74

我的应用程序:我正在尝试旋转图像(使用 OpenCV 和 Python)

旋转图像

目前,我开发了以下代码,它旋转输入图像,用黑色边框填充它,给我 A。我想要的是 B - 旋转图像中最大可能的区域裁剪窗口。我称其为轴对齐的边界框。

这与Rotate 和 crop基本相同,但是我无法得到该问题的答案。此外,该答案显然仅对方形图像有效。我的图像是矩形的。

代码给A:

import cv2
import numpy as np


def getTranslationMatrix2d(dx, dy):
    """
    Returns a numpy affine transformation matrix for a 2D translation of
    (dx, dy)
    """
    return np.matrix([[1, 0, dx], [0, 1, dy], [0, 0, 1]])


def rotateImage(image, angle):
    """
    Rotates the given image about it's centre
    """

    image_size = (image.shape[1], image.shape[0])
    image_center = tuple(np.array(image_size) / 2)

    rot_mat = np.vstack([cv2.getRotationMatrix2D(image_center, angle, 1.0), [0, 0, 1]])
    trans_mat = np.identity(3)

    w2 = image_size[0] * 0.5
    h2 = image_size[1] * 0.5

    rot_mat_notranslate = np.matrix(rot_mat[0:2, 0:2])

    tl = (np.array([-w2, h2]) * rot_mat_notranslate).A[0]
    tr = (np.array([w2, h2]) * rot_mat_notranslate).A[0]
    bl = (np.array([-w2, -h2]) * rot_mat_notranslate).A[0]
    br = (np.array([w2, -h2]) * rot_mat_notranslate).A[0]

    x_coords = [pt[0] for pt in [tl, tr, bl, br]]
    x_pos = [x for x in x_coords if x > 0]
    x_neg = [x for x in x_coords if x < 0]

    y_coords = [pt[1] for pt in [tl, tr, bl, br]]
    y_pos = [y for y in y_coords if y > 0]
    y_neg = [y for y in y_coords if y < 0]

    right_bound = max(x_pos)
    left_bound = min(x_neg)
    top_bound = max(y_pos)
    bot_bound = min(y_neg)

    new_w = int(abs(right_bound - left_bound))
    new_h = int(abs(top_bound - bot_bound))
    new_image_size = (new_w, new_h)

    new_midx = new_w * 0.5
    new_midy = new_h * 0.5

    dx = int(new_midx - w2)
    dy = int(new_midy - h2)

    trans_mat = getTranslationMatrix2d(dx, dy)
    affine_mat = (np.matrix(trans_mat) * np.matrix(rot_mat))[0:2, :]
    result = cv2.warpAffine(image, affine_mat, new_image_size, flags=cv2.INTER_LINEAR)

    return result
4

12 回答 12

108

这个解决方案/实现背后的数学相当于这个类比问题的解决方案,但公式被简化并避免了奇异性。这是与其他解决方案具有相同界面的 python 代码largest_rotated_rect,但在几乎所有情况下都提供了更大的区域(始终被证明是最佳的):

def rotatedRectWithMaxArea(w, h, angle):
  """
  Given a rectangle of size wxh that has been rotated by 'angle' (in
  radians), computes the width and height of the largest possible
  axis-aligned rectangle (maximal area) within the rotated rectangle.
  """
  if w <= 0 or h <= 0:
    return 0,0

  width_is_longer = w >= h
  side_long, side_short = (w,h) if width_is_longer else (h,w)

  # since the solutions for angle, -angle and 180-angle are all the same,
  # if suffices to look at the first quadrant and the absolute values of sin,cos:
  sin_a, cos_a = abs(math.sin(angle)), abs(math.cos(angle))
  if side_short <= 2.*sin_a*cos_a*side_long or abs(sin_a-cos_a) < 1e-10:
    # half constrained case: two crop corners touch the longer side,
    #   the other two corners are on the mid-line parallel to the longer line
    x = 0.5*side_short
    wr,hr = (x/sin_a,x/cos_a) if width_is_longer else (x/cos_a,x/sin_a)
  else:
    # fully constrained case: crop touches all 4 sides
    cos_2a = cos_a*cos_a - sin_a*sin_a
    wr,hr = (w*cos_a - h*sin_a)/cos_2a, (h*cos_a - w*sin_a)/cos_2a

  return wr,hr

这是该功能与其他解决方案的比较:

