如何使用相机计算正方形物体相对于二维平面图像的角度？

Question

我用一个倒挂在桌子上方的摄像头拍摄了一张照片。在桌子上，我有一个正方形的物体或一张卡片。我已成功检测到该对象并找到其中心坐标（质心）。现在我想找到物体相对于图像的旋转角度。考虑2D图像平面中的所有内容。如何计算角度？ 这张图片代表了我试图实现的目标：

Answer 1

我找到了解决办法。正如我在上面的问题中所说，我编写代码来执行所需的操作。我使用的是OpenCV 4+Python 3.8.3+Spyder IDE

这是我的工作代码：

# This code is used to Find the Origin and Rotation Angle of a Rectangle

#First of all place a blue colored rectangle card on the table below the camera
# Then execute the code. The code will detect the Rectangle in Blue color then find the origin and rotation values. 

#[Resources]
# https://stackoverflow.com/questions/34237253/detect-centre-and-angle-of-rectangles-in-an-image-using-opencv
# https://opencv-python-tutroals.readthedocs.io/en/latest/py_tutorials/py_imgproc/py_contours/py_contours_begin/py_contours_begin.html#how-to-draw-the-contours
# https://opencv-python-tutroals.readthedocs.io/en/latest/py_tutorials/py_imgproc/py_contours/py_contour_features/py_contour_features.html#b-rotated-rectangle
# https://stackoverflow.com/questions/52247821/find-width-and-height-of-rotatedrect

import numpy as np
import cv2
import sys
import yaml
import os
import warnings
warnings.filterwarnings("ignore")

#Global Variables
cx = 0.0    #x locaton of Rectangle
cy = 0.0    #y location of Rectangle
angle = 0.0 #Angle of rotation of Rectangle

if __name__ == "__main__":
    while(1):
        try:
            cap = cv2.VideoCapture(0, cv2.CAP_DSHOW)
   
            while(1):
                _,frame = cap.read()
                k = cv2.waitKey(5)
                if k == 27: #exit by pressing Esc key
                    cv2.destroyAllWindows()
                    sys.exit()
                if k == 13: #Save the centroid and angle values of the rectangle in a file
                    result_file = r'rectangle_position.yaml'    
                    try:
                        os.remove(result_file)  #Delete old file first
                    except:
                        pass
                    print("Saving Rectangle Position Matrix in: ",result_file)
                    data={"rect_position": [cx,cy,angle]}
                    with open(result_file, "w") as f:
                        yaml.dump(data, f, default_flow_style=False)
                
                #Detecting Blue Color
                red = np.matrix(frame[:,:,2])  #extracting red layer (layer No 2) from RGB
                green = np.matrix(frame[:,:,1]) #extracting green layer (layer No 1) from RGB
                blue = np.matrix(frame[:,:,0])  #extracting blue layer (layer No 0) from RGB
                #it will display only the Blue colored objects bright with black background
                blue_only = np.int16(blue)-np.int16(red)-np.int16(green)
                blue_only[blue_only<0] =0
                blue_only[blue_only>255] =255
                blue_only = np.uint8(blue_only)            
                # cv2.namedWindow('blue_only', cv2.WINDOW_AUTOSIZE)
                # cv2.imshow("blue_only",blue_only)
                # cv2.waitKey(1)
                
                #https://opencv-python-tutroals.readthedocs.io/en/latest/py_tutorials/py_imgproc/py_thresholding/py_thresholding.html#otsus-binarization
                #Gaussian filtering
                blur = cv2.GaussianBlur(blue_only,(5,5),cv2.BORDER_DEFAULT)
                #Otsu's thresholding
                ret3,thresh = cv2.threshold(blur,0,255,cv2.THRESH_BINARY+cv2.THRESH_OTSU)
                cv2.namedWindow('Threshold', cv2.WINDOW_AUTOSIZE)
                cv2.imshow("Threshold",thresh)
                cv2.waitKey(1)
                #Finding Conture of detected Rectangle
                contours,hierarchy = cv2.findContours(thresh,cv2.RETR_TREE,cv2.CHAIN_APPROX_NONE)
    
    
                for contour in contours:
                    area = cv2.contourArea(contour)
                    if area>100000:
                        contours.remove(contour)
                 
                cnt = contours[0] #Conture of our rectangle
                
                #https://stackoverflow.com/a/34285205/3661547
                #fit bounding rectangle around contour            
                rotatedRect = cv2.minAreaRect(cnt)
                #getting centroid, width, height and angle of the rectangle conture
                (cx, cy), (width, height), angle = rotatedRect
                
                #centetoid of the rectangle conture
                cx=int(cx)
                cy=int(cy)
                print (cx,cy) #centroid of conture of rectangle
                               
                # we want to choose the Shorter edge of the rotated rect to compute the angle between Vertical
                #https://stackoverflow.com/a/21427814/3661547
                if(width > height):
                    angle = angle+180
                else:
                    angle = angle+90
                print("Angle b/w shorter side with Image Vertical: \n", angle)
                
                
                #Draw rectangle around the detected object
                #https://opencv-python-tutroals.readthedocs.io/en/latest/py_tutorials/py_imgproc/py_contours/py_contours_begin/py_contours_begin.html#how-to-draw-the-contours
                im = cv2.drawContours(frame,[cnt],0,(0,0,255),2)                
                cv2.circle(im, (cx,cy), 2,(200, 255, 0),2) #draw center
                cv2.putText(im, str("Angle: "+str(int(angle))), (int(cx)-40, int(cy)+60), cv2.FONT_HERSHEY_SIMPLEX, 0.5, (0,0,255), 1, cv2.LINE_AA)
                cv2.putText(im, str("Center: "+str(cx)+","+str(cy)), (int(cx)-40, int(cy)-50), cv2.FONT_HERSHEY_SIMPLEX, 0.5, (0,0,255), 1, cv2.LINE_AA)
                cv2.namedWindow('Detected Rect', cv2.WINDOW_AUTOSIZE)
                cv2.imshow('Detected Rect',im)
                cv2.waitKey(1)

        except Exception as e:
            print("Error in Main Loop\n",e)
            cv2.destroyAllWindows()
            sys.exit()
    
    cv2.destroyAllWindows()

该代码运行良好，可以计算矩形的原点及其相对于图像垂直方向的旋转角度

结果：

我从以下链接获得了帮助：

• Detect centre and angle of rectangles in an image using Opencv
• https://opencv-python-tutroals.readthedocs.io/en/latest/py_tutorials/py_imgproc/py_contours/py_contours_begin/py_contours_begin.html#how-to-draw-the-contours
• https://opencv-python-tutroals.readthedocs.io/en/latest/py_tutorials/py_imgproc/py_contours/py_contour_features/py_contour_features.html#b-rotated-rectangle
• Find width and height of RotatedRect