивающий прямоугольник имеет координаты от (1,1) до (6,3). Центр масс вычисляется как среднее координат всех пикселей blob, в нашем случае по оси X это будет (3*1+3*2+3*3+4+2*5+2*6)/14, или округлённо 4. По оси Y это будет (4*1+5*2+5*3)/14, или округлённо 2. То есть центр масс находится в координате (4,2), не относящейся к «телу» blob.

Эти геометрические свойства уже дают нам довольно много информации о blob. Например, мы можем фильтровать blob по площади, чтобы удалять небольшие пятна шума. Также можно вычислять соотношение сторон (ширина/высота) ограничивающего прямоугольника, чтобы отфильтровывать очень тонкие или очень широкие blob. Соотношение между реальной площадью и ограничивающим прямоугольником blob позволяет отфильтровывать недостаточно компактные blob. У прямоугольников соотношение близко к 1.0, у кругов — к pi/4 = 0.785, а у линий приближается к нулю.

Другими подсказками будут позиция центра масс, ориентация с использованием моментов или форма контура. Существует достаточно простой способ трассировки контура blob при помощи алгоритма трассировки окрестности Мура. Он начинает с известного пикселя границы и следует по контуру по часовой стрелке, проверяя соседние пиксели, пока не вернётся в начальный пиксель:

struct gs_contour { struct gs_rect box; struct gs_point start; unsigned length; };
void gs_trace_contour(struct gs_image img, struct gs_image visited, struct gs_contour *c) {
  static const int dx[] = {1, 1, 0, -1, -1, -1, 0, 1};
  static const int dy[] = {0, 1, 1, 1, 0, -1, -1, -1};
  c->length = 0;
  c->box = (struct gs_rect){c->start.x, c->start.y, 1, 1};
  struct gs_point p = c->start;
  unsigned dir = 7, seenstart = 0;
  for (;;) {
    if (!visited.data[p.y * visited.w + p.x]) c->length++;
    visited.data[p.y * visited.w + p.x] = 255;
    int ndir = (dir + 1) % 8, found = 0;
    for (int i = 0; i < 8; i++) {
      int d = (ndir + i) % 8, nx = p.x + dx[d], ny = p.y + dy[d];
      if (nx >= 0 && nx < (int)img.w && ny >= 0 && ny < (int)img.h &&
          img.data[ny * img.w + nx] > 128) {
        p = (struct gs_point){nx, ny};
        dir = (d + 6) % 8;
        found = 1;
        break;
      }
    }
    if (!found) break;  // открытый контур
    c->box.x = GS_MIN(c->box.x, p.x);
    c->box.y = GS_MIN(c->box.y, p.y);
    c->box.w = GS_MAX(c->box.w, p.x - c->box.x + 1);
    c->box.h = GS_MAX(c->box.h, p.y - c->box.y + 1);
    if (p.x == c->start.x && p.y == c->start.y) {
      if (seenstart) break;
      seenstart = 1;
    }
  }
}

Таким образом можно получать контуры всех blob и анализировать их формы или сравнивать длины контуров (периметр) с площадью blob. Также можно аппроксимировать контуры прямыми отрезками при помощи алгоритма Рамера — Дугласа — Пекера, заменяющего кривую последовательностью отрезков прямых с сохранением общей формы.

Всё это здорово, если мы хотим распознавать простые объекты на статическом изображении. Но, что если нам нужно распознавать или отслеживать более сложные объекты, такие как лица, автомобили или пешеходы?

Ключевые точки и дескрипторы

Ключевая точка (keypoint) — это определённый участок изображения, уникальный и надёжно распознаваемый вне зависимости от масштаба, поворота и освещения объекта.

На практике, ключевые точки часто оказываются углами (также называемыми «признаками», feature). Один из самых интуитивно понятных алгоритмов распознавания признаков — это FAST (Features from Accelerated Segment Test). Он исследует окружность из 16 пикселей вокруг пикселя-кандидата (в 4 пикселях от него). Если как минимум 9 смежных пикселей в этой окружности r=4px вокруг пикселя P одновременно ярче или темнее, то пиксель-кандидат считается углом:

..............
......012.....
.....F...3....
....E.....4...
....D..P..5...
....C.....6...
.....B...7....
......A98.....
..............

Этот алгоритм прост, однако на реальных изображениях находит слишком много признаков. Решить эту проблему можно, записывая «оценку» (score) каждого признака и сохраняя только точки с наибольшей оценкой. Оценку можно вычислить как сумму абсолютных разностей между пикселем-кандидатом и смежными пикселями в окружности или как минимальную разность между центральным пикселем и пикселями на окружности.

  gs_assert(gs_valid(img) && kps && nkps > 0);
  static const int dx[16] = {0, 1, 2, 3, 3, 3, 2, 1, 0, -1, -2, -3, -3, -3, -2, -1};
  static const int dy[16] = {-3, -3, -2, -1, 0, 1, 2, 3, 3, 3, 2, 1, 0, -1, -2, -3};
  unsigned n = 0;
  // первый проход: вычисляем карту оценок
  for (unsigned y = 3; y < img.h - 3; y++) {
    for (unsigned x = 3; x < img.w - 3; x++) {
      uint8_t p = img.data[y * img.w + x];
      int run = 0, score = 0;
      for (int i = 0; i < 16 + 9; i++) {
        int idx = (i % 16);
        uint8_t v = img.data[(y + dy[idx]) * img.w + (x + dx[idx])];
        if (v > p + threshold) {
          run = (run > 0) ? run + 1 : 1;
        } else if (v < p - threshold) {
          run = (run < 0) ? run - 1 : -1;
        } else {
          run = 0;
        }
        if (run >= 9 || run <= -9) {
          score = 255;
          for (int j = 0; j < 16; j++) {
            int d = gs_get(img, x + dx[j], y + dy[j]) - p;
            if (d < 0) d = -d;
            if (d < score) score = d;
          }
          break;
        }
      }
      scoremap.data[y * img.w + x] = score;
    }
  }
  // второй проход: отбрасывание немаксимальных значений
  for (unsigned y = 3; y < img.h - 3; y++) {
    for (unsigned x = 3; x < img.w - 3; x++) {
      int s = scoremap.data[y * img.w + x], is_max = 1;
      if (s == 0) continue;
      for (int yy = -1; yy <= 1 && is_max; yy++) {
        for (int xx = -1; xx <= 1; xx++) {
          if (xx == 0 && yy == 0) continue;
          if (scoremap.data[(y + yy) * img.w + (x + xx)] > s) {
            is_max = 0;
            break;
          }
        }
      }
      if (is_max && n < nkps) kps[n++] = (struct gs_keypoint){{x, y}, (unsigned)s, 0, {0}};
    }
  }
  return n;
}
FAST keypoints detection

Обратите внимание, как на фотографии кота распознаются ключевые точки в углах и таких уникальных признаках, как глаза, нос, усы и так далее. Но как использовать ключевые точки для распознавания объектов?