>>> wl,hl = largest_rotated_rect(1500,500,math.radians(20))
>>> print (wl,hl),', area=',wl*hl
(828.2888697391496, 230.61639227890998) , area= 191016.990904
>>> wm,hm = rotatedRectWithMaxArea(1500,500,math.radians(20))
>>> print (wm,hm),', area=',wm*hm
(730.9511000407718, 266.044443118978) , area= 194465.478358

angle旋转图像的[0,pi/2[边界框中的角度(宽度,w高度h)具有以下尺寸:

  • 宽度w_bb = w*cos_a + h*sin_a
  • 高度h_bb = w*sin_a + h*cos_a

如果w_rh_r计算出的裁剪图像的最佳宽度和高度,则边界框的插图为:

  • 水平方向:(w_bb-w_r)/2
  • 垂直方向:(h_bb-h_r)/2

证明:

寻找具有最大面积的两条平行线之间的轴对齐矩形是一个具有一个参数的优化问题,例如x,如下图所示: 动画参数

s表示两条平行线之间的距离(它将变成旋转矩形的较短边)。那么广受欢迎的矩形的边a,分别与, ,b有一个恒定的比率,即 x = a sin α 和 (sx) = b cos α:xs-x

在此处输入图像描述

所以最大化面积a*b意味着最大化x*(s-x)。因为我们知道直角三角形的“高度定理” x*(s-x) = p*q = h*h。因此在 处达到最大面积x = s-x = s/2,即平行线之间的两个角 E、G 在中线上:

在此处输入图像描述

此解决方案仅在此最大矩形适合旋转矩形时才有效。因此,对角线EG不得长于l旋转矩形的另一边。自从

EG = AF + DH = s/2*(cot α + tan α) = s/(2 sin α cos α) = s/sin 2*α

我们有条件 s ≤ l sin 2 α,其中 s 和 l 是旋转矩形的短边和长边。

在 s > l sin 2 α 的情况下,该参数x必须小于(小于 s/2)并且 st 所需矩形的所有角都位于旋转矩形的一侧。这导致方程

x*cot α + (sx)*tan α = l

给出 x = sin α*(l cos α - s sin α)/cos 2*α。从 a = x/sin α 和 b = (sx)/cos α 我们得到上面使用的公式。

于 2013-05-27T18:40:05.273 回答
32

因此,在研究了许多声称的解决方案之后,我终于找到了一种可行的方法;AndriMagnus Hoff关于计算旋转矩形中的最大矩形的答案。

下面的 Python 代码包含感兴趣的方法 - largest_rotated_rect- 和一个简短的演示。

import math
import cv2
import numpy as np


def rotate_image(image, angle):
    """
    Rotates an OpenCV 2 / NumPy image about it's centre by the given angle
    (in degrees). The returned image will be large enough to hold the entire
    new image, with a black background
    """

    # Get the image size
    # No that's not an error - NumPy stores image matricies backwards
    image_size = (image.shape[1], image.shape[0])
    image_center = tuple(np.array(image_size) / 2)

    # Convert the OpenCV 3x2 rotation matrix to 3x3
    rot_mat = np.vstack(
        [cv2.getRotationMatrix2D(image_center, angle, 1.0), [0, 0, 1]]
    )

    rot_mat_notranslate = np.matrix(rot_mat[0:2, 0:2])

    # Shorthand for below calcs
    image_w2 = image_size[0] * 0.5
    image_h2 = image_size[1] * 0.5

    # Obtain the rotated coordinates of the image corners
    rotated_coords = [
        (np.array([-image_w2,  image_h2]) * rot_mat_notranslate).A[0],
        (np.array([ image_w2,  image_h2]) * rot_mat_notranslate).A[0],
        (np.array([-image_w2, -image_h2]) * rot_mat_notranslate).A[0],
        (np.array([ image_w2, -image_h2]) * rot_mat_notranslate).A[0]
    ]

    # Find the size of the new image
    x_coords = [pt[0] for pt in rotated_coords]
    x_pos = [x for x in x_coords if x > 0]
    x_neg = [x for x in x_coords if x < 0]

    y_coords = [pt[1] for pt in rotated_coords]
    y_pos = [y for y in y_coords if y > 0]
    y_neg = [y for y in y_coords if y < 0]

    right_bound = max(x_pos)
    left_bound = min(x_neg)
    top_bound = max(y_pos)
    bot_bound = min(y_neg)

    new_w = int(abs(right_bound - left_bound))
    new_h = int(abs(top_bound - bot_bound))

