python - 在 warpAffine 变换后，如何将点重新映射或恢复到其以前的坐标系？

Question

我正在使用模板匹配 (TM) 来查找图像中所有M 的位置(左侧第一张图像)，但我将匹配点的位置(指旋转 ROI 内的位置)重新映射回原始图像时遇到问题:

问题是我需要在这一点上反转(撤消)warpAffine 变换，并且我的计算并不完美，正如您在上面最右侧的橙色框图像中看到的那样。

我已经研究了 SO 中与该主题相关的所有帖子，但没有一个真正有帮助，因为我试图逆转的操作稍微复杂一些:

• Center of rotated cv::Rect
• How can I remap a point after an image rotation?

简单来说，这个应用程序有什么作用？

1. 首先加载图像:original image和 template ;
2. 它创建 8 个 ROI 及其所需的旋转角度。稍后使用旋转角度来校正 M 的方向，使其保持水平并且对于 TM 来说“看起来很漂亮”；
3. 循环迭代列表中的每个 ROI:选择一个 ROI，使用 rotate_bound() 旋转它，然后对其执行 TM。；
4. 当 TM 操作成功并找到该字母时，它会尝试将定义匹配位置的点从旋转的 ROI 重新映射到坐标中。原始 ROI，然后可用于指定原始图像内匹配的正确位置。

主要问题似乎是撤消由 rotate_bound() 创建的旋转矩阵中定义的所有操作。顺便说一句，如果您从未听说过这个功能，这里有一个 good reference .

如何修复重映射计算？

这是一个Short, Self Contained, Correct (Compilable), Example :

import cv2
import numpy as np

# rotate_bound: helper function that rotates the image adds some padding to avoid cutting off parts of it
# reference: https://www.pyimagesearch.com/2017/01/02/rotate-images-correctly-with-opencv-and-python/
def rotate_bound(image, angle):
    # grab the dimensions of the image and then determine the center
    (h, w) = image.shape[:2]
    (cX, cY) = (w // 2, h // 2)

    # grab the rotation matrix (applying the negative of the angle to rotate clockwise), then grab the sine and cosine
    # (i.e., the rotation components of the matrix)
    M = cv2.getRotationMatrix2D((cX, cY), -angle, 1.0)
    cos = np.abs(M[0, 0])
    sin = np.abs(M[0, 1])

    # compute the new bounding dimensions of the image
    nW = int(np.multiply(h, sin) + np.multiply(w, cos))
    nH = int(np.multiply(h, cos) + np.multiply(w, sin))

    # adjust the rotation matrix to take into account translation
    M[0, 2] += (nW / 2) - cX
    M[1, 2] += (nH / 2) - cY

    # perform rotation and return the image (white background) along with the Rotation Matrix
    return cv2.warpAffine(image, M, (nW, nH), borderValue=(255,255,255)), M


# Step 1 - Load images
input_img = cv2.imread("target.png", cv2.IMREAD_GRAYSCALE)
template_img = cv2.imread("template.png", cv2.IMREAD_GRAYSCALE)
matches_dbg_img = cv2.cvtColor(input_img, cv2.COLOR_GRAY2BGR) # for debugging purposes

# Step 2 - Generate some ROIs
# each ROI contains the x,y,w,h and angle (degree) to rotate the box and make its M appear horizontal
roi_w = 26
roi_h = 26

roi_list = []
roi_list.append((112, 7, roi_w, roi_h, 0))
roi_list.append((192, 36, roi_w, roi_h, -45))
roi_list.append((227, 104, roi_w, roi_h, -90))
roi_list.append((195, 183, roi_w, roi_h, -135))
roi_list.append((118, 216, roi_w, roi_h, -180))
roi_list.append((49, 196, roi_w, roi_h, -225))
roi_list.append((10, 114, roi_w, roi_h, -270))
roi_list.append((36, 41, roi_w, roi_h, -315))

# debug: draw green ROIs
rois_dbg_img = cv2.cvtColor(input_img, cv2.COLOR_GRAY2BGR)
for roi in roi_list:
    x, y, w, h, angle = roi
    x2 = x + w
    y2 = y + h
    cv2.rectangle(rois_dbg_img, (x, y), (x2, y2), (0,255,0), 2)

cv2.imwrite('target_rois.png', rois_dbg_img)
cv2.imshow('ROIs', rois_dbg_img)
cv2.waitKey(0)
cv2.destroyWindow('ROIs')


# Step 3 - Select a ROI, crop and rotate it, then perform Template Matching
for i, roi in enumerate(roi_list):
    x, y, w, h, angle = roi
    roi_cropped = input_img[y:y+h, x:x+w]
    roi_rotated, M = rotate_bound(roi_cropped, angle)

    # debug: display each rotated ROI
    #cv2.imshow('ROIs-cropped-rotated', roi_rotated)
    #cv2.waitKey(0)

    # debug: dump roi to the disk (before/after rotation)
    filename = 'target_roi' + str(i)
    cv2.imwrite(filename + '.png', roi_cropped)
    cv2.imwrite(filename + '_rotated.png', roi_rotated)