Здесь на помощь приходит ORB. Он надстраивается поверх того же распознавателя углов FAST, пытается находить резкие изменения яркости, но также добавляет ещё два компонента: ориентацию и дескриптор.

После нахождения углов ORB определяет их ориентацию, вычисляя моменты изображения на небольшом участке вокруг каждой ключевой точки. Благодаря этому у каждой ключевой точки появляется угол, по сути, сообщающий, где у неё «верх».

Дескриптор — это компактное описание локального участка изображения вокруг ключевой точки, инвариантное относительно масштаба и поворота. В ORB используется модифицированная версия дескриптора BRIEF (Binary Robust Independent Elementary Features), позволяющая хитрым образом кодировать участок изображения в виде небольшой битовой строки.

Дескриптор просто сравнивает яркости битов, и если один пиксель светлее другого, то соответствующий бит получает значение 1, а в противном случае 0. Выполнив серию таких сравнений, можно создать двоичную строку, описывающую локальный участок изображения.

Дескриптор имеет длину 256 бит; для каждого из 256 «сэмплов» мы при помощи псевдослучайной таблицы поиска выбираем две точки сэмплирования внутри площади участка и кодируем следующий бит, как 0 или 1 в зависимости от относительных значений пикселей.

Сравнение ключевых точек становится тривиальной задачей, достаточно просто выполнить XOR двух битовых строк и посчитать биты.

Так как ключевые точки не зависят от поворота и условий освещения, можно использовать их для распознавания объектов в различных сценариях.

Последним дополнением этого алгоритма станет многократное изменение размера/масштаба изображения и распознавание ключевых точек в разных масштабах. Благодаря этому можно распознавать объекты, которые ближе или дальше от камеры, повёрнуты на любой угол или частично скрыты.

ORB keypoints detection

LBP-каскады

Ключевые точки и дескрипторы отлично подходят для распознавания произвольных объектов, но иногда нам нужен более специализированное решение для определённых типов объектов, например, лиц, транспорта или жестов. Тут нам приходят на помощь каскадные классификаторы, применяемые, например, в методе Виолы — Джонса.

Вместо сложных признаков Хаара, применяемых в алгоритме Виолы — Джонса, можно использовать нечто более простое: локальные бинарные шаблоны (Local Binary Patterns, LBP). LBP — это мощный дескриптор текстур. Он исследует 8 соседей каждого пикселя, и если сосед ярче центрального пикселя, записывает 1, а в противном случае 0. Так мы получаем 8-битное число, описывающее локальную текстуру.

«Каскад» — это последовательность простых классификаторов, или «этапов». На каждом из этапов исследуется окно изображения и применяется несколько признаков LBP для определения того, может ли это окно содержать интересующий объект (например, лицо).

  • Если окно не проходит проверку на любом из этапов, оно немедленно отбрасывается. Это очень быстрый процесс.

  • Окно классифицируется, как положительное распознавание, только если оно прошло все этапы.

Такая структура позволяет классификатору быстро отбрасывать подавляющую часть площади изображения и сосредоточить вычислительные ресурсы только на областях с высоким потенциалом. Перемещая это окно распознавания по всему изображению (и во множестве разных масштабов), можно находить объекты конкретного заранее обученного класса. В Grayskull есть предварительно обученный детектор лиц анфас, использующий именно эту методику.

LBP face detection

Выше показан результат работы LBP-каскадного классификатора, успешно распознавшего лицо сэра Гэри Олдмена во всём разнообразии его ролей. Слева выбрано минимальное количество соседей, равное 4, а справа — 14. Благодаря этому слева распознаётся больше лиц, но и возникает больше ложноположительных срабатываний, а справа выполняется более консервативное распознавание, обнаруживающее только полностью видимые лица анфас.

Заключение

Мы проделали путь от скромного пикселя до сложного распознавания объектов, использовав для всего этого лишь простые структуры C и фундаментальные алгоритмы. Мы попробовали манипулировать пикселями, применять фильтры для обработки изображений, сегментировать объекты при помощи thresholding и подчищать их. Также мы научились находить и анализировать blob, распознавать устойчивые ключевые точки при помощи FAST и ORB, и, наконец, использовали LBP-каскады для распознавания специализированных объектов.

В этом и заключается фундаментальная философия Grayskull: срывание покрова таинственности с компьютерного зрения созданием минимального, свободного от зависимостей и понятного набора инструментов. Она доказывает, что для получения приемлемых результатов не всегда нужны тяжеловесные библиотеки или фреймворки глубокого обучения, особенно в системах с ограниченными ресурсами.

По сути, изображения — это просто прямоугольники из чисел, поэтому благодаря основам знаний алгоритмов можно научить компьютер видеть их. Как всегда, я рекомендую вам изучить репозиторий, экспериментировать с кодом и, может быть, даже попробовать собрать собственный простой проект CV!

Источник

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    CRYPTO SCAM RECOVERY SUCCESSFUL – A TESTIMONIAL OF LOST PASSWORD TO YOUR DIGITAL WALLET BACK. My name is Robert Alfred, Am from Australia. I’m sharing my experience in the hope that it helps others who have been victims of crypto scams. A few months ago, I fell victim to a fraudulent crypto investment scheme linked to a broker company. I had invested heavily during a time when Bitcoin prices were rising, thinking it was a good opportunity. Unfortunately, I was scammed out of $120,000 AUD and the broker denied me access to my digital wallet and assets. It was a devastating experience that caused many sleepless nights. Crypto scams are increasingly common and often involve fake trading platforms, phishing attacks, and misleading investment opportunities. In my desperation, a friend from the crypto community recommended Capital Crypto Recovery Service, known for helping victims recover lost or stolen funds. After doing some research and reading multiple positive reviews, I reached out to Capital Crypto Recovery. I provided all the necessary information—wallet addresses, transaction history, and communication logs. Their expert team responded immediately and began investigating. Using advanced blockchain tracking techniques, they were able to trace the stolen Dogecoin, identify the scammer’s wallet, and coordinate with relevant authorities to freeze the funds before they could be moved. Incredibly, within 24 hours, Capital Crypto Recovery successfully recovered the majority of my stolen crypto assets. I was beyond relieved and truly grateful. Their professionalism, transparency, and constant communication throughout the process gave me hope during a very difficult time. If you’ve been a victim of a crypto scam, I highly recommend them with full confidence contacting: Email: [email protected] Telegram: @Capitalcryptorecover Contact: [email protected] Call/Text: +1 (336) 390-6684 Website: https://recovercapital.wixsite.com/capital-crypto-rec-1