    # We require a translation matrix to keep the image centred
    trans_mat = np.matrix([
        [1, 0, int(new_w * 0.5 - image_w2)],
        [0, 1, int(new_h * 0.5 - image_h2)],
        [0, 0, 1]
    ])

    # Compute the tranform for the combined rotation and translation
    affine_mat = (np.matrix(trans_mat) * np.matrix(rot_mat))[0:2, :]

    # Apply the transform
    result = cv2.warpAffine(
        image,
        affine_mat,
        (new_w, new_h),
        flags=cv2.INTER_LINEAR
    )

    return result


def largest_rotated_rect(w, h, angle):
    """
    Given a rectangle of size wxh that has been rotated by 'angle' (in
    radians), computes the width and height of the largest possible
    axis-aligned rectangle within the rotated rectangle.

    Original JS code by 'Andri' and Magnus Hoff from Stack Overflow

    Converted to Python by Aaron Snoswell
    """

    quadrant = int(math.floor(angle / (math.pi / 2))) & 3
    sign_alpha = angle if ((quadrant & 1) == 0) else math.pi - angle
    alpha = (sign_alpha % math.pi + math.pi) % math.pi

    bb_w = w * math.cos(alpha) + h * math.sin(alpha)
    bb_h = w * math.sin(alpha) + h * math.cos(alpha)

    gamma = math.atan2(bb_w, bb_w) if (w < h) else math.atan2(bb_w, bb_w)

    delta = math.pi - alpha - gamma

    length = h if (w < h) else w

    d = length * math.cos(alpha)
    a = d * math.sin(alpha) / math.sin(delta)

    y = a * math.cos(gamma)
    x = y * math.tan(gamma)

    return (
        bb_w - 2 * x,
        bb_h - 2 * y
    )


def crop_around_center(image, width, height):
    """
    Given a NumPy / OpenCV 2 image, crops it to the given width and height,
    around it's centre point
    """

    image_size = (image.shape[1], image.shape[0])
    image_center = (int(image_size[0] * 0.5), int(image_size[1] * 0.5))

    if(width > image_size[0]):
        width = image_size[0]

    if(height > image_size[1]):
        height = image_size[1]

    x1 = int(image_center[0] - width * 0.5)
    x2 = int(image_center[0] + width * 0.5)
    y1 = int(image_center[1] - height * 0.5)
    y2 = int(image_center[1] + height * 0.5)

    return image[y1:y2, x1:x2]


def demo():
    """
    Demos the largest_rotated_rect function
    """

    image = cv2.imread("lenna_rectangle.png")
    image_height, image_width = image.shape[0:2]

    cv2.imshow("Original Image", image)

    print "Press [enter] to begin the demo"
    print "Press [q] or Escape to quit"

    key = cv2.waitKey(0)
    if key == ord("q") or key == 27:
        exit()

    for i in np.arange(0, 360, 0.5):
        image_orig = np.copy(image)
        image_rotated = rotate_image(image, i)
        image_rotated_cropped = crop_around_center(
            image_rotated,
            *largest_rotated_rect(
                image_width,
                image_height,
                math.radians(i)
            )
        )

        key = cv2.waitKey(2)
        if(key == ord("q") or key == 27):
            exit()

        cv2.imshow("Original Image", image_orig)
        cv2.imshow("Rotated Image", image_rotated)
        cv2.imshow("Cropped Image", image_rotated_cropped)

    print "Done"


if __name__ == "__main__":
    demo()

图像旋转演示

只需将此图像(裁剪以证明它适用于非方形图像)放在与上述文件相同的目录中,然后运行它。

于 2013-05-27T09:39:04.580 回答
15

祝贺伟大的工作!我想将 OpenCV 中的代码与 C++ 库一起使用,因此我进行了以下转换。也许这种方法可能对其他人有所帮助。

#include <iostream>
#include <opencv.hpp>

#define PI 3.14159265359

using namespace std;

double degree_to_radian(double angle)
{
    return angle * PI / 180;
}

cv::Mat rotate_image (cv::Mat image, double angle)
{
    // Rotates an OpenCV 2 image about its centre by the given angle
    // (in radians). The returned image will be large enough to hold the entire
    // new image, with a black background

    cv::Size image_size = cv::Size(image.rows, image.cols);
    cv::Point image_center = cv::Point(image_size.height/2, image_size.width/2);