    # perform template matching
    res = cv2.matchTemplate(roi_rotated, template_img, cv2.TM_CCOEFF_NORMED)
    (_, score, _, (pos_x, pos_y)) = cv2.minMaxLoc(res)
    print('TM score=', score)

    # Step 4 - When a TM is found, revert the rotation of matched point so that it represents a location in the original image
    # Note: pos_x and pos_y define the location of the matched template in a rotated ROI
    threshold = 0.75
    if (score >= threshold):

        # debug in cropped image
        print('find_k_symbol: FOUND pos_x=', pos_x, 'pos_y=', pos_y, 'w=', template_img.shape[1], 'h=', template_img.shape[0])
        rot_output_roi = cv2.cvtColor(roi_rotated, cv2.COLOR_GRAY2BGR)
        cv2.rectangle(rot_output_roi, (pos_x, pos_y), (pos_x + template_img.shape[1], pos_y + template_img.shape[0]), (0, 165, 255), 2) # orange
        cv2.imshow('rot-matched-template', rot_output_roi)
        cv2.waitKey(0)
        cv2.destroyWindow('rot-matched-template')

        ###
        # How to convert the location of the matched template (pos_x, pos_y) to points in roi_cropped?
        # (which is the ROI before rotation)
        ###

        # extract variables from the rotation matrix
        M_x = M[0][2]
        M_y = M[1][2]
        #print('M_x=', M_x, '\tM_y=', M_y)
        M_cosx = M[0][0]
        M_msinx = M[0][1]
        #print('M_cosx=', M_cosx, '\tM_msinx=', M_msinx)
        M_siny = M[1][0]
        M_cosy = M[1][1]
        #print('M_siny=', M_siny, '\tM_cosy=', M_cosy)

        # undo translation:
        dst1_x = pos_x - M_x
        dst1_y = pos_y - M_y

        # undo rotation:
        # after this operation, (new_pos_x, new_pos_y) should already be a valid point in the original ROI
        new_pos_x =  M_cosx * dst1_x - M_msinx * dst1_y
        new_pos_y = -M_siny * dst1_x + M_cosy  * dst1_y

        # debug: create the bounding rect of the detected symbol in the original input image
        detected_x = x + int(new_pos_x)
        detected_y = y + int(new_pos_y)
        detected_w = template_img.shape[1]
        detected_h = template_img.shape[0]
        detected_rect = (detected_x, detected_y, detected_w, detected_h)

        print('find_k_symbol: detected_x=', detected_x, 'detected_y=', detected_y, 'detected_w=', detected_w, 'detected_h=', detected_h)
        print()

        cv2.rectangle(matches_dbg_img, (detected_x, detected_y), (detected_x + detected_w, detected_y + detected_h), (0, 165, 255), 2) # orange
        cv2.imwrite('target_matches.png', matches_dbg_img)
        cv2.imshow('matches', matches_dbg_img)
        cv2.waitKey(0)

再次，以下是运行应用程序所需的图像:original image和 template image .

Answer 1

您已经差不多完成了 - 所缺少的只是将边界框矩形围绕其左上角旋转已知的角度，然后绘制这个旋转的矩形。

自 cv2.rectangle只绘制直立的矩形，我们需要一些替代方案。一种选择是将矩形表示为其角点列表(为了保持一致性，假设从左上角开始按顺时针顺序)。然后我们可以使用 cv2.polylines 将其绘制为穿过这 4 个点的闭合折线。 .

<小时/>

要旋转矩形，我们需要对其所有角点应用几何变换。为此，我们首先使用 cv2.getRotationMatrix2D 获得一个变换矩阵.

我们将角点转换为齐次坐标，并计算变换矩阵与转置坐标数组的点积。

为了方便(将每个点放在单行上)，我们转置结果。

# Rotate rectangle defined by (x,y,w,h) around its top left corner (x,y) by given angle
def rotate_rectangle(x, y, w, h, angle):
    # Generate homogenous coordinates of the corners
    # Start top left, go clockwise
    corners = np.array([
        (x, y, 1)
        , (x + w, y, 1)
        , (x + w, y + h, 1)
        , (x, y + h, 1)
    ], np.int32)
    # Create rotation matrix to transform the coordinates
    m_rot = cv2.getRotationMatrix2D((x, y), angle, 1.0)
    # Apply transformation
    rotated_points = np.dot(m_rot, corners.T).T
    return rotated_points

<小时/>

现在，我们首先确定旋转边界框的角点，而不是调用 cv2.rectangle:

rot_points = rotate_rectangle(detected_x, detected_y, detected_w, detected_h, angle)

由于cv2.polylines需要整数坐标，我们 round值和convert the datatype数组的:

rot_points = np.round(rot_points).astype(np.int32)

最后通过 4 个角点绘制一条闭合多段线:

cv2.polylines(matches_dbg_img, [rot_points], True, (0, 165, 255), 2)

<小时/>