  • 24.06.26 22:01 robertalfred175

    CRYPTO SCAM RECOVERY SUCCESSFUL – A TESTIMONIAL OF LOST PASSWORD TO YOUR DIGITAL WALLET BACK. My name is Robert Alfred, Am from Australia. I’m sharing my experience in the hope that it helps others who have been victims of crypto scams. A few months ago, I fell victim to a fraudulent crypto investment scheme linked to a broker company. I had invested heavily during a time when Bitcoin prices were rising, thinking it was a good opportunity. Unfortunately, I was scammed out of $120,000 AUD and the broker denied me access to my digital wallet and assets. It was a devastating experience that caused many sleepless nights. Crypto scams are increasingly common and often involve fake trading platforms, phishing attacks, and misleading investment opportunities. In my desperation, a friend from the crypto community recommended Capital Crypto Recovery Service, known for helping victims recover lost or stolen funds. After doing some research and reading multiple positive reviews, I reached out to Capital Crypto Recovery. I provided all the necessary information—wallet addresses, transaction history, and communication logs. Their expert team responded immediately and began investigating. Using advanced blockchain tracking techniques, they were able to trace the stolen Dogecoin, identify the scammer’s wallet, and coordinate with relevant authorities to freeze the funds before they could be moved. Incredibly, within 24 hours, Capital Crypto Recovery successfully recovered the majority of my stolen crypto assets. I was beyond relieved and truly grateful. Their professionalism, transparency, and constant communication throughout the process gave me hope during a very difficult time. If you’ve been a victim of a crypto scam, I highly recommend them with full confidence contacting: Email: [email protected] Telegram: @Capitalcryptorecover Contact: [email protected] Call/Text: +1 (336) 390-6684 Website: https://recovercapital.wixsite.com/capital-crypto-rec-1

  • 25.06.26 21:13 Emilie Safi

    A fraudulent investment scheme operated by BTCMining.limited functions as a fake return scam. In this setup, scammers lure victims with false promises of high returns. Through manipulative tactics, they gain individuals' trust and convince them to invest, ultimately leading to financial loss. If you have ever faced a cyber threat or fallen victim to an online crypto scam and need to reach the authorities, I recommend contacting [email protected], [email protected], WhatsApp +19852969146, telegram @resqprofirm. They are a legitimate team that helps victims of online crypto scams using advanced tools.

  • 25.06.26 21:25 Emilie Safi

    So I ended up losing $38,000 to this platform. At first, they kept asking me to put in more money so I could get into my portfolio. I did that, but then they wouldn’t let me withdraw anything—just kept asking for more deposits. It got way too suspicious, so I stopped. I found this company called ResQProfirm on Google and told them what happened. They got in touch, asked me to walk them through everything, and I gave them all the proof I had. They did an amazing job tracking down my money and getting it back. Big thanks to them at [email protected] and on WhatsApp at +19852969146. Please be careful out there and always research before investing.

  • 26.06.26 01:04 robertalfred175

    CRYPTO SCAM RECOVERY SUCCESSFUL – A TESTIMONIAL OF LOST PASSWORD TO YOUR DIGITAL WALLET BACK. My name is Robert Alfred, Am from Australia. I’m sharing my experience in the hope that it helps others who have been victims of crypto scams. A few months ago, I fell victim to a fraudulent crypto investment scheme linked to a broker company. I had invested heavily during a time when Bitcoin prices were rising, thinking it was a good opportunity. Unfortunately, I was scammed out of $120,000 AUD and the broker denied me access to my digital wallet and assets. It was a devastating experience that caused many sleepless nights. Crypto scams are increasingly common and often involve fake trading platforms, phishing attacks, and misleading investment opportunities. In my desperation, a friend from the crypto community recommended Capital Crypto Recovery Service, known for helping victims recover lost or stolen funds. After doing some research and reading multiple positive reviews, I reached out to Capital Crypto Recovery. I provided all the necessary information—wallet addresses, transaction history, and communication logs. Their expert team responded immediately and began investigating. Using advanced blockchain tracking techniques, they were able to trace the stolen Dogecoin, identify the scammer’s wallet, and coordinate with relevant authorities to freeze the funds before they could be moved. Incredibly, within 24 hours, Capital Crypto Recovery successfully recovered the majority of my stolen crypto assets. I was beyond relieved and truly grateful. Their professionalism, transparency, and constant communication throughout the process gave me hope during a very difficult time. If you’ve been a victim of a crypto scam, I highly recommend them with full confidence contacting: Email: [email protected] Telegram: @Capitalcryptorecover Contact: [email protected] Call/Text: +1 (336) 390-6684 Website: https://recovercapital.wixsite.com/capital-crypto-rec-1

  • 26.06.26 01:04 robertalfred175

    CRYPTO SCAM RECOVERY SUCCESSFUL – A TESTIMONIAL OF LOST PASSWORD TO YOUR DIGITAL WALLET BACK. My name is Robert Alfred, Am from Australia. I’m sharing my experience in the hope that it helps others who have been victims of crypto scams. A few months ago, I fell victim to a fraudulent crypto investment scheme linked to a broker company. I had invested heavily during a time when Bitcoin prices were rising, thinking it was a good opportunity. Unfortunately, I was scammed out of $120,000 AUD and the broker denied me access to my digital wallet and assets. It was a devastating experience that caused many sleepless nights. Crypto scams are increasingly common and often involve fake trading platforms, phishing attacks, and misleading investment opportunities. In my desperation, a friend from the crypto community recommended Capital Crypto Recovery Service, known for helping victims recover lost or stolen funds. After doing some research and reading multiple positive reviews, I reached out to Capital Crypto Recovery. I provided all the necessary information—wallet addresses, transaction history, and communication logs. Their expert team responded immediately and began investigating. Using advanced blockchain tracking techniques, they were able to trace the stolen Dogecoin, identify the scammer’s wallet, and coordinate with relevant authorities to freeze the funds before they could be moved. Incredibly, within 24 hours, Capital Crypto Recovery successfully recovered the majority of my stolen crypto assets. I was beyond relieved and truly grateful. Their professionalism, transparency, and constant communication throughout the process gave me hope during a very difficult time. If you’ve been a victim of a crypto scam, I highly recommend them with full confidence contacting: Email: [email protected] Telegram: @Capitalcryptorecover Contact: [email protected] Call/Text: +1 (336) 390-6684 Website: https://recovercapital.wixsite.com/capital-crypto-rec-1

  • 26.06.26 02:48 Miriam Rocha

    I trusted this platform with $120,000 of my hard-earned money. Then they started asking for more deposits just so I could access my own portfolio. I paid, but every withdrawal request was denied. They kept pushing for more money. I finally stopped it just felt wrong. Desperate, I found ResQProfirm on Google. They didn't just hear me out; they truly listened. I shared all my proof, and they launched an investigation. Thanks to their hard work, they tracked and returned my funds. From the bottom of my heart, thank you to [email protected] and their WhatsApp +19852969146. Please stay safe and always verify a platform before investing

  • 26.06.26 02:52 Miško Bakić

    I got my $232,000 refund thanks to [email protected] and WhatsApp +19852969146. Highly recommended for anyone in a similar situation.