    // Convert the OpenCV 3x2 matrix to 3x3
    cv::Mat rot_mat = cv::getRotationMatrix2D(image_center, angle, 1.0);
    double row[3] = {0.0, 0.0, 1.0};
    cv::Mat new_row = cv::Mat(1, 3, rot_mat.type(), row);
    rot_mat.push_back(new_row);


    double slice_mat[2][2] = {
        {rot_mat.col(0).at<double>(0), rot_mat.col(1).at<double>(0)},
        {rot_mat.col(0).at<double>(1), rot_mat.col(1).at<double>(1)}
    };

    cv::Mat rot_mat_nontranslate = cv::Mat(2, 2, rot_mat.type(), slice_mat);

    double image_w2 = image_size.width * 0.5;
    double image_h2 = image_size.height * 0.5;

    // Obtain the rotated coordinates of the image corners
    std::vector<cv::Mat> rotated_coords;

    double image_dim_d_1[2] = { -image_h2, image_w2 };
    cv::Mat image_dim = cv::Mat(1, 2, rot_mat.type(), image_dim_d_1);
    rotated_coords.push_back(cv::Mat(image_dim * rot_mat_nontranslate));


    double image_dim_d_2[2] = { image_h2, image_w2 };
    image_dim = cv::Mat(1, 2, rot_mat.type(), image_dim_d_2);
    rotated_coords.push_back(cv::Mat(image_dim * rot_mat_nontranslate));


    double image_dim_d_3[2] = { -image_h2, -image_w2 };
    image_dim = cv::Mat(1, 2, rot_mat.type(), image_dim_d_3);
    rotated_coords.push_back(cv::Mat(image_dim * rot_mat_nontranslate));


    double image_dim_d_4[2] = { image_h2, -image_w2 };
    image_dim = cv::Mat(1, 2, rot_mat.type(), image_dim_d_4);
    rotated_coords.push_back(cv::Mat(image_dim * rot_mat_nontranslate));


    // Find the size of the new image
    vector<double> x_coords, x_pos, x_neg;
    for (int i = 0; i < rotated_coords.size(); i++)
    {
        double pt = rotated_coords[i].col(0).at<double>(0);
        x_coords.push_back(pt);
        if (pt > 0)
            x_pos.push_back(pt);
        else
            x_neg.push_back(pt);
    }

    vector<double> y_coords, y_pos, y_neg;
    for (int i = 0; i < rotated_coords.size(); i++)
    {
        double pt = rotated_coords[i].col(1).at<double>(0);
        y_coords.push_back(pt);
        if (pt > 0)
            y_pos.push_back(pt);
        else
            y_neg.push_back(pt);
    }


    double right_bound = *max_element(x_pos.begin(), x_pos.end());
    double left_bound = *min_element(x_neg.begin(), x_neg.end());
    double top_bound = *max_element(y_pos.begin(), y_pos.end());
    double bottom_bound = *min_element(y_neg.begin(), y_neg.end());

    int new_w = int(abs(right_bound - left_bound));
    int new_h = int(abs(top_bound - bottom_bound));

    // We require a translation matrix to keep the image centred
    double trans_mat[3][3] = {
        {1, 0, int(new_w * 0.5 - image_w2)},
        {0, 1, int(new_h * 0.5 - image_h2)},
        {0, 0, 1},
    };


    // Compute the transform for the combined rotation and translation
    cv::Mat aux_affine_mat = (cv::Mat(3, 3, rot_mat.type(), trans_mat) * rot_mat);
    cv::Mat affine_mat = cv::Mat(2, 3, rot_mat.type(), NULL);
    affine_mat.push_back(aux_affine_mat.row(0));
    affine_mat.push_back(aux_affine_mat.row(1));

    // Apply the transform
    cv::Mat output;
    cv::warpAffine(image, output, affine_mat, cv::Size(new_h, new_w), cv::INTER_LINEAR);

    return output;
}

cv::Size largest_rotated_rect(int h, int w, double angle)
{
    // Given a rectangle of size wxh that has been rotated by 'angle' (in
    // radians), computes the width and height of the largest possible
    // axis-aligned rectangle within the rotated rectangle.

