Transform Rectangle to trapezoid for perspective

Question

I have picture from front-view. and I want to turn this into bird's eye view. Now I want to calculate for each point in the rectangle (x,y) what will be transformed x,y in the trapezoid.

there must be a formula for this transformation with a given x and y and also the angle of the trapezoid (a).

I am programming in C and using opencv.

Thanks a lot in advance.

Answer 1

I was able to figure out a way for your problem.

Here is the code I used for the same:

Importing the required packages:

import cv2
import numpy as np

Reading the image to be used:

filename = '1.jpg'
img = cv2.imread(filename)
cv2.imwrite('img.jpg',img)

Storing the height and width of the image in separate variables:

ih, iw, _ = img.shape

Creating a black window whose size is bigger than that of the image and storing its height and width in separate variables:

black = np.zeros((ih + 300, iw + 300, 3), np.uint8)
cv2.imwrite('black.jpg',black)
bh, bw, _ = black.shape

Storing the 4 corner points of the image in an array:

pts_src = np.array([[0.0, 0.0],[float(iw), 0.0],[float(iw), float(ih)],[0.0,float(ih)]])

Storing the 4 corner points of the trapezoid to be obtained:

pts_dst = np.array([[bw * 0.25, 0],[bw * 0.75, 0.0],[float(bw), float(bh)],[0.0,float(bh)]])

Calculating the homography matrix using pts_src and pts_dst:

h, status = cv2.findHomography(pts_src, pts_dst)

Warping the given rectangular image into the trapezoid:

im_out = cv2.warpPerspective(img, h, (black.shape[1],black.shape[0]))
cv2.imwrite("im_outImage.jpg", im_out)

cv2.waitKey(0)
cv2.destroyAllWindows()

If you alter the values in the array pts_dst you will be able to get different kinds of quadrilaterals.

Answer 2

Did you consider the homography transform. You use this to create or correct perspective in an image, I think that it is exactly what you want.

With OpenCV, you can use the method cv::findHomography(). The arguments are the 4 initial points (vertices of your rectangle) and the 4 final points (the vertices of the trapeze). You get a transformation matrix that you can then use with cv::warpPerspective() or cv::perspectiveTransform().