  • 26.06.26 02:56 Asunción Herrera

    A recovery of $48,330 was facilitated by [email protected]. Individuals who have experienced financial fraud may consider contacting this service.

  • 26.06.26 15:05 Riley Stephens

    If withdrawals keep getting denied, stay calm. I went through the same, and this firm helped me recover everything. Their assistance was outstanding. Contact: [ResQProFirm @Gmail|•|com], Telegram: ResQprofirm, WhatsApp: <+198> <5296> <9146>.

  • 26.06.26 15:09 Antonio Riley

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  • 28.06.26 00:37 kimberlyhebertt673

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  • 28.06.26 00:37 kimberlyhebertt673

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  • 29.06.26 11:57 Lisadonato0726

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  • 29.06.26 22:37 riley777

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  • 30.06.26 15:08 wendytaylor015

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  • 30.06.26 15:08 wendytaylor015

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  • 02.07.26 01:22 Lieneke Bonnema

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  • 02.07.26 01:26 Clara Morin

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  • 04.07.26 15:32 Fraddy Pual

    There are few companies I trust as much as FUNDSRETRIEVER. When I lost $653,000 in Ethereum to a ruthless scam, I thought my life would never be the same. The betrayal cut deep, but I refused to give up. I searched tirelessly for a legitimate way to recover what was stolen, and finally found FUNDSRETRIEVER—the most competent and compassionate recovery team I could have imagined. They handled my case with precision and care, and in the end, my entire ETH wallet was restored. More than the money, they gave me back my hope and happiness. I'm sharing my story because I want others to know that recovery is possible. If a scam has taken from you, don't hesitate—contact FUNDSRETRIEVER today. Email: FUNDSRETRIEVER1@ Gmail.com | WhatsApp: +1 603-512-1448 | Telegram: @FUNDSRETRIEVER

  • 05.07.26 14:44 lydiassmith567

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  • 05.07.26 14:44 lydiassmith567

    HIRE A HACKER YOUR STOLEN CRYPTO RECOVERY / BTC / USDT / ETH WITH THE HELP OF CAPITAL CRYPTO RECOVER. I want to share my experience publicly regarding cryptocurrency wallet recovery, I highly recommend you to contact CAPITAL CRYPTO RECOVER, a professional private investigator in the Bitcoin world. They have a certified expert security team specializing in Bitcoin Recovery Services and have helped many people worldwide recover their lost funds. My wife and I were defrauded by an online manipulator posing as an experienced crypto investment professional. We lost $9.2 Million Stolen BTC in cryptocurrency and were left feeling homeless. After spending hours searching for a reliable crypto recovery service, I discovered CAPITAL CRYPTO RECOVER online. By patiently explaining my situation to their team, I was able to recover all my funds. Remarkably, my money was returned to my wallet in less than 24 hours. I am extremely grateful to CAPITAL CRYPTO RECOVER for their excellent assistance—they truly were a godsend in my difficult situation. If you have fallen victim to a cryptocurrency scam, you can reach CAPITAL CRYPTO RECOVER through the following channels Email: [email protected] OR Call/Text: +1 (336) 390-6684 Contact: [email protected] Website: https://recovercapital.wixsite.com/capital-crypto-rec-1

  • 06.07.26 16:20 Olga Ognjanović

    Having trouble withdrawing funds from an investment platform? ResQprofirm provides fund recovery assistance for individuals seeking help with investment-related disputes. I reached out to them after experiencing problems with an investment platform, and I appreciated their professionalism and support throughout the process. If you're facing a similar situation, act promptly, keep records of your transactions and communications, and seek assistance from a qualified recovery service or the appropriate authorities. Contact: Email: [email protected] Telegram: @ResQprofirm WhatsApp: +1 985 296 9146

  • 06.07.26 16:31 Joseph Weigl

    Invest wisely and stay cautious. Don't be influenced by promises of unusually high returns or convincing sales pitches from brokers. I learned this the hard way after falling victim to an investment scam that promised huge profits. Fortunately, I acted quickly and reported the incident to a recovery firm for assistance. Contact: Email: [email protected] Telegram: @Resqprofirm WhatsApp: +1 985 296 9146

  • 06.07.26 16:33 Jaran Løvlien

    A heartfelt thank you to RESQPRO FIRM for their commitment and professionalism throughout the investigation of my case. Their team worked diligently and helped recover assets valued at $88,000, which were returned to my wallet. I truly appreciate their support, clear communication, and dedication, and I'm grateful for the assistance I received. Contact: Email: [email protected] Telegram: @Resqprofirm WhatsApp: +1 985 296 9146

  • 07.07.26 18:00 robertalfred175

    CRYPTO SCAM RECOVERY SUCCESSFUL – A TESTIMONIAL OF LOST PASSWORD TO YOUR DIGITAL WALLET BACK. My name is Robert Alfred, Am from Australia. I’m sharing my experience in the hope that it helps others who have been victims of crypto scams. A few months ago, I fell victim to a fraudulent crypto investment scheme linked to a broker company. I had invested heavily during a time when Bitcoin prices were rising, thinking it was a good opportunity. Unfortunately, I was scammed out of $120,000 AUD and the broker denied me access to my digital wallet and assets. It was a devastating experience that caused many sleepless nights. Crypto scams are increasingly common and often involve fake trading platforms, phishing attacks, and misleading investment opportunities. In my desperation, a friend from the crypto community recommended Capital Crypto Recovery Service, known for helping victims recover lost or stolen funds. After doing some research and reading multiple positive reviews, I reached out to Capital Crypto Recovery. I provided all the necessary information—wallet addresses, transaction history, and communication logs. Their expert team responded immediately and began investigating. Using advanced blockchain tracking techniques, they were able to trace the stolen Dogecoin, identify the scammer’s wallet, and coordinate with relevant authorities to freeze the funds before they could be moved. Incredibly, within 24 hours, Capital Crypto Recovery successfully recovered the majority of my stolen crypto assets. I was beyond relieved and truly grateful. Their professionalism, transparency, and constant communication throughout the process gave me hope during a very difficult time. If you’ve been a victim of a crypto scam, I highly recommend them with full confidence contacting: Email: [email protected] Telegram: @Capitalcryptorecover Contact: [email protected] Call/Text: +1 (336) 390-6684 Website: https://recovercapital.wixsite.com/capital-crypto-rec-1