    // Original JS code by 'Andri' and Magnus Hoff from Stack Overflow

    // Converted to Python by Aaron Snoswell (https://stackoverflow.com/questions/16702966/rotate-image-and-crop-out-black-borders)
    // Converted to C++ by Eliezer Bernart

    int quadrant = int(floor(angle/(PI/2))) & 3;
    double sign_alpha = ((quadrant & 1) == 0) ? angle : PI - angle;
    double alpha = fmod((fmod(sign_alpha, PI) + PI), PI);

    double bb_w = w * cos(alpha) + h * sin(alpha);
    double bb_h = w * sin(alpha) + h * cos(alpha);

    double gamma = w < h ? atan2(bb_w, bb_w) : atan2(bb_h, bb_h);

    double delta = PI - alpha - gamma;

    int length = w < h ? h : w;

    double d = length * cos(alpha);
    double a = d * sin(alpha) / sin(delta);
    double y = a * cos(gamma);
    double x = y * tan(gamma);

    return cv::Size(bb_w - 2 * x, bb_h - 2 * y);
}

// for those interested in the actual optimum - contributed by coproc
#include <algorithm>
cv::Size really_largest_rotated_rect(int h, int w, double angle)
{
  // Given a rectangle of size wxh that has been rotated by 'angle' (in
  // radians), computes the width and height of the largest possible
  // axis-aligned rectangle within the rotated rectangle.
  if (w <= 0 || h <= 0)
    return cv::Size(0,0);

  bool width_is_longer = w >= h;
  int side_long = w, side_short = h;
  if (!width_is_longer)
    std::swap(side_long, side_short);

  // since the solutions for angle, -angle and pi-angle are all the same,
  // it suffices to look at the first quadrant and the absolute values of sin,cos:
  double sin_a = fabs(sin(angle)), cos_a = fabs(cos(angle));
  double wr,hr;
  if (side_short <= 2.*sin_a*cos_a*side_long)
  {
    // half constrained case: two crop corners touch the longer side,
    // the other two corners are on the mid-line parallel to the longer line
    double x = 0.5*side_short;
    wr = x/sin_a;
    hr = x/cos_a;
    if (!width_is_longer)
      std::swap(wr,hr);
  }
  else
  { 
    // fully constrained case: crop touches all 4 sides
    double cos_2a = cos_a*cos_a - sin_a*sin_a;
    wr = (w*cos_a - h*sin_a)/cos_2a;
    hr = (h*cos_a - w*sin_a)/cos_2a;
  }

  return cv::Size(wr,hr);
}

cv::Mat crop_around_center(cv::Mat image, int height, int width)
{
    // Given a OpenCV 2 image, crops it to the given width and height,
    // around it's centre point

    cv::Size image_size = cv::Size(image.rows, image.cols);
    cv::Point image_center = cv::Point(int(image_size.height * 0.5), int(image_size.width * 0.5));

    if (width > image_size.width)
        width = image_size.width;

    if (height > image_size.height)
        height = image_size.height;

    int x1 = int(image_center.x - width  * 0.5);
    int x2 = int(image_center.x + width  * 0.5);
    int y1 = int(image_center.y - height * 0.5);
    int y2 = int(image_center.y + height * 0.5);


    return image(cv::Rect(cv::Point(y1, x1), cv::Point(y2,x2)));
}

void demo(cv::Mat image)
{
    // Demos the largest_rotated_rect function
    int image_height = image.rows;
    int image_width = image.cols;

    for (float i = 0.0; i < 360.0; i+=0.5)
    {
        cv::Mat image_orig = image.clone();
        cv::Mat image_rotated = rotate_image(image, i);

        cv::Size largest_rect = largest_rotated_rect(image_height, image_width, degree_to_radian(i));
        // for those who trust math (added by coproc):
        cv::Size largest_rect2 = really_largest_rotated_rect(image_height, image_width, degree_to_radian(i));
        cout << "area1 = " << largest_rect.height * largest_rect.width << endl;
        cout << "area2 = " << largest_rect2.height * largest_rect2.width << endl;

        cv::Mat image_rotated_cropped = crop_around_center(
                    image_rotated,
                    largest_rect.height,
                    largest_rect.width
                    );

        cv::imshow("Original Image", image_orig);
        cv::imshow("Rotated Image", image_rotated);
        cv::imshow("Cropped image", image_rotated_cropped);

        if (char(cv::waitKey(15)) == 'q')
            break;
    }

}

int main (int argc, char* argv[])
{
    cv::Mat image = cv::imread(argv[1]);

    if (image.empty())
    {
        cout << "> The input image was not found." << endl;
        exit(EXIT_FAILURE);
    }

    cout << "Press [s] to begin or restart the demo" << endl;
    cout << "Press [q] to quit" << endl;

