Compute homography for a virtual camera with opencv

Question

I have an image of a planar surface, and I want to compute an image warping that gives me a synthetic view of the same planar surface seen from a virtual camera located at another point in the 3d space.

So, given an image I1 I want to compute an image I2 that represents the image I1 seen from a virtual camera.

In theory, there exists an homography that relates these two images.

How do I compute this homography given the camera pose of the virtual camera, as well as it's matrix of internal parameters?

I'm using opencv's warpPerspective() function to apply this homography and generate the image warped.

Thanks in advance.

Answer 1

Ok, found this post (Opencv virtually camera rotating/translating for bird's eye view), where I found some code doing what I needed.

However, I noticed that the rotation in Y had a sign error (-sin instead of sin) . Here's my solution adapted for python. I'm new to python, sorry if I'm doing something ugly.

import cv2
import numpy as np

rotXdeg = 90
rotYdeg = 90
rotZdeg = 90
f = 500
dist = 500

def onRotXChange(val):
    global rotXdeg
    rotXdeg = val
def onRotYChange(val):
    global rotYdeg
    rotYdeg = val
def onRotZChange(val):
    global rotZdeg
    rotZdeg = val
def onFchange(val):
    global f
    f=val
def onDistChange(val):
    global dist
    dist=val

if __name__ == '__main__':

    #Read input image, and create output image
    src = cv2.imread('/home/miquel/image.jpeg')
    dst = np.ndarray(shape=src.shape,dtype=src.dtype)

    #Create user interface with trackbars that will allow to modify the parameters of the transformation
    wndname1 = "Source:"
    wndname2 = "WarpPerspective: "
    cv2.namedWindow(wndname1, 1)
    cv2.namedWindow(wndname2, 1)
    cv2.createTrackbar("Rotation X", wndname2, rotXdeg, 180, onRotXChange)
    cv2.createTrackbar("Rotation Y", wndname2, rotYdeg, 180, onRotYChange)
    cv2.createTrackbar("Rotation Z", wndname2, rotZdeg, 180, onRotZChange)
    cv2.createTrackbar("f", wndname2, f, 2000, onFchange)
    cv2.createTrackbar("Distance", wndname2, dist, 2000, onDistChange)

    #Show original image
    cv2.imshow(wndname1, src)

    h , w = src.shape[:2]

    while True:

        rotX = (rotXdeg - 90)*np.pi/180
        rotY = (rotYdeg - 90)*np.pi/180
        rotZ = (rotZdeg - 90)*np.pi/180

        #Projection 2D -> 3D matrix
        A1= np.matrix([[1, 0, -w/2],
                       [0, 1, -h/2],
                       [0, 0, 0   ],
                       [0, 0, 1   ]])

        # Rotation matrices around the X,Y,Z axis
        RX = np.matrix([[1,           0,            0, 0],
                        [0,np.cos(rotX),-np.sin(rotX), 0],
                        [0,np.sin(rotX),np.cos(rotX) , 0],
                        [0,           0,            0, 1]])

        RY = np.matrix([[ np.cos(rotY), 0, np.sin(rotY), 0],
                        [            0, 1,            0, 0],
                        [ -np.sin(rotY), 0, np.cos(rotY), 0],
                        [            0, 0,            0, 1]])

        RZ = np.matrix([[ np.cos(rotZ), -np.sin(rotZ), 0, 0],
                        [ np.sin(rotZ), np.cos(rotZ), 0, 0],
                        [            0,            0, 1, 0],
                        [            0,            0, 0, 1]])

        #Composed rotation matrix with (RX,RY,RZ)
        R = RX * RY * RZ

        #Translation matrix on the Z axis change dist will change the height
        T = np.matrix([[1,0,0,0],
                       [0,1,0,0],
                       [0,0,1,dist],
                       [0,0,0,1]])

        #Camera Intrisecs matrix 3D -> 2D
        A2= np.matrix([[f, 0, w/2,0],
                       [0, f, h/2,0],
                       [0, 0,   1,0]])

        # Final and overall transformation matrix
        H = A2 * (T * (R * A1))

        # Apply matrix transformation
        cv2.warpPerspective(src, H, (w, h), dst, cv2.INTER_CUBIC)

        #Show the image
        cv2.imshow(wndname2, dst)
        cv2.waitKey(1)