  • 07.07.26 18:01 robertalfred175

    CRYPTO SCAM RECOVERY SUCCESSFUL – A TESTIMONIAL OF LOST PASSWORD TO YOUR DIGITAL WALLET BACK. My name is Robert Alfred, Am from Australia. I’m sharing my experience in the hope that it helps others who have been victims of crypto scams. A few months ago, I fell victim to a fraudulent crypto investment scheme linked to a broker company. I had invested heavily during a time when Bitcoin prices were rising, thinking it was a good opportunity. Unfortunately, I was scammed out of $120,000 AUD and the broker denied me access to my digital wallet and assets. It was a devastating experience that caused many sleepless nights. Crypto scams are increasingly common and often involve fake trading platforms, phishing attacks, and misleading investment opportunities. In my desperation, a friend from the crypto community recommended Capital Crypto Recovery Service, known for helping victims recover lost or stolen funds. After doing some research and reading multiple positive reviews, I reached out to Capital Crypto Recovery. I provided all the necessary information—wallet addresses, transaction history, and communication logs. Their expert team responded immediately and began investigating. Using advanced blockchain tracking techniques, they were able to trace the stolen Dogecoin, identify the scammer’s wallet, and coordinate with relevant authorities to freeze the funds before they could be moved. Incredibly, within 24 hours, Capital Crypto Recovery successfully recovered the majority of my stolen crypto assets. I was beyond relieved and truly grateful. Their professionalism, transparency, and constant communication throughout the process gave me hope during a very difficult time. If you’ve been a victim of a crypto scam, I highly recommend them with full confidence contacting: Email: [email protected] Telegram: @Capitalcryptorecover Contact: [email protected] Call/Text: +1 (336) 390-6684 Website: https://recovercapital.wixsite.com/capital-crypto-rec-1

  • 09.07.26 19:06 Toivo Walli

    I lost 8.56btc to a fake Bitcoin mining site, I tried withdrawing but couldn't approved my process, I reported to !R£SQPROFIRM! via °R£SQproFirm°àt°gmail•com° °tEL£°gram=R£SQprofirm °whaT°Zap+198°52°96°91°46

  • 09.07.26 19:10 Misty Alexander

    Ongoing messages demanding more money before approving withdrawals are a major red flag. Stop engaging and report the incident to a trusted re­covery team. For professional support, you can contact R£sQprofirm using °ResQproFirm°àt°g,*ma'il(•)¢m°, TEL£gram ResQprofirm, or |whaTZap| +1-985-296-9146.

  • 09.07.26 19:13 Clara Soto

    Anyone receiving continued requests for additional deposits from a scam platform should immediately cut off communication and submit the case to a reputable re­covery service for investigation. R£sQprofirm is a dependable firm you can reach at °ResQproFirm°àt°g,*ma'il(•)¢om°, TEL£gram ResQprofirm, or |whaTZap| +1-985-296-9146.

  • 12.07.26 03:30 Kora Baltacha

    Time is critical. Act now by reaching out to a reputable, seasoned recovery specialist who will guide you every step of the way. You'll need to submit transaction proof, scammer details, and any other useful information. Armed with this, the experts can trace and attempt to pull your money back from the scammers' hidden accounts or wallets. Best of all, R£sQprofirm provides recovery help without charging any upfront fees. Contact them immediately via Telegram @ResQprofirm, WhatsApp +19852969146, or email [email protected].

  • 12.07.26 03:33 Pahal Mathew

    It's important to move proactively by engaging an experienced recovery specialist. They will assist you throughout the process. To help them, provide: · Transaction evidence · Scammer information · Any additional relevant details The experts will then track and try to retrieve your funds from the scammers' hidden accounts or wallets. R£sQprofirm offers recovery assistance with no upfront fees. Contact: Telegram: @ResQprofirm WhatsApp: +19852969146 Email: [email protected]

  • 13.07.26 23:49 [email protected]

    One of the biggest concerns I have about cryptocurrency is the lack of regulation. It creates opportunities for scammers to invent convincing stories and fraudulent investment schemes. Unfortunately, some social media platforms continue to display these ads because they profit from them, even after users report them.I personally clicked on a Facebook advertisement for a company called Chickenfastmining and ended up losing more than $120,000 in a scam. I reported the ad, but nothing was done. Later, through a Reddit community, I found a recovery service called CYBERBERSPY that, in my personal experience, they helped me recover $110,000 of my lost funds. If you've been a victim of a cryptocurrency scam, don't lose hope. Explore your options carefully, and always verify the legitimacy of any recovery service before trusting them or paying any fees. Based on my own experience, CYBERBERSPY was helpful to me and i was able to recover my funds back, but I encourage everyone to do their own research before using any recovery service.i highly recommend: ([email protected])

  • 15.07.26 11:53 Sarah Green

    Thank you for showing that success is possible regardless of where someone starts. Your encouragement, valuable advice, and continuous support have inspired me throughout my $160,457k crypto investment recovery journey. I truly appreciate your kindness and dedication. Resqprofirm @gmail.com Telegram: Resqprofirm

  • 15.07.26 11:58 Lily Gagné

    I sincerely appreciate you for proving that anyone can overcome challenges and achieve success. Your unwavering support throughout my trading investment scam of $88,890 recovery journey has been truly inspiring, and your guidance and wisdom have meant a great deal to me. Thank you for everything ResQprofirm@ gmail.com, ResQprofirm on the telegram.

  • 16.07.26 21:38 patricialovick86

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  • 16.07.26 21:38 patricialovick86

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  • 04.08.26 11:05 Kisnoles

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  • 19.08.26 14:50 BAYER7043

    My account was locked, and I couldn’t access my own information until [email protected] +447476618364 whats?up? helped me recover it. This lady hacker was kind and professional, but this experience showed me how risky account lockouts can be. If you’re facing the same problem, do not panic consult her A. S. A. P. Be careful with recovery agents outchea, and research their name, business, and reviews before sharing any details. Never send passwords, security codes, banking information, or copies of your ID unless you’ve confirmed who you’re dealing with. Be wary of promises that sound too good to be true, especially claims that require little information or guarantee instant access with outrageous fees.