    while (true)
    {
        cv::imshow("Original Image", image);
        char opt = char(cv::waitKey(0));
        switch (opt) {
        case 's':
            demo(image);
            break;
        case 'q':
            return EXIT_SUCCESS;
        default:
            break;
        }
    }

    return EXIT_SUCCESS;
}
于 2014-11-25T21:29:10.030 回答
6

TensorFlow 中的旋转和裁剪

我个人在 TensorFlow 中需要这个函数,感谢 Aaron Snoswell,我可以实现这个函数。

def _rotate_and_crop(image, output_height, output_width, rotation_degree, do_crop):
    """Rotate the given image with the given rotation degree and crop for the black edges if necessary
    Args:
        image: A `Tensor` representing an image of arbitrary size.
        output_height: The height of the image after preprocessing.
        output_width: The width of the image after preprocessing.
        rotation_degree: The degree of rotation on the image.
        do_crop: Do cropping if it is True.
    Returns:
        A rotated image.
    """

    # Rotate the given image with the given rotation degree
    if rotation_degree != 0:
        image = tf.contrib.image.rotate(image, math.radians(rotation_degree), interpolation='BILINEAR')

        # Center crop to ommit black noise on the edges
        if do_crop == True:
            lrr_width, lrr_height = _largest_rotated_rect(output_height, output_width, math.radians(rotation_degree))
            resized_image = tf.image.central_crop(image, float(lrr_height)/output_height)    
            image = tf.image.resize_images(resized_image, [output_height, output_width], method=tf.image.ResizeMethod.BILINEAR, align_corners=False)

    return image

def _largest_rotated_rect(w, h, angle):
    """
    Given a rectangle of size wxh that has been rotated by 'angle' (in
    radians), computes the width and height of the largest possible
    axis-aligned rectangle within the rotated rectangle.
    Original JS code by 'Andri' and Magnus Hoff from Stack Overflow
    Converted to Python by Aaron Snoswell
    Source: http://stackoverflow.com/questions/16702966/rotate-image-and-crop-out-black-borders
    """

    quadrant = int(math.floor(angle / (math.pi / 2))) & 3
    sign_alpha = angle if ((quadrant & 1) == 0) else math.pi - angle
    alpha = (sign_alpha % math.pi + math.pi) % math.pi

    bb_w = w * math.cos(alpha) + h * math.sin(alpha)
    bb_h = w * math.sin(alpha) + h * math.cos(alpha)

    gamma = math.atan2(bb_w, bb_w) if (w < h) else math.atan2(bb_w, bb_w)

    delta = math.pi - alpha - gamma

    length = h if (w < h) else w

    d = length * math.cos(alpha)
    a = d * math.sin(alpha) / math.sin(delta)

    y = a * math.cos(gamma)
    x = y * math.tan(gamma)

    return (
        bb_w - 2 * x,
        bb_h - 2 * y
    )

如果您需要在 TensorFlow 中进一步实现示例和可视化,可以使用此存储库。我希望这对其他人有帮助。

于 2018-06-18T09:41:06.330 回答
5

为简洁起见,一个小的更新利用了优秀的imutils库。

def rotated_rect(w, h, angle):
    """
    Given a rectangle of size wxh that has been rotated by 'angle' (in
    radians), computes the width and height of the largest possible
    axis-aligned rectangle within the rotated rectangle.

    Original JS code by 'Andri' and Magnus Hoff from Stack Overflow

    Converted to Python by Aaron Snoswell
    """
    angle = math.radians(angle)
    quadrant = int(math.floor(angle / (math.pi / 2))) & 3
    sign_alpha = angle if ((quadrant & 1) == 0) else math.pi - angle
    alpha = (sign_alpha % math.pi + math.pi) % math.pi

    bb_w = w * math.cos(alpha) + h * math.sin(alpha)
    bb_h = w * math.sin(alpha) + h * math.cos(alpha)

    gamma = math.atan2(bb_w, bb_w) if (w < h) else math.atan2(bb_w, bb_w)

    delta = math.pi - alpha - gamma

    length = h if (w < h) else w

    d = length * math.cos(alpha)
    a = d * math.sin(alpha) / math.sin(delta)

    y = a * math.cos(gamma)
    x = y * math.tan(gamma)

    return (bb_w - 2 * x, bb_h - 2 * y)

def crop(img, w, h):
    x, y = int(img.shape[1] * .5), int(img.shape[0] * .5)

    return img[
        int(np.ceil(y - h * .5)) : int(np.floor(y + h * .5)),
        int(np.ceil(x - w * .5)) : int(np.floor(x + h * .5))
    ]

def rotate(img, angle):
    # rotate, crop and return original size
    (h, w) = img.shape[:2]
    img = imutils.rotate_bound(img, angle)
    img = crop(img, *rotated_rect(w, h, angle))
    img = cv2.resize(img,(w,h),interpolation=cv2.INTER_AREA)
    return img
于 2018-09-25T20:06:53.850 回答
3