  • 20.08.26 11:32 michaeldavenport218

    I was recently scammed out of $53,000 by a fraudulent Bitcoin investment scheme, which added significant stress to my already difficult health issues, as I was also facing cancer surgery expenses. Desperate to recover my funds, I spent hours researching and consulting other victims, which led me to discover the excellent reputation of Capital Crypto Recover, I came across a Google post It was only after spending many hours researching and asking other victims for advice that I discovered Capital Crypto Recovery’s stellar reputation. I decided to contact them because of their successful recovery record and encouraging client testimonials. I had no idea that this would be the pivotal moment in my fight against cryptocurrency theft. Thanks to their expert team, I was able to recover my lost cryptocurrency back. The process was intricate, but Capital Crypto Recovery's commitment to utilizing the latest technology ensured a successful outcome. I highly recommend their services to anyone who has fallen victim to cryptocurrency fraud. For assistance contact [email protected] and on Telegram OR WhatsApp Number +1 (336)390-6684 via email: [email protected] you can visit his website: https://recovercapital.wixsite.com/capital-crypto-rec-1

  • 20.08.26 11:32 michaeldavenport218

    I was recently scammed out of $53,000 by a fraudulent Bitcoin investment scheme, which added significant stress to my already difficult health issues, as I was also facing cancer surgery expenses. Desperate to recover my funds, I spent hours researching and consulting other victims, which led me to discover the excellent reputation of Capital Crypto Recover, I came across a Google post It was only after spending many hours researching and asking other victims for advice that I discovered Capital Crypto Recovery’s stellar reputation. I decided to contact them because of their successful recovery record and encouraging client testimonials. I had no idea that this would be the pivotal moment in my fight against cryptocurrency theft. Thanks to their expert team, I was able to recover my lost cryptocurrency back. The process was intricate, but Capital Crypto Recovery's commitment to utilizing the latest technology ensured a successful outcome. I highly recommend their services to anyone who has fallen victim to cryptocurrency fraud. For assistance contact [email protected] and on Telegram OR WhatsApp Number +1 (336)390-6684 via email: [email protected] you can visit his website: https://recovercapital.wixsite.com/capital-crypto-rec-1

  • 23.08.26 20:02 leslieyee

    Excellent analysis by /dataviz! I was particularly struck by how strictly the order is defined: "data meaning first, color last" and how the validator actually adjusts the palette according to OKLCH, color blindness, and WCAG standards. These rules greatly improve the quality of charts. By the way, a similar approach to clean and legible charts is highly valued in trading—for example, on the ExpertOption platform, the interface and price visualization are designed to ensure information is read instantly and without unnecessary noise.

  • 25.08.26 13:44 lydiassmith567

    HIRE A HACKER YOUR STOLEN CRYPTO RECOVERY / BTC / USDT / ETH WITH THE HELP OF CAPITAL CRYPTO RECOVER. I want to share my experience publicly regarding cryptocurrency wallet recovery, I highly recommend you to contact CAPITAL CRYPTO RECOVER, a professional private investigator in the Bitcoin world. They have a certified expert security team specializing in Bitcoin Recovery Services and have helped many people worldwide recover their lost funds. My wife and I were defrauded by an online manipulator posing as an experienced crypto investment professional. We lost $9.2 Million Stolen BTC in cryptocurrency and were left feeling homeless. After spending hours searching for a reliable crypto recovery service, I discovered CAPITAL CRYPTO RECOVER online. By patiently explaining my situation to their team, I was able to recover all my funds. Remarkably, my money was returned to my wallet in less than 24 hours. I am extremely grateful to CAPITAL CRYPTO RECOVER for their excellent assistance—they truly were a godsend in my difficult situation. If you have fallen victim to a cryptocurrency scam, you can reach CAPITAL CRYPTO RECOVER through the following channels Email: [email protected] OR Call/WhatsApp: +1 (336) 390-6684 Contact: [email protected] Website: https://recovercapital.wixsite.com/capital-crypto-rec-1

  • 25.08.26 13:44 lydiassmith567

    HIRE A HACKER YOUR STOLEN CRYPTO RECOVERY / BTC / USDT / ETH WITH THE HELP OF CAPITAL CRYPTO RECOVER. I want to share my experience publicly regarding cryptocurrency wallet recovery, I highly recommend you to contact CAPITAL CRYPTO RECOVER, a professional private investigator in the Bitcoin world. They have a certified expert security team specializing in Bitcoin Recovery Services and have helped many people worldwide recover their lost funds. My wife and I were defrauded by an online manipulator posing as an experienced crypto investment professional. We lost $9.2 Million Stolen BTC in cryptocurrency and were left feeling homeless. After spending hours searching for a reliable crypto recovery service, I discovered CAPITAL CRYPTO RECOVER online. By patiently explaining my situation to their team, I was able to recover all my funds. Remarkably, my money was returned to my wallet in less than 24 hours. I am extremely grateful to CAPITAL CRYPTO RECOVER for their excellent assistance—they truly were a godsend in my difficult situation. If you have fallen victim to a cryptocurrency scam, you can reach CAPITAL CRYPTO RECOVER through the following channels Email: [email protected] OR Call/WhatsApp: +1 (336) 390-6684 Contact: [email protected] Website: https://recovercapital.wixsite.com/capital-crypto-rec-1

  • 30.08.26 15:37 [email protected]

    Discovering I had been defrauded, I searched online for services claiming to recover stolen ETH. I contacted several companies, but none succeeded. Although some claimed they could trace assets or recover funds, I could not verify their success or recover my money. I later found SYLVESTER BRYANT Recovery through Google. After contacting him, he recovered 450,000,00. He can be reached at [email protected] or WhatsApp at +1 512 577 7957.

  • 30.08.26 15:37 [email protected]

    Discovering I had been defrauded, I searched online for services claiming to recover stolen ETH. I contacted several companies, but none succeeded. Although some claimed they could trace assets or recover funds, I could not verify their success or recover my money. I later found SYLVESTER BRYANT Recovery through Google. After contacting him, he recovered 450,000,00. He can be reached at [email protected] or WhatsApp at +1 512 577 7957.