受 Coprox 令人惊叹的工作的启发,我编写了一个函数,它与 Coprox 的代码一起形成了一个完整的解决方案(因此可以通过复制和粘贴来轻松使用它)。下面的 rotate_max_area 函数只返回一个没有黑色边界的旋转图像。

def rotate_bound(image, angle):
    # CREDIT: https://www.pyimagesearch.com/2017/01/02/rotate-images-correctly-with-opencv-and-python/
    (h, w) = image.shape[:2]
    (cX, cY) = (w // 2, h // 2)
    M = cv2.getRotationMatrix2D((cX, cY), -angle, 1.0)
    cos = np.abs(M[0, 0])
    sin = np.abs(M[0, 1])
    nW = int((h * sin) + (w * cos))
    nH = int((h * cos) + (w * sin))
    M[0, 2] += (nW / 2) - cX
    M[1, 2] += (nH / 2) - cY
    return cv2.warpAffine(image, M, (nW, nH))


def rotate_max_area(image, angle):
    """ image: cv2 image matrix object
        angle: in degree
    """
    wr, hr = rotatedRectWithMaxArea(image.shape[1], image.shape[0],
                                    math.radians(angle))
    rotated = rotate_bound(image, angle)
    h, w, _ = rotated.shape
    y1 = h//2 - int(hr/2)
    y2 = y1 + int(hr)
    x1 = w//2 - int(wr/2)
    x2 = x1 + int(wr)
    return rotated[y1:y2, x1:x2]
于 2018-01-04T18:37:19.590 回答
2

迅捷解决方案

感谢 coproc 的出色解决方案。这是swift中的代码

// Given a rectangle of size.width x size.height that has been rotated by 'angle' (in
// radians), computes the width and height of the largest possible
// axis-aligned rectangle (maximal area) within the rotated rectangle.
func rotatedRectWithMaxArea(size: CGSize, angle: CGFloat) -> CGSize {
    let w = size.width
    let h = size.height

    if(w <= 0 || h <= 0) {
        return CGSize.zero
    }

    let widthIsLonger = w >= h
    let (sideLong, sideShort) = widthIsLonger ? (w, h) : (w, h)

    // since the solutions for angle, -angle and 180-angle are all the same,
    // if suffices to look at the first quadrant and the absolute values of sin,cos:
    let (sinA, cosA) = (sin(angle), cos(angle))
    if(sideShort <= 2*sinA*cosA*sideLong || abs(sinA-cosA) < 1e-10) {
        // half constrained case: two crop corners touch the longer side,
        // the other two corners are on the mid-line parallel to the longer line
        let x = 0.5*sideShort
        let (wr, hr) = widthIsLonger ? (x/sinA, x/cosA) : (x/cosA, x/sinA)
        return CGSize(width: wr, height: hr)
    } else {
        // fully constrained case: crop touches all 4 sides
        let cos2A = cosA*cosA - sinA*sinA
        let (wr, hr) = ((w*cosA - h*sinA)/cos2A, (h*cosA - w*sinA)/cos2A)
        return CGSize(width: wr, height: hr)
    }
}
于 2018-01-29T23:31:28.613 回答
1

对 Coprox 于 2013 年 5 月 27 日给出的上述最受青睐的解决方案的更正:当 cosa = cosb infinity 导致最后两行。通过在前面的 if 选择器中添加“或 cosa 等于 cosb”来解决。

补充:如果您不知道原始的未旋转的 nx 和 ny,但只有旋转的帧(或图像),则找到仅包含此框的框(我通过删除空白 = 单色边框来做到这一点)并首先反向运行程序找到 nx 和 ny 的大小。如果图像被旋转成一个太小的框架,以至于它被沿着侧面切割(成八角形),我首先找到完整包含框架的 x 和 y 扩展。但是,这也不适用于 45 度左右的角度,结果是正方形,而不是保持未旋转的纵横比。对我来说,这个程序只能在 30 度内正常工作。