  • 01.09.26 11:16 lisawerth897

    My Experience With Cryptocurrency — CAPITAL CRYPTO RECOVER I lost over $82,000 in Bitcoin after falling victim to a fraudulent online investment scheme. After realizing I had been scammed, I spent considerable time researching possible ways to recover my funds. During my research, I came across CAPITAL CRYPTO RECOVER and decided to contact them after reading their reported success record and encouraging client positive reviews and testimonials. Their team guided me through the recovery process, and I was grateful to successfully recover my lost cryptocurrency. The experience was challenging, but I appreciated the assistance and support I received throughout the process. I’m sharing my experience in the hope that it may encourage other victims to carefully research their options and verify any recovery service before proceeding. I will forever be thankful to you CAPITAL CRYPTO RECOVER 📧 [email protected] 🌐 Website: recovercapital.wixsite.com/capital-crypto-rec-1 📧 [email protected] 📞 Call/WhatsApp: +1 (336) 390-6684

  • 01.09.26 11:16 lisawerth897

    My Experience With Cryptocurrency — CAPITAL CRYPTO RECOVER I lost over $82,000 in Bitcoin after falling victim to a fraudulent online investment scheme. After realizing I had been scammed, I spent considerable time researching possible ways to recover my funds. During my research, I came across CAPITAL CRYPTO RECOVER and decided to contact them after reading their reported success record and encouraging client positive reviews and testimonials. Their team guided me through the recovery process, and I was grateful to successfully recover my lost cryptocurrency. The experience was challenging, but I appreciated the assistance and support I received throughout the process. I’m sharing my experience in the hope that it may encourage other victims to carefully research their options and verify any recovery service before proceeding. I will forever be thankful to you CAPITAL CRYPTO RECOVER 📧 [email protected] 🌐 Website: recovercapital.wixsite.com/capital-crypto-rec-1 📧 [email protected] 📞 Call/WhatsApp: +1 (336) 390-6684

  • 01.09.26 17:34 Garry42

    Really crazy world. These fraudsters go at any length to steal your hard earned funds. I have been a victim of a bitcoin scam about 7 months back. A Con artist gained access to my cashapp account through a phishing scam. They stole $409,000. I was really devastated. I did everything to get back my funds by contacting the FBI but they claimed there was nothing they could do. A friend told me about a recovery expert. He helps fight against various phishing and investment scams and they were able to help trace and recover my funds even though it took over 2 days. you can reach out to him through recoverydarek@gmail. com . I can guarantee his services are still active.

  • 01.09.26 17:34 Garry42

    Really crazy world. These fraudsters go at any length to steal your hard earned funds. I have been a victim of a bitcoin scam about 7 months back. A Con artist gained access to my cashapp account through a phishing scam. They stole $409,000. I was really devastated. I did everything to get back my funds by contacting the FBI but they claimed there was nothing they could do. A friend told me about a recovery expert. He helps fight against various phishing and investment scams and they were able to help trace and recover my funds even though it took over 2 days. you can reach out to him through recoverydarek@gmail. com . I can guarantee his services are still active.

  • 02.09.26 03:43 kimberlyhebertt6877

    I invested in bitcoin trading After losing $78.4 USDT) linked to a romance fraud scam worth of cryptocurrency through an online investment platform and later discovered it was a scam. After extensive research for recovery options, I contacted CAPITAL CRYPTO RECOVER based on positive client reviews and recommendations. Their professional security team guided me through the recovery process using advanced technology, and I was able to recover my lost cryptocurrency successfully. I am truly grateful for their support and assistance during such a difficult experience. I will advise you to contact CAPITAL CRYPTO RECOVER helped me recover my funds. For anyone facing similar issues, Website: https://recovercapital.wixsite.com/capital-crypto-rec-1 Email: [email protected] Telegram: @Capitalcryptorecover Contact: [email protected] WhatsApp/Text Number: +1 (336) 390-6684

  • 02.09.26 03:43 kimberlyhebertt6877

    I invested in bitcoin trading After losing $78.4 USDT) linked to a romance fraud scam worth of cryptocurrency through an online investment platform and later discovered it was a scam. After extensive research for recovery options, I contacted CAPITAL CRYPTO RECOVER based on positive client reviews and recommendations. Their professional security team guided me through the recovery process using advanced technology, and I was able to recover my lost cryptocurrency successfully. I am truly grateful for their support and assistance during such a difficult experience. I will advise you to contact CAPITAL CRYPTO RECOVER helped me recover my funds. For anyone facing similar issues, Website: https://recovercapital.wixsite.com/capital-crypto-rec-1 Email: [email protected] Telegram: @Capitalcryptorecover Contact: [email protected] WhatsApp/Text Number: +1 (336) 390-6684

  • 04.09.26 21:51 Kovengray

    Recovering your lost investment funds as the case might be, is not what you can do alone, you’d require the service of a trained recovery specialist. A recovery specialist is a person or a group of people who are well equipped to work around the brokerage network. They have vast knowledge about the whole network and have the right software and private keys to follow any transaction. I was ripped off trading online to an investment broker, good thing I got every penny back through the help of Gavin ray he’s a genius Contact : Gavinray78 at gmail com or WhatsApp +1 352 322 2096 It is also important to be patient and really calm during the process.

  • 05.09.26 21:38 [email protected]

    I invested 45,000  Euro, and later aggreviated to 198,000 Euro.  I requested  to place ‎Withdrawal of my funds to be paid to my Bank account. But nothing happened I was subjected to pay more fee until I can get my funds on my account, i got in touch with Theodore ryan here on this platform who had helped a lot of people, I followed all instructions and he legally got back my withheld funds, I got threatened by the company that if I don’t pay they will get my account frozen, all thanks to Theodore ryan and I highly recommend him to anyone dealing with an unregulated broker company… contact him on his Gmail - theodoreryan318@  gmail .  com

  • 09.09.26 21:31 lisawerth897

    My Experience With Cryptocurrency — CAPITAL CRYPTO RECOVER I lost over $82,000 in Bitcoin after falling victim to a fraudulent online investment scheme. After realizing I had been scammed, I spent considerable time researching possible ways to recover my funds. During my research, I came across CAPITAL CRYPTO RECOVER and decided to contact them after reading their reported success record and encouraging client positive reviews and testimonials. Their team guided me through the recovery process, and I was grateful to successfully recover my lost cryptocurrency. The experience was challenging, but I appreciated the assistance and support I received throughout the process. I’m sharing my experience in the hope that it may encourage other victims to carefully research their options and verify any recovery service before proceeding. I will forever be thankful to you CAPITAL CRYPTO RECOVER 📧 [email protected] 🌐 Website: recovercapital.wixsite.com/capital-crypto-rec-1 📧 [email protected] 📞 Call/WhatsApp: +1 (336) 390-6684

  • 09.09.26 21:31 lisawerth897

    My Experience With Cryptocurrency — CAPITAL CRYPTO RECOVER I lost over $82,000 in Bitcoin after falling victim to a fraudulent online investment scheme. After realizing I had been scammed, I spent considerable time researching possible ways to recover my funds. During my research, I came across CAPITAL CRYPTO RECOVER and decided to contact them after reading their reported success record and encouraging client positive reviews and testimonials. Their team guided me through the recovery process, and I was grateful to successfully recover my lost cryptocurrency. The experience was challenging, but I appreciated the assistance and support I received throughout the process. I’m sharing my experience in the hope that it may encourage other victims to carefully research their options and verify any recovery service before proceeding. I will forever be thankful to you CAPITAL CRYPTO RECOVER 📧 [email protected] 🌐 Website: recovercapital.wixsite.com/capital-crypto-rec-1 📧 [email protected] 📞 Call/WhatsApp: +1 (336) 390-6684

  • 09.09.26 23:22 Fraddy Pual

    Hearing that these individuals are focusing on other people makes me very sad. I had a similar situation with them and lost a lot of money, but after learning about (Cruxcipherteam @ proton DoT me), whataqq:+168160-15021, telegram: @Cruxcipherteam I was able to get my money back. It's critical that we all be watchful and keep reporting these occurrences.