还是很棒的日常!它解决了我在天文图像对齐方面的烦恼。

于 2017-12-24T12:39:31.977 回答
1

也许更简单的解决方案是:

def crop_image(image, angle):
    h, w = image.shape
    tan_a = abs(np.tan(angle * np.pi / 180))
    b = int(tan_a / (1 - tan_a ** 2) * (h - w * tan_a))
    d = int(tan_a / (1 - tan_a ** 2) * (w - h * tan_a))
    return image[d:h - d, b:w - b]

无需像许多人那样计算旋转矩形的高度和宽度,只需找到旋转图像时形成的黑色三角形的高度即可。

于 2019-07-08T11:06:28.453 回答
0

以正确的顺序旋转图像

 import cv2
 import pytesseract
 import urllib
 import numpy as np
 import re
 import imutils #added
 import PIL

 image = cv2.imread('my_pdf_madan_m/page_1.jpg')

 gray = cv2.cvtColor(image, cv2.COLOR_BGR2GRAY)
 gray = cv2.bitwise_not(gray)

 rot_data = pytesseract.image_to_osd(image);
 print("[OSD] "+rot_data)
 rot = re.search('(?<=Rotate: )\d+', 
 rot_data).group(0)

 angle = float(rot)

 # rotate the image to deskew it
 rotated = imutils.rotate_bound(image, angle) #added


 #  TODO: Rotated image can be saved here
 print(pytesseract.image_to_osd(rotated));

 # Run tesseract OCR on image
 text = pytesseract.image_to_string(rotated, 
 lang='eng', config="--psm 6")
 print(text)
于 2021-05-27T06:31:22.100 回答
0

通过手工计算并查看原始帖子,我发现伽玛计算的一个小错字。它实际上应该是:

gamma = math.atan2(bb_w, bb_h) if (w < h) else math.atan2(bb_h, bb_w)

于 2022-02-18T10:16:09.597 回答
0

最近为 Pytorch 实现了一个解决方案。它可能会派上用场。也可能与“随机旋转变换”一起使用。只需读取变换使用的特定角度,然后将其与 PyTorch 变换一起使用。函数简单地接收一批图像并通过裁剪进行随机旋转。

import torchvision.transforms as transforms
import math

def _largest_rotated_rect(w, h, angle):
"""
Given a rectangle of size wxh that has been rotated by 'angle' (in
radians), computes the width and height of the largest possible
axis-aligned rectangle within the rotated rectangle.
Original JS code by 'Andri' and Magnus Hoff from Stack Overflow
Converted to Python by Aaron Snoswell
Source: http://stackoverflow.com/questions/16702966/rotate-image-and-crop-out-black-borders
"""

quadrant = int(math.floor(angle / (math.pi / 2))) & 3
sign_alpha = angle if ((quadrant & 1) == 0) else math.pi - angle
alpha = (sign_alpha % math.pi + math.pi) % math.pi

bb_w = w * math.cos(alpha) + h * math.sin(alpha)
bb_h = w * math.sin(alpha) + h * math.cos(alpha)

gamma = math.atan2(bb_w, bb_w) if (w < h) else math.atan2(bb_w, bb_w)

delta = math.pi - alpha - gamma

length = h if (w < h) else w

d = length * math.cos(alpha)
a = d * math.sin(alpha) / math.sin(delta)

y = a * math.cos(gamma)
x = y * math.tan(gamma)

return (
    bb_w - 2 * x,
    bb_h - 2 * y
)


def _rotate_and_crop(image, output_height=32, output_width=32):
"""Rotate the given image with the given rotation degree and crop for the black edges if necessary. For my case, image sizes are 32x32.
Args:
    image: A Batch of Tensors- normally from a dataloader.
    output_height: The height of the image after preprocessing.
    output_width: The width of the image after preprocessing.
Returns:
    A rotated image.
"""

# Rotate the given image with the given rotation degree
rotation_transform = transforms.RandomRotation((0, 360))
angle_rot = rotation_transform.angle_rot #you will have to read it from the pytorch library

lrr_width, lrr_height = _largest_rotated_rect(output_height, output_width, math.radians(angle_rot))
croped_image = transforms.CenterCrop((lrr_height, lrr_width))
resize_transform = transforms.Resize(size=(output_height, output_width))

transform = transforms.Compose([rotation_transform, croped_image, resize_transform, transforms.RandomHorizontalFlip(),
                                               transforms.ToTensor(),
                                               ])

image = transform(image)

return image
于 2021-09-02T12:13:04.623 回答