  • 11.09.26 03:23 kimberlyhebertt6877

    I invested in bitcoin trading After losing $78.4 USDT) linked to a romance fraud scam worth of cryptocurrency through an online investment platform and later discovered it was a scam. After extensive research for recovery options, I contacted CAPITAL CRYPTO RECOVER based on positive client reviews and recommendations. Their professional security team guided me through the recovery process using advanced technology, and I was able to recover my lost cryptocurrency successfully. I am truly grateful for their support and assistance during such a difficult experience. I will advise you to contact CAPITAL CRYPTO RECOVER helped me recover my funds. For anyone facing similar issues, Website: https://recovercapital.wixsite.com/capital-crypto-rec-1 Email: [email protected] Telegram: @Capitalcryptorecover Contact: [email protected] WhatsApp/Text Number: +1 (336) 390-6684

  • 11.09.26 03:23 kimberlyhebertt6877

    I invested in bitcoin trading After losing $78.4 USDT) linked to a romance fraud scam worth of cryptocurrency through an online investment platform and later discovered it was a scam. After extensive research for recovery options, I contacted CAPITAL CRYPTO RECOVER based on positive client reviews and recommendations. Their professional security team guided me through the recovery process using advanced technology, and I was able to recover my lost cryptocurrency successfully. I am truly grateful for their support and assistance during such a difficult experience. I will advise you to contact CAPITAL CRYPTO RECOVER helped me recover my funds. For anyone facing similar issues, Website: https://recovercapital.wixsite.com/capital-crypto-rec-1 Email: [email protected] Telegram: @Capitalcryptorecover Contact: [email protected] WhatsApp/Text Number: +1 (336) 390-6684

  • 15.09.26 03:35 elioduncan

    I fell victim to a freelance web development contract scam that ultimately cost me CAD 4,000. It all started when I came across a job posting on Indeed Canada, a popular online job portal. The position seemed perfect: a freelance web developer role for an established company looking for someone to design and build a fully functional e-commerce website. The job promised a high payment of CAD 20,000 upon successful completion, which sounded like a great opportunity for me to gain experience and earn decent pay.The employer, who introduced himself as a project manager from a "well-known" tech company, was very persuasive and professional in our initial communication. He explained that the project involved developing a user-friendly, responsive online store for their client and that they had a strict timeline to meet. He assured me that the payment would be made promptly after completing the tasks. However, before starting the work, he told me that I would need to pay an upfront fee of CAD 4,000 to cover certain software tools and licensing fees required for the project. This was supposedly a part of their company policy for freelance contractors, ensuring access to their premium resources. The idea of working on a professional project, coupled with the promise of a substantial payout, convinced me to pay the upfront fee.As soon as I made the payment, the project manager became increasingly difficult to reach. He initially responded to my emails and provided some vague instructions on what the project would entail, but as time went on, communication slowed to a complete halt. I never received the required tools or any proper project details. My emails went unanswered, and any attempts to contact the company were met with silence. After waiting for weeks, I realized that I had been scammed.Desperate to recover my money, I turned to TechY Force Cyber Retrieval, a service that specializes in helping victims of online scams. They helped me track the payment and took legal steps to pursue the fraudsters. Through their guidance, I was able to recover the full CAD 4,000. TechY Force Cyber Retrieval worked with my bank to reverse the transaction and liaised with the authorities to trace the scammer's details.This was a hard lesson, and I now know to be highly cautious about online job offers that require upfront payments. It is crucial to research companies thoroughly and avoid any job that seems too good to be true, especially when it involves paying money upfront. WhatsApp https://wa.link/2x6ktp Mail. [email protected]

  • 15.09.26 15:45 lydiassmith567

    HIRE A HACKER YOUR STOLEN CRYPTO RECOVERY / BTC / USDT / ETH WITH THE HELP OF CAPITAL CRYPTO RECOVER. I want to share my experience publicly regarding cryptocurrency wallet recovery, I highly recommend you to contact CAPITAL CRYPTO RECOVER, a professional private investigator in the Bitcoin world. They have a certified expert security team specializing in Bitcoin Recovery Services and have helped many people worldwide recover their lost funds. My wife and I were defrauded by an online manipulator posing as an experienced crypto investment professional. We lost $9.2 Million Stolen BTC in cryptocurrency and were left feeling homeless. After spending hours searching for a reliable crypto recovery service, I discovered CAPITAL CRYPTO RECOVER online. By patiently explaining my situation to their team, I was able to recover all my funds. Remarkably, my money was returned to my wallet in less than 24 hours. I am extremely grateful to CAPITAL CRYPTO RECOVER for their excellent assistance—they truly were a godsend in my difficult situation. If you have fallen victim to a cryptocurrency scam, you can reach CAPITAL CRYPTO RECOVER through the following channels Email: [email protected] OR Call/WhatsApp: +1 (336) 390-6684 Contact: [email protected] Website: https://recovercapital.wixsite.com/capital-crypto-rec-1

  • 15.09.26 15:45 lydiassmith567

    HIRE A HACKER YOUR STOLEN CRYPTO RECOVERY / BTC / USDT / ETH WITH THE HELP OF CAPITAL CRYPTO RECOVER. I want to share my experience publicly regarding cryptocurrency wallet recovery, I highly recommend you to contact CAPITAL CRYPTO RECOVER, a professional private investigator in the Bitcoin world. They have a certified expert security team specializing in Bitcoin Recovery Services and have helped many people worldwide recover their lost funds. My wife and I were defrauded by an online manipulator posing as an experienced crypto investment professional. We lost $9.2 Million Stolen BTC in cryptocurrency and were left feeling homeless. After spending hours searching for a reliable crypto recovery service, I discovered CAPITAL CRYPTO RECOVER online. By patiently explaining my situation to their team, I was able to recover all my funds. Remarkably, my money was returned to my wallet in less than 24 hours. I am extremely grateful to CAPITAL CRYPTO RECOVER for their excellent assistance—they truly were a godsend in my difficult situation. If you have fallen victim to a cryptocurrency scam, you can reach CAPITAL CRYPTO RECOVER through the following channels Email: [email protected] OR Call/WhatsApp: +1 (336) 390-6684 Contact: [email protected] Website: https://recovercapital.wixsite.com/capital-crypto-rec-1

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